{"id":28873,"date":"2024-10-31T14:13:24","date_gmt":"2024-10-31T10:43:24","guid":{"rendered":"https:\/\/caeassistant.com\/?p=28873"},"modified":"2026-05-02T11:44:17","modified_gmt":"2026-05-02T08:14:17","slug":"hashin-%e5%a4%b1%e6%95%88%e5%87%86%e5%88%99-hashin-%e6%8d%9f%e5%9d%8f-abaqus","status":"publish","type":"post","link":"https:\/\/dev.caeassistant.com\/zh\/%e5%8d%9a%e5%ae%a2\/hashin-%e5%a4%b1%e6%95%88%e5%87%86%e5%88%99-hashin-%e6%8d%9f%e5%9d%8f-abaqus\/","title":{"rendered":"\u4ec0\u4e48\u662f Hashin \u5931\u6548\u51c6\u5219\uff1f | Abaqus \u4e2d\u7684 Hashin \u635f\u4f24"},"content":{"rendered":"<div class=\"wpb-content-wrapper\"><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u6211\u4eec\u5982\u4f55\u9884\u6d4ba\u7684\u786e\u5207\u65f6\u523b\uff1f <span style=\"color: #333333;\">\u590d\u5408\u6750\u6599<\/span> \u5728\u538b\u529b\u4e0b\u4f1a\u5931\u6548\u5417\uff1f\u54c8\u8f9b\u5931\u6548\u51c6\u5219\u901a\u8fc7\u5206\u89e3\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u590d\u6742\u7684\u5931\u6548\u884c\u4e3a\uff0c\u4e3a\u5de5\u7a0b\u5e08\u9884\u6d4b\u635f\u4f24\u53d1\u751f\u7684\u65b9\u5f0f\u548c\u65f6\u95f4\u63d0\u4f9b\u4e86\u5f3a\u6709\u529b\u7684\u7b54\u6848\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">Hashin\u635f\u4f24\u51c6\u5219\u662f\u4e13\u95e8\u4e3a\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u5f00\u53d1\u7684\u3002\u5b83\u80fd\u591f\u8bc6\u522b\u5931\u6548\u53d1\u751f\u5728\u7ea4\u7ef4\u8fd8\u662f\u57fa\u4f53\u4e2d\uff0c\u4ece\u800c\u66f4\u6e05\u6670\u5730\u5c55\u73b0\u6750\u6599\u5728\u5e94\u529b\u4f5c\u7528\u4e0b\u7684\u884c\u4e3a\u3002\u8fd9\u79cd\u65b9\u6cd5\u4f7f\u5176\u9002\u7528\u4e8e\u4eff\u771f\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u6d89\u53ca\u591a\u79cd\u5e94\u529b\u7c7b\u578b\u7684\u60c5\u51b5\uff0c\u800c\u8fd9\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5341\u5206\u5e38\u89c1\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u672c\u7bc7\u535a\u5ba2\u4e2d\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u63a2\u8ba8\u54c8\u8f9b\u635f\u4f24\u51c6\u5219\uff0c\u89e3\u91ca\u5176\u4e8c\u7ef4\u548c\u4e09\u7ef4\u5f62\u5f0f\u53ca\u5176\u533a\u522b\u3002\u6211\u4eec\u8fd8\u5c06\u4f7f\u7528\u56fe\u5f62\u7528\u6237\u754c\u9762 (GUI) \u548c\u5b50\u7a0b\u5e8f\u7b49\u65b9\u5f0f\uff0c\u5728 Abaqus \u4e2d\u63a2\u7d22\u54c8\u8f9b\u635f\u4f24\u51c6\u5219\u3002 <span style=\"color: #333333;\">UMAT<\/span>, \u4e3a\u5de5\u7a0b\u5e08\u5982\u4f55\u5229\u7528\u8fd9\u4e00\u5f3a\u5927\u7684\u7406\u8bba\u6765\u6a21\u62df\u590d\u5408\u6750\u6599\u635f\u4f24\u63d0\u4f9b\u4e86\u89c1\u89e3\u3002.<\/span><\/p>\n<table>\n<thead>\n<tr>\n<th>Item<\/th>\n<th>\u63cf\u8ff0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>Applicable materials<\/strong><\/td>\n<td>Fiber-reinforced composites (UD &amp; laminated)<\/td>\n<\/tr>\n<tr>\n<td><strong>Failure type<\/strong><\/td>\n<td>Progressive damage (mode-based)<\/td>\n<\/tr>\n<tr>\n<td><strong>Failure modes<\/strong><\/td>\n<td>Fiber tension, fiber compression, matrix tension, matrix compression<\/td>\n<\/tr>\n<tr>\n<td><strong>Implementation in Abaqus<\/strong><\/td>\n<td>Built-in (Damage Initiation + Evolution)<\/td>\n<\/tr>\n<tr>\n<td><strong>Required inputs<\/strong><\/td>\n<td>Tensile\/compressive strengths + shear strength<\/td>\n<\/tr>\n<tr>\n<td><strong>Typical use case<\/strong><\/td>\n<td>Damage initiation + progressive failure simulation<\/td>\n<\/tr>\n<tr>\n<td><strong>2D vs 3D<\/strong><\/td>\n<td>2D: plane stress laminates \/ 3D: solid composites<\/td>\n<\/tr>\n<tr>\n<td><strong>Main advantage<\/strong><\/td>\n<td>Separates fiber and matrix failure mechanisms<\/td>\n<\/tr>\n<tr>\n<td><strong>Main limitation<\/strong><\/td>\n<td>No intrinsic strain-rate or impact dependency<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><section data-vc-full-width=\"true\" data-vc-full-width-temp=\"true\" data-vc-full-width-init=\"false\" class=\"vc_section vc_custom_1744108144281 vc_section-has-fill\"><div data-vc-full-width=\"true\" data-vc-full-width-temp=\"true\" data-vc-full-width-init=\"false\" class=\"vc_row wpb_row vc_row-fluid vc_custom_1744103735075 vc_row-has-fill 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responsive_spacing=&#8221;eyJwYXJhbV90eXBlIjoid29vZG1hcnRfcmVzcG9uc2l2ZV9zcGFjaW5nIiwic2VsZWN0b3JfaWQiOiI2ODI5OGJhMDdmMWU2Iiwic2hvcnRjb2RlIjoid29vZG1hcnRfaW5mb19ib3giLCJkYXRhIjp7InRhYmxldCI6e30sIm1vYmlsZSI6e319fQ==&#8221; wd_z_index=&#8221;no&#8221;][\/woodmart_info_box][\/woodmart_info_box_carousel]<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-4\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_raw_code wpb_raw_html wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<div style=\"text-align: left\" class=\"sender-form-field\" data-sender-form-id=\"9648239f6840d13etio\"><\/div>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row-full-width vc_clearfix\"><\/div><\/section><div class=\"vc_row-full-width vc_clearfix\"><\/div><div class=\"vc_row wpb_row vc_row-fluid vc_custom_1776852851738 vc_row-has-fill vc_row-o-equal-height vc_row-flex\"><div class=\"wpb_column vc_column_container vc_col-sm-4\/5\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t\n\t\t<\/div>\n\t<\/div>\n\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h2 style=\"text-align: left;\"><span style=\"color: #ff6600;\">What are the Hashin Failure Criteria?<\/span><\/h2>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">Hashin\u5931\u6548\u51c6\u5219\u662f\u4e00\u79cd\u5931\u6548\u7406\u8bba\uff0c\u65e8\u5728\u9884\u6d4b\u590d\u5408\u6750\u6599\uff08\u4f8b\u5982\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff09\u4e2d\u4e0d\u540c\u7c7b\u578b\u7684\u635f\u4f24\u3002\u8be5\u51c6\u5219\u7531Zvi Hashin\u5f00\u53d1\uff0c\u533a\u5206\u4e86\u7ea4\u7ef4\u5931\u6548\u548c\u57fa\u4f53\u5931\u6548\uff0c\u4e0e\u6700\u5927\u5e94\u529b\u6216\u5e94\u53d8\u7406\u8bba\u7b49\u4f20\u7edf\u51c6\u5219\u76f8\u6bd4\uff0c\u80fd\u591f\u66f4\u8be6\u7ec6\u5730\u9884\u6d4b\u590d\u5408\u6750\u6599\u7684\u5931\u6548\u673a\u5236\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">Hashin\u5931\u6548\u51c6\u5219\u6839\u636e\u635f\u4f24\u53d1\u751f\u5728\u7ea4\u7ef4\u8fd8\u662f\u57fa\u4f53\u4e2d\u6765\u533a\u5206\u5931\u6548\u6a21\u5f0f\u3002\u5b83\u9488\u5bf9\u4e0d\u540c\u7c7b\u578b\u7684\u635f\u4f24\u91c7\u7528\u4e0d\u540c\u7684\u65b9\u7a0b\uff0c\u8fd9\u4e9b\u65b9\u7a0b\u57fa\u4e8e\u590d\u5408\u6750\u6599\u4e2d\u5e38\u89c1\u7684\u7269\u7406\u5931\u6548\u6a21\u5f0f\u3002\u8fd9\u4f7f\u5f97\u8be5\u51c6\u5219\u5728\u5e94\u7528\u4e8e\u7ea4\u7ef4\u589e\u5f3a\u805a\u5408\u7269\u7b49\u590d\u6742\u6750\u6599\u65f6\u66f4\u52a0\u7cbe\u786e\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u54c8\u8f9b\u51c6\u5219\u662f\u4e00\u79cd\u4ea4\u4e92\u5f0f\u5931\u6548\u51c6\u5219\uff0c\u56e0\u4e3a\u5b83\u8003\u8651\u4e86\u591a\u79cd\u5e94\u529b\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u72ec\u7acb\u7684\u62c9\u5e94\u529b\u6216\u526a\u5e94\u529b\u3002\u8fd9\u4f7f\u5f97\u5b83\u975e\u5e38\u9002\u7528\u4e8e\u590d\u5408\u6750\u6599\uff0c\u56e0\u4e3a\u590d\u5408\u6750\u6599\u7684\u5931\u6548\u662f\u7531\u591a\u79cd\u5e94\u529b\u540c\u65f6\u4f5c\u7528\u5bfc\u81f4\u7684\u3002.<\/span><\/p>\n<h3>Damage in Composite Materials<\/h3>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u590d\u5408\u6750\u6599\uff0c\u4f8b\u5982\u7ea4\u7ef4\u589e\u5f3a\u805a\u5408\u7269\uff0c\u7531\u4e8e\u5176\u975e\u5747\u8d28\u6027\uff0c\u4f1a\u901a\u8fc7\u591a\u79cd\u673a\u5236\u53d1\u751f\u635f\u4f24\u3002\u590d\u5408\u6750\u6599\u7684\u635f\u4f24\u5341\u5206\u590d\u6742\uff0c\u53ef\u4ee5\u4ee5\u4e0d\u540c\u7684\u5f62\u5f0f\u51fa\u73b0\uff1a<\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u57fa\u4f53\u5f00\u88c2<\/strong>\u590d\u5408\u6750\u6599\u7684\u57fa\u4f53\uff08\u805a\u5408\u7269\u6216\u6811\u8102\uff09\u4e2d\u53ef\u80fd\u4f1a\u5f62\u6210\u88c2\u7eb9\uff0c\u5bfc\u81f4\u627f\u8f7d\u80fd\u529b\u4e0b\u964d\u3002.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u7ea4\u7ef4\u65ad\u88c2<\/strong>\u7ea4\u7ef4\u662f\u4e3b\u8981\u7684\u627f\u8f7d\u6750\u6599\uff0c\u5728\u538b\u529b\u4e0b\u4f1a\u65ad\u88c2\uff0c\u5bfc\u81f4\u521a\u5ea6\u548c\u5f3a\u5ea6\u5927\u5e45\u4e0b\u964d\u3002.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u5206\u5c42<\/strong>\u5c42\u538b\u590d\u5408\u6750\u6599\u4e2d\u5404\u5c42\u4e4b\u95f4\u7684\u5206\u79bb\u79f0\u4e3a\u5206\u5c42\uff0c\u5206\u5c42\u4f1a\u5927\u5927\u524a\u5f31\u7ed3\u6784\u5f3a\u5ea6\u3002.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u7ea4\u7ef4\u57fa\u4f53\u8131\u7c98<\/strong>\u7ea4\u7ef4\u4e0e\u57fa\u4f53\u4e4b\u95f4\u7684\u7c98\u5408\u53ef\u80fd\u4f1a\u5931\u6548\uff0c\u5bfc\u81f4\u57fa\u4f53\u4e0e\u7ea4\u7ef4\u4e4b\u95f4\u4f20\u9012\u8f7d\u8377\u7684\u80fd\u529b\u4e0b\u964d\u3002.<\/span><\/li>\n<\/ul>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-28874 size-full\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/1.png\" alt=\"\u53d7\u635f\u7684\u590d\u5408\u6750\u6599 \" width=\"456\" height=\"280\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/1.png 456w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/1-300x184.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/1-430x264.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/1-62x38.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/1-150x92.png 150w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe1\uff1a <em>\u53d7\u635f\u590d\u5408\u6750\u6599[\u53c2\u8003\u6587\u732e]<\/em><\/p>\n<h3>Why Hashin&#8217;s theory?<\/h3>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">Hashin\u5931\u6548\u51c6\u5219\u56e0\u5176\u80fd\u591f\u9884\u6d4b\u57fa\u4f53\u548c\u7ea4\u7ef4\u7684\u5931\u6548\u800c\u88ab\u5e7f\u6cdb\u5e94\u7528\u3002\u8be5\u51c6\u5219\u4e5f\u5e94\u7528\u4e8e\u8ba1\u7b97\u6a21\u62df\u4e2d\uff0c\u4f8b\u5982\u2026\u2026<span style=\"color: #333333;\"> \u6709\u9650\u5143\u5206\u6790<\/span> \u5f53\u9700\u8981\u7cbe\u786e\u9884\u6d4b\u590d\u5408\u6750\u6599\u5931\u6548\u65f6\uff0c\u53ef\u91c7\u7528\u6709\u9650\u5143\u5206\u6790\uff08FEA\uff09\u3002\u6211\u4eec\u91c7\u7528\u8be5\u7406\u8bba\u7684\u539f\u56e0\u662f\uff1a<\/span><\/p>\n<ul>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>\u590d\u5408\u6750\u6599\u5931\u6548\u9884\u6d4b\u7684\u51c6\u786e\u6027<\/strong>\u4e0e\u6700\u5927\u5e94\u529b\u6216\u5e94\u53d8\u7406\u8bba\u4e0d\u540c\uff0cHashin \u51c6\u5219\u8003\u8651\u4e86\u7ea4\u7ef4\u548c\u57fa\u4f53\u7684\u4e0d\u540c\u5931\u6548\u6a21\u5f0f\uff0c\u80fd\u591f\u66f4\u51c6\u786e\u5730\u8868\u793a\u590d\u5408\u6750\u6599\u7684\u5931\u6548\u65b9\u5f0f\u3002.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>\u7ea4\u7ef4\u548c\u57fa\u4f53\u7684\u4e0d\u540c\u5931\u6548\u6a21\u5f0f<\/strong>Hashin \u51c6\u5219\u5206\u522b\u8bc4\u4f30\u7ea4\u7ef4\u548c\u57fa\u4f53\u7684\u5931\u6548\uff0c\u4ece\u800c\u53ef\u4ee5\u5bf9\u590d\u5408\u6750\u6599\u7684\u4e24\u4e2a\u90e8\u5206\u8fdb\u884c\u660e\u786e\u4e14\u5b9e\u9645\u7684\u5931\u6548\u9884\u6d4b\u3002.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>\u591a\u529f\u80fd\u6027<\/strong>\uff1a\u5b83\u65e2\u53ef\u7528\u4e8e\u62c9\u4f38\u5931\u6548\u6a21\u5f0f\uff0c\u4e5f\u53ef\u7528\u4e8e\u538b\u7f29\u5931\u6548\u6a21\u5f0f\uff0c\u56e0\u6b64\u9002\u7528\u4e8e\u5404\u79cd\u8f7d\u8377\u6761\u4ef6\u3002.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>\u6709\u9650\u5143\u5206\u6790\u4e2d\u7684\u5b9e\u73b0<\/strong>Hashin\u51c6\u5219\u901a\u5e38\u5728\u6709\u9650\u5143\u8f6f\u4ef6\uff08\u5982Abaqus\uff09\u4e2d\u5b9e\u73b0\uff0c\u4ece\u800c\u80fd\u591f\u5bf9\u590d\u5408\u6750\u6599\u7684\u884c\u4e3a\u8fdb\u884c\u8be6\u7ec6\u6a21\u62df\u3002.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>\u9002\u7528\u4e8e\u590d\u6742\u8f7d\u8377<\/strong>\u5b83\u8003\u8651\u4e86\u590d\u5408\u6750\u6599\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5e38\u89c1\u7684\u7ec4\u5408\u8f7d\u8377\u6761\u4ef6\u3002.<\/span><\/li>\n<\/ul>\n<table style=\"width: 100%; border-collapse: collapse; background-color: #dbdbdb;\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\">\u5982\u679c\u60a8\u9700\u8981\u6df1\u5165\u7684\u57f9\u8bad\uff0c\u6211\u4eec\u7684 Abaqus \u8bfe\u7a0b\u53ef\u4ee5\u6ee1\u8db3\u60a8\u7684\u9700\u6c42\u3002\u8bf7\u8bbf\u95ee\u6211\u4eec\u7684\u7f51\u7ad9\u3002 <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/caeassistant.com\/abaqus-course\/\" target=\"_blank\" rel=\"noopener\">Abaqus\u8bfe\u7a0b<\/a><\/span> \u7acb\u5373\u67e5\u627e\u6700\u9002\u5408\u60a8\u9700\u6c42\u7684\u8bfe\u7a0b\uff0c\u5e76\u5c06\u60a8\u7684 Abaqus \u77e5\u8bc6\u63d0\u5347\u5230\u65b0\u7684\u6c34\u5e73\uff01<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span style=\"color: #ff6600;\">2D and 3D form of Hashin Damage Criteria Theory<\/span><\/h2>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u00a0Hashin\u635f\u4f24\u51c6\u5219\uff08Hashin\u5931\u6548\u51c6\u5219\uff09\u65e2\u9002\u7528\u4e8e\u4e8c\u7ef4\u5e94\u529b\u72b6\u6001\uff0c\u4e5f\u9002\u7528\u4e8e\u4e09\u7ef4\u5e94\u529b\u72b6\u6001\u3002\u4e24\u79cd\u5f62\u5f0f\u7684\u57fa\u672c\u601d\u60f3\u76f8\u540c\uff0c\u4f46\u6240\u8003\u8651\u7684\u5e94\u529b\u5206\u91cf\u4f1a\u6839\u636e\u5206\u6790\u662f\u5728\u4e8c\u7ef4\u8fd8\u662f\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u8fdb\u884c\u800c\u6709\u6240\u4e0d\u540c\u3002.<\/span><\/p>\n<table>\n<thead>\n<tr>\n<th>\u6545\u969c\u6a21\u5f0f<\/th>\n<th>2D Hashin<\/th>\n<th>3D Hashin<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>Fiber Tension<\/strong><\/td>\n<td>$\\left( \\frac{\\sigma_{11}}{X_T} \\right)^2 + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1$<\/td>\n<td>$\\left( \\frac{\\sigma_{11}}{X_T} \\right)^2 + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{13}}{S_{13}} \\right)^2 \\ge 1$<\/td>\n<\/tr>\n<tr>\n<td><strong>Fiber Compression<\/strong><\/td>\n<td>$\\left( \\frac{\\sigma_{11}}{X_c} \\right)^2 \\ge 1$<\/td>\n<td>$\\left( \\frac{\\sigma_{11}}{X_c} \\right)^2 \\ge 1$<\/td>\n<\/tr>\n<tr>\n<td><strong>Matrix Tension<\/strong><\/td>\n<td>$\\left( \\frac{\\sigma_{22}}{Y_T} \\right)^2 + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1$<\/td>\n<td>$\\left( \\frac{\\sigma_{22} + \\sigma_{33}}{Y_T} \\right)^2 + \\frac{\\sigma_{23}^2 &#8211; \\sigma_{22}\\sigma_{33}}{S_{23}^2} + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{13}}{S_{13}} \\right)^2 \\ge 1$<\/td>\n<\/tr>\n<tr>\n<td><strong>Matrix Compression<\/strong><\/td>\n<td>$\\left( \\frac{\\sigma_{22}}{2S_T} \\right)^2 + \\left[ \\left( \\frac{Y_c}{2S_T} \\right)^2 &#8211; 1 \\right] \\frac{\\sigma_{22}}{Y_c} + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1$<\/td>\n<td>$\\frac{\\sigma_{22} + \\sigma_{33}}{Y_c} \\left[ \\left( \\frac{Y_c}{2S_{23}} \\right)^2 &#8211; 1 \\right] + \\left( \\frac{\\sigma_{22} + \\sigma_{33}}{4S_{23}^2} \\right)^2 + \\frac{\\sigma_{23}^2 &#8211; \\sigma_{22}\\sigma_{33}}{S_{23}^2} + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{13}}{S_{13}} \\right)^2 \\ge 1$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">Hashin\u635f\u4f24\u51c6\u5219\u7684\u4e8c\u7ef4\u5f62\u5f0f\u548c\u4e09\u7ef4\u5f62\u5f0f\u7684\u4e3b\u8981\u533a\u522b\u5728\u4e8e\u6240\u6d89\u53ca\u7684\u5e94\u529b\u5206\u91cf\u7684\u6570\u91cf\uff1a<\/span><\/p>\n<ul>\n<li>\n<p data-path-to-node=\"1,0,0\"><span style=\"font-size: 14pt;\"><b data-path-to-node=\"1,0,0\" data-index-in-node=\"0\">2D Form:<\/b> In 2D, we typically deal with a plane stress state, which includes normal stresses in two directions (<span class=\"math-inline\" data-math=\"\\sigma_{11}, \\sigma_{22}\" data-index-in-node=\"111\">$\\sigma_{11}, \\sigma_{22}$<\/span>) and shear stress in the plane (<span class=\"math-inline\" data-math=\"\\tau_{12}\" data-index-in-node=\"168\">$\\tau_{12}$<\/span>).<\/span><\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"1,1,0\"><span style=\"font-size: 14pt;\"><b data-path-to-node=\"1,1,0\" data-index-in-node=\"0\">3D Form:<\/b> In 3D, the stresses are expanded to include normal stresses in three directions (<span class=\"math-inline\" data-math=\"\\sigma_{11}, \\sigma_{22}, \\sigma_{33}\" data-index-in-node=\"90\">$\\sigma_{11}, \\sigma_{22}, \\sigma_{33}$<\/span>\uff09\u4ee5\u53ca\u4e09\u4e2a\u5e73\u9762\u4e0a\u7684\u526a\u5e94\u529b\uff08<span class=\"math-inline\" data-math=\"\\tau_{12}, \\tau_{23}, \\tau_{13}\" data-index-in-node=\"169\">$\\tau_{12}, \\tau_{23}, \\tau_{13}$<\/span>).<\/span><\/p>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4e00\u822c\u6765\u8bf4\uff0c\u4e8c\u7ef4\u5206\u6790\u4fa7\u91cd\u4e8e\u5e73\u9762\u5185\u7684\u4e24\u4e2a\u65b9\u5411\uff08\u901a\u5e38\u79f0\u4e3a 1-2 \u5e73\u9762\uff09\uff0c\u800c\u4e09\u7ef4\u5206\u6790\u5219\u5305\u62ec\u6240\u6709\u5e94\u529b\uff0c\u4f8b\u5982\u5e73\u9762\u5916\u5e94\u529b\u3002.<\/span><\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-28880\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2.png\" alt=\"\u4e8c\u7ef4\u548c\u4e09\u7ef4\u5e94\u529b\u5206\u91cf\" width=\"644\" height=\"246\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2.png 862w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2-300x115.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2-430x164.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2-768x293.png 768w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2-62x24.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2-600x229.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2-725x277.png 725w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/2-2-150x57.png 150w\" sizes=\"(max-width: 644px) 100vw, 644px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe2\uff1a <em>\u4e8c\u7ef4\u548c\u4e09\u7ef4\u5e94\u529b\u5206\u91cf<\/em><\/p>\n<h3>2D Hashin Damage Criteria (hashin failure criteria\u200b) Theory<\/h3>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u4e8c\u7ef4\u54c8\u8f9b\u5931\u6548\u51c6\u5219\u4e2d\uff0c\u6211\u4eec\u91cd\u70b9\u5173\u6ce8\u9762\u5185\u5e94\u529b\u3002\u7ea4\u7ef4\u548c\u57fa\u4f53\u5728\u62c9\u4f38\u548c\u538b\u7f29\u4e0b\u7684\u5931\u6548\u65b9\u7a0b\u5747\u57fa\u4e8e\u8fd9\u4e9b\u9762\u5185\u5e94\u529b\u5206\u91cf\u63a8\u5bfc\u5f97\u51fa\u3002.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><strong>\u7ea4\u7ef4\u5f20\u529b\uff082D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u7ea4\u7ef4\u5f20\u529b\u7684\u5224\u5b9a\u6807\u51c6\u662f\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\left( \\frac{\\sigma_{11}}{X_T} \\right)^2 + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1\">$$\\left( \\frac{\\sigma_{11}}{X_T} \\right)^2 + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1$$<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5728\u54ea\u91cc\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"\\sigma_{11}\" data-index-in-node=\"0\">$\\sigma_{11}$ :<\/span>\u00a0\u662f\u7ea4\u7ef4\u65b9\u5411\u7684\u7eb5\u5411\u5e94\u529b\u3002.<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"X_T\" data-index-in-node=\"0\">$X_T$ :<\/span>\u00a0\u662f\u7ea4\u7ef4\u7684\u7eb5\u5411\u62c9\u4f38\u5f3a\u5ea6\u3002.<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"\\tau_{12}\" data-index-in-node=\"0\">$\\tau_{12}$ :<\/span>\u00a0\u662f\u526a\u5207\u5e94\u529b\u3002.<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"S_L\" data-index-in-node=\"0\">$S_L$ :<\/span>\u00a0\u662f\u7eb5\u5411\u526a\u5207\u5f3a\u5ea6\u3002.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5982\u679c\u6ee1\u8db3\u6b64\u6761\u4ef6\uff0c\u5219\u4f1a\u53d1\u751f\u7ea4\u7ef4\u5728\u62c9\u4f38\u4f5c\u7528\u4e0b\u7684\u65ad\u88c2\u3002.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><strong>\u7ea4\u7ef4\u538b\u7f29\uff082D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5149\u7ea4\u538b\u7f29\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\left( \\frac{\\sigma_{11}}{X_c} \\right)^2 \\ge 1\">$$\\left( \\frac{\\sigma_{11}}{X_c} \\right)^2 \\ge 1$$<\/div>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u54ea\u91cc <span class=\"math-inline\" data-math=\"X_c\" data-index-in-node=\"0\">$X_c$<\/span>\u662f\u7ea4\u7ef4\u7684\u7eb5\u5411\u6297\u538b\u5f3a\u5ea6\u3002\u8be5\u65b9\u7a0b\u8f83\u4e3a\u7b80\u5355\uff0c\u56e0\u4e3a\u7ea4\u7ef4\u7684\u6297\u538b\u7834\u574f\u4e3b\u8981\u53d7\u7eb5\u5411\u5e94\u529b\u63a7\u5236\u3002.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><strong>\u77e9\u9635\u5f20\u529b\uff082D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5bf9\u4e8e\u57fa\u4f53\u5f20\u529b\u800c\u8a00\uff0c\u5931\u6548\u53d7\u4ee5\u4e0b\u56e0\u7d20\u63a7\u5236\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\left( \\frac{\\sigma_{22}}{Y_T} \\right)^2 + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1\">$$\\left( \\frac{\\sigma_{22}}{Y_T} \\right)^2 + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1$$<\/div>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5728\u54ea\u91cc\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"\\sigma_{22}\" data-index-in-node=\"0\">$\\sigma_{22}$ :<\/span>\u662f\u6a2a\u5411\u6b63\u5e94\u529b\uff08\u5782\u76f4\u4e8e\u7ea4\u7ef4\u65b9\u5411\u7684\u5e94\u529b\uff09\u3002.<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"Y_T\" data-index-in-node=\"0\">$Y_T$ :<\/span>\u00a0\u662f\u57fa\u4f53\u7684\u6a2a\u5411\u62c9\u4f38\u5f3a\u5ea6\u3002.<\/span><\/li>\n<\/ul>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><strong>\u77e9\u9635\u538b\u7f29\uff082D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5bf9\u4e8e\u77e9\u9635\u538b\u7f29\uff0c\u5982\u679c\u51fa\u73b0\u4ee5\u4e0b\u60c5\u51b5\uff0c\u5219\u538b\u7f29\u5931\u8d25\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\left( \\frac{\\sigma_{22}}{2S_T} \\right)^2 + \\left&#091; \\left( \\frac{Y_c}{2S_T} \\right)^2 - 1 \\right&#093; \\frac{\\sigma_{22}}{Y_c} + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1\">$$\\left( \\frac{\\sigma_{22}}{2S_T} \\right)^2 + \\left[ \\left( \\frac{Y_c}{2S_T} \\right)^2 &#8211; 1 \\right] \\frac{\\sigma_{22}}{Y_c} + \\left( \\frac{\\tau_{12}}{S_L} \\right)^2 \\ge 1$$<\/div>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5728\u54ea\u91cc\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"Y_c\" data-index-in-node=\"0\">$Y_c$ :<\/span>\u00a0\u662f\u57fa\u4f53\u7684\u6a2a\u5411\u6297\u538b\u5f3a\u5ea6\u3002.<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"S_T\" data-index-in-node=\"0\">$S_T$ :<\/span>\u00a0\u662f\u6a2a\u5411\u526a\u5207\u5f3a\u5ea6\u3002.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u4e8c\u7ef4\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4ec5\u8003\u86511-2\u5e73\u9762\u5185\u7684\u5e94\u529b\uff08\u5e73\u9762\u5185\u7684\u7eb5\u5411\u5e94\u529b\u3001\u6a2a\u5411\u5e94\u529b\u548c\u526a\u5207\u5e94\u529b\uff09\uff0c\u8fd9\u7b80\u5316\u4e86\u5206\u6790\u548c\u65b9\u7a0b\u3002\u5982\u679c\u6ee1\u8db3\u4e0a\u8ff0\u56db\u4e2a\u6761\u4ef6\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\uff0c\u5219\u6839\u636eHashin\u5931\u6548\u51c6\u5219\uff0c\u590d\u5408\u6750\u6599\u5373\u53d1\u751f\u5931\u6548\u3002.<\/span><\/p>\n<h3>3D Hashin Failure Criteria Theory<\/h3>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u4e09\u7ef4\u54c8\u8f9b\u5931\u6548\u51c6\u5219\u4e2d\uff0c\u65b9\u7a0b\u6269\u5c55\u5230\u5305\u542b\u7b2c\u4e09\u65b9\u5411\uff08\u7b2c\u4e09\u8f74\uff0c\u5373\u9762\u5916\u65b9\u5411\uff09\u7684\u5e94\u529b\u3002\u8fd9\u4f7f\u5f97\u5931\u6548\u5206\u6790\u66f4\u52a0\u5168\u9762\uff0c\u56e0\u4e3a\u9762\u5916\u5e94\u529b\u5728\u8bb8\u591a\u5b9e\u9645\u5e94\u7528\u4e2d\u81f3\u5173\u91cd\u8981\u3002.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><strong>\u7ea4\u7ef4\u5f20\u529b\uff083D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7ea4\u7ef4\u62c9\u4f38\u7684\u5931\u6548\u51c6\u5219\u4e0e\u4e4b\u7c7b\u4f3c\uff0c\u4f46\u6709\u6240\u6269\u5c55\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\left( \\frac{\\sigma_{11}}{X_T} \\right)^2 + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{31}}{S_{31}} \\right)^2 \\ge 1\">$$\\left( \\frac{\\sigma_{11}}{X_T} \\right)^2 + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{31}}{S_{31}} \\right)^2 \\ge 1$$<\/div>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5728\u54ea\u91cc\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"\\sigma_{12}, \\sigma_{31}\" data-index-in-node=\"0\">$\\sigma_{12}, \\sigma_{31}$<\/span> and :\u00a0are the shear stresses in different directions.<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><span class=\"math-inline\" data-math=\"S_{12}, S_{31}\" data-index-in-node=\"0\">$S_{12}, S_{31}$ :<\/span>\u00a0\u5206\u522b\u662f\u7eb5\u5411\u548c\u6a2a\u5411\u7684\u526a\u5207\u5f3a\u5ea6\u3002\u5176\u4ed6\u672f\u8bed\u4e0e\u4e8c\u7ef4\u54c8\u8f9b\u51c6\u5219\u4e2d\u7684\u76f8\u540c\u3002.<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><strong>\u7ea4\u7ef4\u538b\u7f29\uff083D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u9488\u5bf9\u4e09\u7ef4\u5149\u7ea4\u538b\u7f29\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\left( \\frac{\\sigma_{11}}{X_c} \\right)^2 \\ge 1\">$$\\left( \\frac{\\sigma_{11}}{X_c} \\right)^2 \\ge 1$$<\/div>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8fd9\u4e0e\u4e8c\u7ef4\u60c5\u51b5\u76f8\u540c\uff0c\u56e0\u4e3a\u538b\u7f29\u7834\u574f\u4ecd\u7136\u4e3b\u8981\u53d7\u7eb5\u5411\u5e94\u529b\u63a7\u5236\u3002.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><strong>\u77e9\u9635\u5f20\u529b\uff083D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5bf9\u4e8e\u4e09\u7ef4\u77e9\u9635\u5f20\u529b\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\left( \\frac{\\sigma_{11} + \\sigma_{33}}{Y_T} \\right)^2 + \\frac{\\sigma_{23}^2 - \\sigma_{22}\\sigma_{33}}{S_{23}^2} + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{31}}{S_{31}} \\right)^2 \\ge 1\">$$\\left( \\frac{\\sigma_{11} + \\sigma_{33}}{Y_T} \\right)^2 + \\frac{\\sigma_{23}^2 &#8211; \\sigma_{22}\\sigma_{33}}{S_{23}^2} + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{31}}{S_{31}} \\right)^2 \\ge 1$$<\/div>\n<ul>\n<li><span style=\"font-size: 14pt;\"><strong>\u77e9\u9635\u538b\u7f29\uff083D\uff09\uff1a<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 14pt;\">\u5bf9\u4e8e\u4e09\u7ef4\u77e9\u9635\u538b\u7f29\uff1a<\/span><\/p>\n<div class=\"math-block\" data-math=\"\\frac{\\sigma_{22} + \\sigma_{33}}{Y_c} \\left&#091; \\left( \\frac{Y_c}{2S_{23}} \\right)^2 - 1 \\right&#093; + \\left( \\frac{\\sigma_{22} + \\sigma_{33}}{4S_{23}^2} \\right)^2 + \\frac{\\sigma_{23}^2 - \\sigma_{22}\\sigma_{33}}{S_{23}^2} + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{31}}{S_{31}} \\right)^2 \\ge 1\">$$\\frac{\\sigma_{22} + \\sigma_{33}}{Y_c} \\left[ \\left( \\frac{Y_c}{2S_{23}} \\right)^2 &#8211; 1 \\right] + \\left( \\frac{\\sigma_{22} + \\sigma_{33}}{4S_{23}^2} \\right)^2 + \\frac{\\sigma_{23}^2 &#8211; \\sigma_{22}\\sigma_{33}}{S_{23}^2} + \\left( \\frac{\\sigma_{12}}{S_{12}} \\right)^2 + \\left( \\frac{\\sigma_{31}}{S_{31}} \\right)^2 \\ge 1$$<\/div>\n<p><span style=\"font-size: 14pt;\">\u6b64\u5916\uff0c\u5728\u56fe 3 \u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u6839\u636e 3D Hashin \u5173\u7cfb\u7ed8\u5236\u7684 Hashin \u5931\u6548\u5305\u7edc\u7ebf\u3002.<\/span><\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-29304\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944.png\" alt=\"\" width=\"894\" height=\"295\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944.png 1131w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-300x99.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-1024x338.png 1024w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-430x142.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-768x253.png 768w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-62x20.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-600x198.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-725x239.png 725w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-114944-150x49.png 150w\" sizes=\"(max-width: 894px) 100vw, 894px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe 3\uff1a <em>\u6545\u969c\u5305\u7edc\u7ebf\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-29305\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115201.png\" alt=\"\" width=\"76\" height=\"25\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115201.png 137w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115201-62x20.png 62w\" sizes=\"(max-width: 76px) 100vw, 76px\" \/>\u00a0<\/em><em>\u6839\u636e\u54c8\u8f9b\u7684\u6807\u51c6\u9884\u6d4b<\/em><\/p>\n<h3>Differences Between 2D and 3D Hashin Forms<\/h3>\n<table>\n<thead>\n<tr>\n<th>\u7c7b\u522b<\/th>\n<th>2D Hashin<\/th>\n<th>3D Hashin<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>Dimensions<\/strong><\/td>\n<td>Focuses on in-plane stresses ($\\sigma_{11}$, $\\sigma_{22}$, $\\tau_{12}$)<\/td>\n<td>Includes out-of-plane stresses<\/td>\n<\/tr>\n<tr>\n<td><strong>Failure Modes<\/strong><\/td>\n<td>Fiber tension, fiber compression, matrix tension, matrix compression<\/td>\n<td>Same failure modes<\/td>\n<\/tr>\n<tr>\n<td><strong>Equations<\/strong><\/td>\n<td>Simpler, fewer stress components<\/td>\n<td>More complex, and involves additional normal and shear stresses<\/td>\n<\/tr>\n<tr>\n<td><strong>\u5e94\u7528\u7a0b\u5e8f<\/strong><\/td>\n<td>2D laminar composites (thin laminates)<\/td>\n<td>3D bulk composites or situations with significant out-of-plane stresses<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u4e8c\u7ef4\u54c8\u8f9b\u51c6\u5219\u7528\u4e8e\u5206\u6790\u5e94\u529b\u4e3b\u8981\u5c40\u9650\u4e8e\u4e8c\u7ef4\u7684\u6750\u6599\uff0c\u4f8b\u5982\u8584\u5c42\u5408\u677f\u6216\u677f\u72b6\u7ed3\u6784\u3002\u800c\u4e09\u7ef4\u54c8\u8f9b\u51c6\u5219\u5219\u5bf9\u4e8e\u8f83\u539a\u7684\u590d\u5408\u6750\u6599\u6216\u9762\u5916\u5e94\u529b\u663e\u8457\u7684\u6750\u6599\u81f3\u5173\u91cd\u8981\u3002\u4e24\u79cd\u51c6\u5219\u90fd\u80fd\u6709\u6548\u9884\u6d4b\u5931\u6548\uff0c\u4f46\u5176\u5e94\u7528\u53d6\u51b3\u4e8e\u590d\u5408\u6750\u6599\u7684\u5e94\u529b\u72b6\u6001\u3002.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-28905\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/3-2.png\" alt=\"\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u7684\u635f\u4f24\" width=\"517\" height=\"371\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/3-2.png 680w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/3-2-300x215.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/3-2-430x309.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/3-2-62x44.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/3-2-600x431.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/3-2-150x108.png 150w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe 4\uff1a <em>\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u7684\u635f\u4f24[<a href=\"https:\/\/www.researchgate.net\/figure\/llustration-of-failure-modes-described-in-Hashin-type-failure-criteria-Doitrand-and_fig3_319405586\" target=\"_blank\" rel=\"nofollow noopener\"><span style=\"color: #0000ff;\">\u53c2\u8003<\/span><\/a>]<\/em><\/p>\n<p><span style=\"font-size: 14pt;\">\u8fd9\u91cc\uff0c\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u7bc7\u5173\u4e8e\u5728 Abaqus \u4e2d\u8fdb\u884c 3D Hashin \u635f\u4f24\u6a21\u62df\u7684\u5b8c\u6574\u6559\u7a0b\uff0c\u6807\u9898\u4e3a\u201c<a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\">\u590d\u5408\u6750\u6599\u4e09\u7ef4\u8fde\u7eed\u4f53Abaqus Hashin\u6e10\u8fdb\u635f\u4f24<\/span><\/a>\u201c\u3002\u201d.<\/span><\/p>\n<h2><span style=\"color: #ff6600;\">Hashin Damage Criteria in Abaqus: Using GUI and subroutines for simulation (UMAT -USDFLD)<\/span><\/h2>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728 Abaqus \u4e2d\uff0cHashin \u635f\u4f24\u51c6\u5219\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u56fe\u5f62\u7528\u6237\u754c\u9762 (GUI) \u5b9e\u73b0\u3002 <span style=\"color: #333333;\">\u590d\u5408\u635f\u4f24<\/span> \u5efa\u6a21\u65b9\u9762\uff0cAbaqus \u63d0\u4f9b\u4e86\u4e00\u4e2a\u5185\u7f6e\u7684\u635f\u4f24\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u91c7\u7528 Hashin \u51c6\u5219\u6765\u5206\u6790\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u591a\u8f74\u8f7d\u8377\u6761\u4ef6\u4e0b\u7684\u6e10\u8fdb\u635f\u4f24\u5206\u6790\u3002\u6b64\u5916\uff0cHashin \u51c6\u5219\u4e5f\u53ef\u4ee5\u901a\u8fc7 Abaqus \u4e2d\u7684 UMAT \u7b49\u5b50\u7a0b\u5e8f\u6765\u5b9e\u73b0\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u89e3\u91ca\u8fd9\u4e9b\u65b9\u6cd5\u3002.<\/span><\/p>\n<h3>Damage Initiation and Damage Evolution<\/h3>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728 Abaqus \u4e2d\uff0c\u635f\u4f24\u840c\u751f\u548c\u635f\u4f24\u6f14\u5316\u662f\u6a21\u62df\u590d\u5408\u6750\u6599\uff08\u5c24\u5176\u662f\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff09\u5931\u6548\u7684\u5173\u952e\u65b9\u9762\u3002\u5b83\u4eec\u4f7f\u7528\u6237\u80fd\u591f\u6a21\u62df\u5931\u6548\u7684\u53d1\u751f\u548c\u968f\u540e\u7684\u6750\u6599\u9000\u5316\uff0c\u4ece\u800c\u771f\u5b9e\u5730\u5c55\u73b0\u590d\u5408\u6750\u6599\u7ed3\u6784\u5728\u8f7d\u8377\u4f5c\u7528\u4e0b\u7684\u5931\u6548\u8fc7\u7a0b\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u635f\u4f24\u8d77\u59cb\u662f\u6307\u6750\u6599\u7531\u4e8e\u6240\u65bd\u52a0\u7684\u5e94\u529b\u6216\u5e94\u53d8\u800c\u5f00\u59cb\u5931\u6548\u6216\u6027\u80fd\u9000\u5316\u7684\u70b9\u3002\u5bf9\u4e8e\u590d\u5408\u6750\u6599\uff0c\u635f\u4f24\u8d77\u59cb\u901a\u5e38\u662f\u7531\u4e8e\u7ea4\u7ef4\u65ad\u88c2\u3001\u57fa\u4f53\u5f00\u88c2\u6216\u5206\u5c42\u9020\u6210\u7684\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u8f7d\u8377\u6761\u4ef6\u548c\u6750\u6599\u5c5e\u6027\u3002\u5728 Abaqus \u4e2d\uff0c\u635f\u4f24\u8d77\u59cb\u7684\u5224\u5b9a\u57fa\u4e8e\u5931\u6548\u51c6\u5219\u3002\u5bf9\u4e8e\u590d\u5408\u6750\u6599\uff0c\u901a\u5e38\u4f7f\u7528 Hashin \u51c6\u5219\uff08Abaqus \u4e2d\u7684 Hashin \u635f\u4f24\u51c6\u5219\uff09\uff0c\u8be5\u51c6\u5219\u5206\u522b\u8bc6\u522b\u7ea4\u7ef4\u548c\u57fa\u4f53\u7684\u5931\u6548\uff08\u62c9\u4f38\u548c\u538b\u7f29\u6a21\u5f0f\uff09\u3002\u60a8\u53ef\u4ee5\u5b66\u4e60\u5982\u4f55\u5bf9\u635f\u4f24\u8d77\u59cb\u8fdb\u884c\u5efa\u6a21\u3002 <a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/#1700035965413-775bb785-a8f0\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\">\u5728\u6211\u4eec\u7684\u6559\u7a0b\u7b2c\u4e00\u6b21\u7814\u8ba8\u4f1a\u4e0a\uff0c\u6211\u4eec\u63a2\u8ba8\u4e86\u57fa\u4e8eHashin\u5931\u6548\u51c6\u5219\u7684\u635f\u4f24\u8d77\u59cb\u95ee\u9898\u3002<\/span><\/a>.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728 Abaqus \u4e2d\uff0c\u590d\u5408\u6750\u6599\u7684\u635f\u4f24\u8d77\u59cb\u901a\u5e38\u5728\u5c5e\u6027\u6a21\u5757\u4e2d\u5b9a\u4e49\u3002\u5728\u8be5\u6a21\u5757\u4e2d\uff0c\u9009\u62e9\u201c\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u635f\u4f24\u201d\u9009\u9879\uff0c\u5373\u53ef\u8bbf\u95ee Hashin \u5931\u6548\u51c6\u5219\u3002.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-28906\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/4-2.png\" alt=\"Hashin Damage \u5728 Abaqus \u4e2d\" width=\"511\" height=\"655\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/4-2.png 639w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/4-2-234x300.png 234w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/4-2-383x491.png 383w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/4-2-62x79.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/4-2-600x769.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/4-2-150x192.png 150w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe 5\uff1aAbaqus \u4e2d\u7684 Hashin \u635f\u4f24<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u00a0\u8981\u4f7f\u7528\u6b64\u6807\u51c6\uff0c\u5fc5\u987b\u786e\u5b9a\u4ee5\u4e0b\u53c2\u6570\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\">\u7ea4\u7ef4\u62c9\u4f38\u5f3a\u5ea6 <b data-path-to-node=\"3,1,0\" data-index-in-node=\"0\"><span class=\"math-inline\" data-math=\"X_T\" data-index-in-node=\"0\">$X_T$<\/span><\/b><\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u7ea4\u7ef4\u6297\u538b\u5f3a\u5ea6 <span class=\"math-inline\" data-math=\"X_c\" data-index-in-node=\"0\">$X_c$<\/span><\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u57fa\u4f53\u62c9\u4f38\u5f3a\u5ea6 <span class=\"math-inline\" data-math=\"Y_T\" data-index-in-node=\"0\">$Y_T$<\/span><\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u57fa\u4f53\u6297\u538b\u5f3a\u5ea6 <span class=\"math-inline\" data-math=\"Y_c\" data-index-in-node=\"0\">$Y_c$<\/span><\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u7eb5\u5411\u548c\u6a2a\u5411\u526a\u5207\u5f3a\u5ea6 <span class=\"math-inline\" data-math=\"S_L\" data-index-in-node=\"0\">$S_L$<\/span>\u548c<span class=\"math-inline\" data-math=\"S_T\" data-index-in-node=\"0\">$S_T$<\/span>.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u4e0b\u56fe\u663e\u793a\u4e86\u8f6f\u4ef6\u4e2d Hashin \u635f\u4f24 Abaqus \u6240\u9700\u7684\u53c2\u6570\u3002.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-28909\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/5-2.png\" alt=\"Hashin\u5931\u6548\u51c6\u5219\u53c2\u6570\" width=\"805\" height=\"453\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe 6\uff1a <em>Hashin\u5931\u6548\u51c6\u5219\u53c2\u6570<\/em><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u53e6\u4e00\u65b9\u9762\uff0c\u635f\u4f24\u6f14\u5316\u63cf\u8ff0\u4e86\u635f\u4f24\u840c\u751f\u540e\u6750\u6599\u6027\u80fd\u9000\u5316\u7684\u8fdb\u7a0b\uff0c\u4e3a\u6a21\u62df\u5931\u6548\u6269\u5c55\u8fc7\u7a0b\u4e2d\u6750\u6599\u521a\u5ea6\u548c\u5f3a\u5ea6\u7684\u964d\u4f4e\u63d0\u4f9b\u4e86\u4e00\u79cd\u673a\u5236\u3002\u5728\u590d\u5408\u6750\u6599\u4e2d\uff0c\u635f\u4f24\u6f14\u5316\u5bf9\u4e8e\u6a21\u62df\u7ea4\u7ef4\u65ad\u88c2\u3001\u57fa\u4f53\u5f00\u88c2\u548c\u5206\u5c42\u7b49\u73b0\u8c61\u81f3\u5173\u91cd\u8981\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5f53\u590d\u5408\u6750\u6599\u5c42\u5408\u677f\u4e2d\u7279\u5b9a\u6750\u6599\u70b9\u53d1\u751f\u5931\u6548\u65f6\uff0c\u5fc5\u987b\u6839\u636e\u9009\u5b9a\u7684\u9000\u5316\u6a21\u578b\u4fee\u6539\u8be5\u70b9\u7684\u6750\u6599\u5c5e\u6027\u3002\u8fd9\u79cd\u8c03\u6574\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u4e09\u79cd\u9000\u5316\u6a21\u5f0f\u4e4b\u4e00\u8fdb\u884c\uff1a <a href=\"https:\/\/caeassistant.com\/product\/simulation-of-composite-hashin-damage-in-3d-continuum-element-in-abaqus-umatvumatusdfld-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\">\u77ac\u95f4\u964d\u81f3\u96f6<\/span><\/a>, \uff0c\u4e00\u4e2a <a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\">\u964d\u4f4e\u81f3\u6307\u5b9a\u7684\u6052\u5b9a\u5e94\u529b\u6c34\u5e73\uff0c\u6216\u9010\u6e10\u964d\u4f4e<\/span><\/a> \u6cbf\u7740\u9884\u5b9a\u8def\u5f84\u3002\u6bcf\u79cd\u65b9\u6cd5\u90fd\u4ee3\u8868\u4e86\u4e00\u79cd\u4e0d\u540c\u7684\u6750\u6599\u635f\u4f24\u540e\u5b8c\u6574\u6027\u4e27\u5931\u5efa\u6a21\u65b9\u6cd5\uff0c\u5982\u56fe\u6240\u793a\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-29306\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725.png\" alt=\"\" width=\"595\" height=\"361\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725.png 912w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725-300x182.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725-430x261.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725-768x466.png 768w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725-62x38.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725-600x364.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725-725x440.png 725w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/Screenshot-2024-11-20-115725-150x91.png 150w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/span><\/p>\n<p style=\"text-align: center;\">\u56fe 7\uff1a <em>\u590d\u5408\u6750\u6599\u635f\u4f24\u8d77\u59cb\u540e\u5404\u79cd\u6027\u80fd\u7684\u964d\u4f4e<\/em><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u77ac\u65f6\u5f3a\u5ea6\u964d\u4f4e\u4f1a\u6d88\u9664\u5931\u6548\u70b9\u5904\u7684\u6240\u6709\u6750\u6599\u5f3a\u5ea6\uff0c\u4ece\u800c\u6709\u6548\u5730\u4e27\u5931\u5176\u627f\u8f7d\u80fd\u529b\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6052\u5e94\u529b\u5f3a\u5ea6\u964d\u4f4e\u5373\u4f7f\u5728\u5931\u6548\u540e\u4e5f\u80fd\u5c06\u5e94\u529b\u9650\u5236\u5728\u4e00\u4e2a\u56fa\u5b9a\u503c\uff0c\u4ece\u800c\u4fdd\u7559\u4e00\u5b9a\u7684\u6b8b\u4f59\u5f3a\u5ea6\u3002\u6700\u540e\uff0c\u6e10\u8fdb\u5f3a\u5ea6\u964d\u4f4e\u5141\u8bb8\u5f3a\u5ea6\u9010\u6e10\u635f\u5931\uff0c\u6a21\u62df\u635f\u4f24\u968f\u65f6\u95f4\u6216\u6301\u7eed\u8f7d\u8377\u4f5c\u7528\u4e0b\u7684\u6269\u5c55\u8fc7\u7a0b\u3002\u5982\u56fe\u6240\u793a\uff0c\u8fd9\u79cd\u6e10\u8fdb\u5f0f\u964d\u4f4e\u53ef\u4ee5\u662f\u7ebf\u6027\u7684\uff0c\u4e5f\u53ef\u4ee5\u662f\u5176\u4ed6\u51fd\u6570\uff08\u4f8b\u5982\u6307\u6570\u51fd\u6570\uff09\u7684\u51fd\u6570\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u6e10\u8fdb\u5f0f\u635f\u4f24\u4e2d\uff0c\u4e00\u65e6\u635f\u4f24\u5f00\u59cb\uff0c\u6750\u6599\u4e0d\u4f1a\u7acb\u5373\u5931\u6548\uff1b\u76f8\u53cd\uff0c\u968f\u7740\u635f\u4f24\u5728\u7ed3\u6784\u4e2d\u6269\u5c55\uff0c\u6750\u6599\u6027\u80fd\u4f1a\u968f\u65f6\u95f4\u63a8\u79fb\u800c\u9010\u6e10\u9000\u5316\u3002\u635f\u4f24\u6f14\u5316\u901a\u5e38\u7528\u65ad\u88c2\u80fd\u6216\u80fd\u91cf\u8017\u6563\u6765\u5b9a\u4e49\u3002\u5176\u76ee\u7684\u662f\u6a21\u62df\u88c2\u7eb9\u6269\u5c55\u8fc7\u7a0b\u4e2d\u6750\u6599\u5438\u6536\u7684\u80fd\u91cf\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u635f\u4f24\u6f14\u5316\u901a\u5e38\u5305\u542b\u4e00\u4e2a\u8f6f\u5316\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u4f1a\u5728\u635f\u4f24\u8d77\u59cb\u51c6\u5219\u6ee1\u8db3\u540e\u964d\u4f4e\u6750\u6599\u521a\u5ea6\u3002\u4f8b\u5982\uff0c\u4e0e\u7ea4\u7ef4\u6216\u57fa\u4f53\u5931\u6548\u76f8\u5173\u7684\u65ad\u88c2\u80fd\u51b3\u5b9a\u4e86\u635f\u4f24\u53d1\u751f\u540e\u6750\u6599\u521a\u5ea6\u4e0b\u964d\u7684\u901f\u5ea6\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u5b9a\u4e49\u635f\u4f24\u8d77\u59cb\u51c6\u5219\u540e\uff0c\u5373\u53ef\u542f\u7528\u635f\u4f24\u6f14\u5316\u529f\u80fd\u3002Abaqus \u7528\u6237\u5728\u5c5e\u6027\u6a21\u5757\u4e2d\u9009\u62e9\u201c\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u7684\u635f\u4f24\u201d\u5e76\u5b9a\u4e49\u635f\u4f24\u8d77\u59cb\u51c6\u5219\u540e\uff0c\u53ef\u4ee5\u9009\u62e9\u201c\u635f\u4f24\u6f14\u5316\u201d\u6765\u6307\u5b9a\u635f\u4f24\u7684\u6269\u5c55\u65b9\u5f0f\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u8bf7\u8bb0\u4f4f\uff0cAbaqus \u4ec5\u63d0\u4f9b\u7ebf\u6027\u9012\u51cf\u5c5e\u6027\u503c\u7684\u529f\u80fd\u3002\u8981\u5b9e\u73b0\u9664\u7ebf\u6027\u51fd\u6570\u4e4b\u5916\u7684\u9012\u51cf\u5c5e\u6027\u503c\uff0c\u9700\u8981\u4f7f\u7528\u5b50\u7a0b\u5e8f\u5bf9\u76f8\u5173\u51fd\u6570\u8fdb\u884c\u5efa\u6a21\u3002\u4e3a\u6b64\uff0c\u5fc5\u987b\u786e\u5b9a\u6750\u6599\u7684\u521a\u5ea6\u77e9\u9635\uff0c\u8be5\u77e9\u9635\u5b9a\u4e49\u4e86\u5e94\u529b\u4e0e\u5e94\u53d8\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u4e0b\u4e00\u6b65\uff0c\u6211\u4eec\u5c06\u4ecb\u7ecd\u4f7f\u7528\u6237\u80fd\u591f\u5b9e\u73b0\u6b64\u529f\u80fd\u7684\u5b50\u7a0b\u5e8f\u3002.<\/span><\/p>\n<p style=\"text-align: left;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-28910\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1.png\" alt=\"Abaqus\u4e2d\u7684\u635f\u4f24\u6f14\u5316\u9009\u9879\" width=\"531\" height=\"523\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1.png 732w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1-300x295.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1-430x423.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1-62x61.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1-600x590.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1-725x713.png 725w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/6-1-150x148.png 150w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe 8\uff1a <em>Abaqus\u4e2d\u7684\u635f\u4f24\u6f14\u5316\u9009\u9879<\/em><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u8981\u4f7f\u7528\u6e10\u8fdb\u635f\u4f24\u6a21\u578b\uff0c\u5fc5\u987b\u786e\u5b9a\u65ad\u88c2\u80fd\u3002\u8fd9\u4e9b\u6570\u503c\u662f\u901a\u8fc7\u5b9e\u9a8c\u6d4b\u8bd5\u83b7\u5f97\u7684\uff0c\u662f\u6750\u6599\u5e38\u6570\u3002.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-28911\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/7.png\" alt=\"Abaqus\u4e2d\u7684\u635f\u4f24\u6f14\u5316\u53c2\u6570\" width=\"595\" height=\"309\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7.png 793w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7-300x156.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7-430x223.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7-768x399.png 768w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7-62x32.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7-600x312.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7-725x377.png 725w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/7-150x78.png 150w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe 9\uff1a <em>Abaqus\u4e2d\u7684\u635f\u4f24\u6f14\u5316\u53c2\u6570<\/em><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">The below figure presents a piece of the .inp file, where the material parameters associated with the Hashin failure theory have been implemented. In this section, the parameters related to damage initiation and damage evolution are introduced to model the progressive failure behavior.<\/span><\/p>\n<h3><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-47669 size-full\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant.webp\" alt=\"material parameters in Hashin failure theory-CAE Assistant\" width=\"624\" height=\"365\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant.webp 624w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant-300x175.webp 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant-430x252.webp 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant-18x12.webp 18w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant-62x36.webp 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant-600x351.webp 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/material-parameters-in-Hashin-failure-theory-CAE-Assistant-150x88.webp 150w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><\/h3>\n<h3>\u5143\u7d20\u5220\u9664<\/h3>\n<p><span style=\"font-size: 14pt;\">In the present damage modeling framework, the Hashin failure criterion was employed to identify the onset of different composite failure modes, including fiber and matrix failure under tensile and compressive loading conditions. Once the initiation criteria were satisfied, stiffness degradation was introduced through the damage evolution law, and <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/caeassistant.com\/blog\/abaqus-element-deletion-criteria\/\"><strong>Abaqus element deletion<\/strong><\/a><\/span> was activated when the material degradation reached its critical limit. <\/span><\/p>\n<p><span style=\"font-size: 14pt;\">This procedure enables the numerical simulation of severe material failure, crack propagation, and the complete loss of load-carrying capacity in highly damaged regions.<\/span><\/p>\n<h3>Characteristic Element Length<\/h3>\n<p><span style=\"font-size: 14pt;\">The characteristic element length is an important parameter in continuum damage mechanics models based on the Hashin criterion, particularly when damage evolution is defined using fracture energy concepts. Since the predicted softening response may become dependent on mesh size, the characteristic element length is used to regularize the energy dissipation during damage progression.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">In this way, the amount of energy released during failure remains more consistent for different mesh densities, leading to more objective numerical results. Therefore, in combination with the Hashin criterion, the characteristic element length plays a key role in achieving mesh-independent and physically meaningful progressive damage simulations.<\/span><\/p>\n<h3>Subroutine and Hashin failure criteria<\/h3>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">Abaqus \u4e2d\u7684\u5b50\u7a0b\u5e8f\u5141\u8bb8\u7528\u6237\u81ea\u5b9a\u4e49\u6750\u6599\u6a21\u578b\u3001\u672c\u6784\u884c\u4e3a\u548c\u81ea\u5b9a\u4e49\u573a\u53d8\u91cf\u3002Abaqus \u62e5\u6709\u591a\u79cd\u5b50\u7a0b\u5e8f\uff0c\u53ef\u7528\u4e8e\u6269\u5c55\u8f6f\u4ef6\u7684\u9ed8\u8ba4\u529f\u80fd\uff0c\u5305\u62ec\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>UMAT\uff08\u7528\u6237\u6750\u6599\u5b50\u7a0b\u5e8f\uff09<\/strong>\uff1a\u7528\u4e8e Abaqus\/Standard \u4e2d\uff0c\u4e3a\u9759\u6001\u548c\u51c6\u9759\u6001\u95ee\u9898\u5b9a\u4e49\u81ea\u5b9a\u4e49\u6750\u6599\u6a21\u578b\u3002.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>USDFLD\uff08\u7528\u6237\u81ea\u5b9a\u4e49\u5b57\u6bb5\u5b50\u7a0b\u5e8f\uff09<\/strong>\u5141\u8bb8\u7528\u6237\u5b9a\u4e49\u5f71\u54cd\u6750\u6599\u54cd\u5e94\u7684\u81ea\u5b9a\u4e49\u5b57\u6bb5\u53d8\u91cf\u3002.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 14pt;\"><em><strong>\u7b14\u8bb0\uff1a<\/strong> <\/em>\u672c\u6559\u7a0b\u89c6\u9891\u5b8c\u6574\u8bb2\u89e3\u4e86\u5982\u4f55\u4f7f\u7528 UMAT \u548c USDFLD \u5b50\u7a0b\u5e8f\u6765\u6a21\u62df Hashin \u7406\u8bba\u3002\u201c<a href=\"https:\/\/caeassistant.com\/product\/simulation-of-composite-hashin-damage-in-3d-continuum-element-in-abaqus-umatvumatusdfld-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\">\u5728Abaqus\u4e2d\u7528\u4e09\u7ef4\u8fde\u7eed\u4f53\u5355\u5143\u6a21\u62df\u590d\u5408\u6750\u6599Hashin\u635f\u4f24\uff08UMAT-VUMAT-USDFLD\uff09<\/span><\/a>\u201c\u3002\u201d.<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5b50\u7a0b\u5e8f\u4f7f\u7528\u6237\u80fd\u591f\u7075\u6d3b\u5730\u5b9e\u73b0\u66f4\u590d\u6742\u7684\u6750\u6599\u6a21\u578b\u3001\u76f8\u4e92\u4f5c\u7528\u548c\u635f\u4f24\u51c6\u5219\uff0c\u8fd9\u4e9b\u5185\u5bb9\u5728 Abaqus \u7684\u9ed8\u8ba4\u5e93\u4e2d\u53ef\u80fd\u4e0d\u53ef\u7528\u3002\u4f46\u662f\uff0c\u4f55\u65f6\u5e94\u8be5\u5728 Hashin \u635f\u4f24 Abaqus \u5efa\u6a21\u4e2d\u4f7f\u7528\u5b50\u7a0b\u5e8f\u5462\uff1f\u5728\u4ee5\u4e0b\u60c5\u51b5\u4e0b\uff0c\u60a8\u5e94\u8be5\u8003\u8651\u5728 Hashin \u635f\u4f24 Abaqus \u5efa\u6a21\u4e2d\u4f7f\u7528\u5b50\u7a0b\u5e8f\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>\u9700\u8981\u81ea\u5b9a\u4e49\u5931\u8d25\u6807\u51c6<\/strong>\uff1a\u5982\u679c Abaqus \u4e2d\u5185\u7f6e\u7684 Hashin \u635f\u4f24\u51c6\u5219\u4e0d\u8db3\u4ee5\u8fdb\u884c\u5206\u6790\uff0c\u4f8b\u5982\u5f53\u60a8\u9700\u8981\u8003\u8651\u975e\u6807\u51c6\u8f7d\u8377\u6761\u4ef6\u6216\u591a\u5c3a\u5ea6\u5efa\u6a21\u65f6\u3002.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\"><strong>\u6e10\u8fdb\u5f0f\u4f24\u5bb3\u6216\u81ea\u5b9a\u4e49\u4f24\u5bb3\u6f14\u53d8<\/strong>\u5bf9\u4e8e\u8d85\u51fa Abaqus \u9ed8\u8ba4\u63d0\u4f9b\u7684\u66f4\u590d\u6742\u7684\u6e10\u8fdb\u635f\u4f24\u5efa\u6a21\uff0c\u5b50\u7a0b\u5e8f\u5141\u8bb8\u7528\u6237\u5b9a\u4e49\u81ea\u5b9a\u4e49\u635f\u4f24\u6f14\u5316\u89c4\u5f8b\u3002.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u5728\u5b50\u7a0b\u5e8f\u4e2d\u4f7f\u7528 UMAT \u5b50\u7a0b\u5e8f\u6765\u5b9e\u73b0 Hashin \u5931\u6548\u51c6\u5219\uff08Abaqus\/Standard\uff09\uff1a<\/span><\/p>\n<ul style=\"text-align: left;\">\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6b65\u9aa4 1\uff1a\u5b9a\u4e49\u6750\u6599\u884c\u4e3a\uff1a\u5728 UMAT \u5b50\u7a0b\u5e8f\u4e2d\uff0c\u5b9a\u4e49\u590d\u5408\u6750\u6599\u7684\u5e94\u529b-\u5e94\u53d8\u5173\u7cfb\u3002\u4f7f\u7528 Hashin \u5931\u6548\u51c6\u5219\u8ba1\u7b97\u5931\u6548\u8d77\u59cb\u70b9\uff0c\u7136\u540e\u6839\u636e\u635f\u4f24\u72b6\u6001\u964d\u4f4e\u6750\u6599\u521a\u5ea6\u3002.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6b65\u9aa4 2\uff1a\u6e10\u8fdb\u635f\u4f24\uff1a\u5b9e\u65bd\u635f\u4f24\u6f14\u5316\u6a21\u578b\uff0c\u968f\u7740\u635f\u4f24\u7684\u7d2f\u79ef\u964d\u4f4e\u6750\u6599\u521a\u5ea6\uff0c\u5e76\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\u66f4\u65b0\u5e94\u529b\u548c\u5e94\u53d8\u3002.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6b65\u9aa4 3\uff1a\u8f93\u51fa\u53d8\u91cf\uff1a\u5b9a\u4e49\u4eff\u771f\u540e\u8981\u53ef\u89c6\u5316\u7684\u8f93\u51fa\u53d8\u91cf\uff08\u4f8b\u5982\u635f\u4f24\u53c2\u6570\uff09\u3002.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: left;\"><span style=\"font-size: 14pt;\">USDFLD \u5b50\u7a0b\u5e8f\uff1a<\/span><\/p>\n<ul style=\"text-align: left;\">\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u6b65\u9aa4 1\uff1a\u81ea\u5b9a\u4e49\u5b57\u6bb5\u53d8\u91cf\uff1a\u4f7f\u7528 USDFLD \u5b9a\u4e49\u5f71\u54cd\u6750\u6599\u54cd\u5e94\u7684\u81ea\u5b9a\u4e49\u5b57\u6bb5\u53d8\u91cf\uff0c\u4f8b\u5982\u635f\u4f24\u6269\u5c55\u6216\u5e94\u53d8\u8f6f\u5316\u3002.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-size: 14pt;\">\u6b65\u9aa4 2\uff1a\u4e0e\u6750\u6599\u6a21\u578b\u7684\u4ea4\u4e92\uff1aUSDFLD \u4e2d\u5b9a\u4e49\u7684\u573a\u53d8\u91cf\u53ef\u4ee5\u4e0e\u6750\u6599\u6a21\u578b\u4ea4\u4e92\uff0c\u6839\u636e Hashin \u51c6\u5219\u6539\u53d8\u590d\u5408\u6750\u6599\u7684\u521a\u5ea6\u3001\u5f3a\u5ea6\u6216\u5931\u6548\u884c\u4e3a\u3002.<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #ff6600;\">Hashin vs Tsai-Hill vs Tsai-Wu<\/span><\/h2>\n<p><span style=\"font-size: 14pt;\">To evaluate the performance of composite laminates under different loading conditions, several failure criteria have been developed based on distinct mathematical formulations and physical assumptions. Among the most widely used criteria are Hashin, Tsai-Hill, and Tsai-Wu, each offering a different level of accuracy, complexity, and capability in predicting failure initiation. While some criteria are better suited for preliminary strength assessment, others are more appropriate for advanced progressive damage simulations in finite element environments such as Abaqus. The following table presents a technical comparison of these three commonly used composite failure theories.<\/span><\/p>\n<table>\n<thead>\n<tr>\n<th>\u7279\u5f81<\/th>\n<th>\u54c8\u8f9b\u51c6\u5219<\/th>\n<th>\u8521-\u5e0c\u5c14\u51c6\u5219<\/th>\n<th>\u8521-\u5434\u51c6\u5219<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>Application<\/strong><\/td>\n<td>Unidirectional and laminated fiber-reinforced composites<\/td>\n<td>Anisotropic brittle materials and laminated composites<\/td>\n<td>Orthotropic composites under multiaxial loading<\/td>\n<\/tr>\n<tr>\n<td><strong>Failure Mode Identification<\/strong><\/td>\n<td>Yes; Fiber Tension \/ Fiber Compression \/ Matrix Tension \/ Matrix Compression<\/td>\n<td>\u4e0d<\/td>\n<td>\u4e0d<\/td>\n<\/tr>\n<tr>\n<td><strong>Tension-Compression Asymmetry<\/strong><\/td>\n<td>Fully considered<\/td>\n<td>\u6709\u9650\u7684<\/td>\n<td>Fully considered<\/td>\n<\/tr>\n<tr>\n<td><strong>Fiber Orientation Dependence<\/strong><\/td>\n<td>Explicit and direct<\/td>\n<td>Indirect through directional strengths<\/td>\n<td>Explicit through tensor coefficients<\/td>\n<\/tr>\n<tr>\n<td><strong>Sensitivity to In-plane Shear Stress<\/strong><\/td>\n<td>\u9ad8\u7684<\/td>\n<td>\u7f13\u548c<\/td>\n<td>\u9ad8\u7684<\/td>\n<\/tr>\n<tr>\n<td><strong>Matrix Failure Prediction<\/strong><\/td>\n<td>\u51fa\u8272\u7684<\/td>\n<td>\u6709\u9650\u7684<\/td>\n<td>\u7f13\u548c<\/td>\n<\/tr>\n<tr>\n<td><strong>Fiber Failure Prediction<\/strong><\/td>\n<td>\u51fa\u8272\u7684<\/td>\n<td>\u7f13\u548c<\/td>\n<td>\u597d\u7684<\/td>\n<\/tr>\n<tr>\n<td><strong>Progressive Damage Modeling<\/strong><\/td>\n<td>\u51fa\u8272\u7684<\/td>\n<td>\u8d2b\u7a77\u7684<\/td>\n<td>\u7f13\u548c<\/td>\n<\/tr>\n<tr>\n<td><strong>Common Use in Abaqus<\/strong><\/td>\n<td>Damage Initiation + Damage Evolution<\/td>\n<td>Failure Index<\/td>\n<td>Failure Index \/ User Material<\/td>\n<\/tr>\n<tr>\n<td><strong>\u8ba1\u7b97\u6210\u672c<\/strong><\/td>\n<td>\u7f13\u548c<\/td>\n<td>Low<\/td>\n<td>\u7f13\u548c<\/td>\n<\/tr>\n<tr>\n<td><strong>Main Advantage<\/strong><\/td>\n<td>Realistic representation of composite failure mechanisms<\/td>\n<td>Simplicity, speed, minimal material data<\/td>\n<td>Accurate multiaxial failure prediction with tension\/compression asymmetry<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-size: 14pt;\">The comparison shows that no single criterion is universally superior; rather, the appropriate selection depends on the objective of the analysis. Tsai-Hill is often preferred for fast and simplified strength estimation, whereas <a href=\"https:\/\/caeassistant.com\/blog\/tsai-hill-failure-criterion-tsai-wu-criterion\/\"><span style=\"color: #0000ff;\"><strong>Tsai-Wu \u00a0failure criterion<\/strong><\/span><\/a> is more effective for multiaxial stress interaction problems. However, when failure mode identification, stiffness degradation, and damage evolution are required, Hashin is generally considered the most reliable option for composite damage modeling. Therefore, engineers should choose the criterion according to the required fidelity, available material data, and computational objectives.<\/span><\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-1\/5 vc_hidden-sm vc_hidden-xs vc_col-has-fill\"><div class=\"vc_column-inner vc_custom_1776852761500\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p style=\"text-align: center;\"><a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/#1700035965394-a236619d-3ba9\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><strong>Damage criteria for composite materials<\/strong><\/span><\/a><br \/>\n<a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/#1700035965394-a236619d-3ba9\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-30442\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/package1.png\" alt=\"\u54c8\u8f9b\u9010\u6e10\u53d7\u635f\" width=\"315\" height=\"413\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1.png 488w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-229x300.png 229w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-374x491.png 374w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-62x81.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-150x197.png 150w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/a><\/p>\n\n\t\t<\/div>\n\t<\/div>\n\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p style=\"text-align: center;\"><span style=\"font-size: 12pt;\">\u4f24\u5bb3\u8d77\u59cb+ <strong>\u6e10\u8fdb\u6027\u635f\u4f24<\/strong> (<a href=\"https:\/\/caeassistant.com\/product\/simulation-of-composite-hashin-damage-in-3d-continuum-element-in-abaqus-umatvumatusdfld-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><strong>\u68c0\u6d4b\u5230\u6750\u6599\u6027\u80fd\u7acb\u5373\u6216\u7a81\u7136\u4e0b\u964d<\/strong><\/span><\/a>) + \u4f7f\u7528\u5206\u6b65\u6307\u5357 <strong>UMAT<\/strong>, <strong>VUMAT\u3001USDFLD \u5b50\u7a0b\u5e8f<\/strong><\/span><a href=\"https:\/\/caeassistant.com\/product\/simulation-of-composite-hashin-damage-in-3d-continuum-element-in-abaqus-umatvumatusdfld-1\/\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-30443\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG.png\" alt=\"\u54c8\u8f9b\u7a81\u7136\u4f24\u5bb3\" width=\"315\" height=\"429\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG.png 471w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-220x300.png 220w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-361x491.png 361w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-62x84.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-150x204.png 150w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/a><\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p style=\"text-align: center;\"><span style=\"font-size: 14pt;\">\u60f3\u7cbe\u901a Abaqus \u4e2d\u7684\u590d\u5408\u635f\u4f24\u8ba1\u7b97\u5417\uff1f <a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><strong>\u4f7f\u7528 VUMAT \u8fdb\u884c Hashin \u6e10\u8fdb\u6027\u635f\u4f24<\/strong><\/span><\/a> \u975e\u5e38\u9002\u5408\u5efa\u6a21 <strong>\u6e10\u8fdb\u6027\u635f\u5bb3<\/strong> \u5728\u6df1\u5165\u7814\u8ba8\u4f1a\u7684\u5206\u6790\u4e2d\uff0c\u540c\u65f6 <a href=\"https:\/\/caeassistant.com\/product\/simulation-of-composite-hashin-damage-in-3d-continuum-element-in-abaqus-umatvumatusdfld-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><strong>\u7efc\u5408 Hashin \u635f\u4f24\uff08\u5305\u542b UMAT\u3001VUMAT \u548c USDFLD\uff09<\/strong><\/span><\/a> \u91cd\u70b9\u662f <strong>\u7a81\u53d1\u6027\u635f\u5bb3<\/strong> \u901a\u8fc7\u6613\u4e8e\u5b9e\u73b0\u7684\u5b50\u7a0b\u5e8f\u8fdb\u884c\u5206\u6790\u3002\u8bf7\u6839\u636e\u60a8\u7684\u9700\u8981\u70b9\u51fb\u4e0b\u65b9\u5404\u4e2a\u8f6f\u4ef6\u5305\u3002.\u00a0<\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse; background-color: #dbdbdb;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt;\">3D\u8fde\u7eed\u4f53\u5143\u7d20+ <strong>\u54c8\u8f9b\u5931\u6548\u51c6\u5219<\/strong> +\u4f24\u5bb3\u542f\u52a8+ <strong>\u6e10\u8fdb\u6027\u635f\u4f24<\/strong> (<a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><strong>\u57fa\u4e8e\u80fd\u91cf\u7684\u6e10\u8fdb\u5f0f\u964d\u89e3<\/strong><\/span><\/a>) + \u4f7f\u7528\u5206\u6b65\u6307\u5357 <strong>VUMAT \u5b50\u7a0b\u5e8f<\/strong><\/span><\/p>\n<p><a href=\"https:\/\/caeassistant.com\/product\/3d-continuum-hashin-progressive-damage-for-composite-materials-in-abaqus-vumat-subroutine-1\/\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-30442\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/package1.png\" alt=\"\u54c8\u8f9b\u9010\u6e10\u53d7\u635f\" width=\"353\" height=\"463\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1.png 488w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-229x300.png 229w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-374x491.png 374w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-62x81.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package1-150x197.png 150w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/a><\/td>\n<td style=\"width: 50%;\">\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt;\">3D\u8fde\u7eed\u4f53\u5143\u7d20+ <strong>\u54c8\u8f9b\u5931\u6548\u51c6\u5219<\/strong> +\u4f24\u5bb3\u542f\u52a8+ <strong>\u6e10\u8fdb\u6027\u635f\u4f24<\/strong> (<a href=\"https:\/\/caeassistant.com\/product\/simulation-of-composite-hashin-damage-in-3d-continuum-element-in-abaqus-umatvumatusdfld-1\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><strong>\u68c0\u6d4b\u5230\u6750\u6599\u6027\u80fd\u7acb\u5373\u6216\u7a81\u7136\u4e0b\u964d<\/strong><\/span><\/a>) + \u4f7f\u7528\u5206\u6b65\u6307\u5357 <strong>UMAT<\/strong>, <strong>VUMAT\u3001USDFLD \u5b50\u7a0b\u5e8f<\/strong><\/span><a href=\"https:\/\/caeassistant.com\/product\/simulation-of-composite-hashin-damage-in-3d-continuum-element-in-abaqus-umatvumatusdfld-1\/\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-30443\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG.png\" alt=\"\u54c8\u8f9b\u7a81\u7136\u4f24\u5bb3\" width=\"325\" height=\"442\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG.png 471w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-220x300.png 220w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-361x491.png 361w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-62x84.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2024\/10\/package-Hashin-PNG-150x204.png 150w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h2><span style=\"color: #ff6600;\">\u7ed3\u8bba<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u672c\u6587\u63a2\u8ba8\u4e86\u54c8\u8f9b\u635f\u4f24\u51c6\u5219\uff0c\u8fd9\u662f\u4e00\u79cd\u7528\u4e8e\u9884\u6d4b\u590d\u5408\u6750\u6599\uff08\u5c24\u5176\u662f\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff09\u635f\u4f24\u7684\u5931\u6548\u7406\u8bba\u3002\u8be5\u51c6\u5219\u80fd\u591f\u8be6\u7ec6\u5206\u89e3\u5931\u6548\u6a21\u5f0f\uff0c\u4f7f\u5176\u6210\u4e3a\u6709\u9650\u5143\u5206\u6790\u4e2d\u8fdb\u884c\u7cbe\u786e\u6a21\u62df\u7684\u91cd\u8981\u5de5\u5177\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u7406\u89e3\u54c8\u8f9b\u5931\u6548\u51c6\u5219\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u4e3a\u590d\u5408\u6750\u6599\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5404\u4e2a\u884c\u4e1a\uff0c\u51c6\u786e\u9884\u6d4b\u5176\u5931\u6548\u80fd\u591f\u786e\u4fdd\u66f4\u4f18\u7684\u8bbe\u8ba1\u548c\u5b89\u5168\u3002\u6211\u4eec\u9996\u5148\u63a2\u8ba8\u4e86\u590d\u5408\u6750\u6599\u4e2d\u4e0d\u540c\u7684\u635f\u4f24\u673a\u5236\uff0c\u4f8b\u5982\u57fa\u4f53\u5f00\u88c2\u548c\u7ea4\u7ef4\u65ad\u88c2\uff0c\u54c8\u8f9b\u5931\u6548\u51c6\u5219\u6b63\u662f\u9488\u5bf9\u8fd9\u4e9b\u673a\u5236\u800c\u5236\u5b9a\u7684\u3002\u7136\u540e\uff0c\u6211\u4eec\u89e3\u91ca\u4e86\u54c8\u8f9b\u635f\u4f24\u51c6\u5219\u7684\u4e8c\u7ef4\u548c\u4e09\u7ef4\u5f62\u5f0f\uff0c\u5e76\u9610\u8ff0\u4e86\u4e24\u79cd\u60c5\u51b5\u4e0b\u5e94\u529b\u5206\u91cf\u7684\u5904\u7406\u65b9\u5f0f\u3002\u6700\u540e\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u5982\u4f55\u5728Abaqus\u4e2d\u4f7f\u7528\u56fe\u5f62\u7528\u6237\u754c\u9762\uff08GUI\uff09\u6216\u5b50\u7a0b\u5e8f\u6765\u5b9e\u73b0\u54c8\u8f9b\u635f\u4f24\u51c6\u5219\uff0c\u91cd\u70b9\u5173\u6ce8\u635f\u4f24\u7684\u840c\u751f\u548c\u6f14\u5316\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u603b\u7684\u6765\u8bf4\uff0c\u6211\u4eec\u4e86\u89e3\u5230 Hashin \u635f\u4f24\u51c6\u5219\u662f\u6a21\u62df\u590d\u5408\u6750\u6599\u884c\u4e3a\u7684\u6709\u6548\u65b9\u6cd5\uff0c\u4e0e\u4f20\u7edf\u7684\u5931\u6548\u7406\u8bba\u76f8\u6bd4\uff0c\u5b83\u80fd\u63d0\u4f9b\u66f4\u7cbe\u786e\u7684\u9884\u6d4b\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6d4f\u89c8\u6211\u4eec\u5185\u5bb9\u5168\u9762\u7684 Abaqus \u6559\u7a0b\u9875\u9762\uff0c\u5176\u4e2d\u5305\u542b\u514d\u8d39\u7684 PDF \u6307\u5357\u548c\u9002\u5408\u6240\u6709\u6280\u80fd\u6c34\u5e73\u7684\u8be6\u7ec6\u89c6\u9891\u3002\u63a2\u7d22\u514d\u8d39\u548c\u4ed8\u8d39\u5957\u9910\uff0c\u4ee5\u53ca\u9ad8\u6548\u638c\u63e1 Abaqus \u7684\u5fc5\u5907\u4fe1\u606f\u3002\u7acb\u5373\u5f00\u542f\u60a8\u7684 Abaqus \u5b66\u4e60\u4e4b\u65c5\uff01 <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/caeassistant.com\/free-abaqus-tutorial-training-video\/\" target=\"_blank\" rel=\"noopener\">Abaqus\u6559\u7a0b<\/a><\/span> \u73b0\u5728\uff01<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8fd9\u00a0<span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/caeassistant.com\/\" target=\"_blank\" rel=\"noopener\">CAE \u52a9\u624b<\/a><\/span>\u00a0\u6211\u4eec\u81f4\u529b\u4e8e\u6ee1\u8db3\u60a8\u6240\u6709\u7684 CAE \u9700\u6c42\uff0c\u60a8\u7684\u53cd\u9988\u5bf9\u6211\u4eec\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\u81f3\u5173\u91cd\u8981\u3002\u5982\u679c\u60a8\u6709\u4efb\u4f55\u7591\u95ee\u6216\u9047\u5230\u4efb\u4f55\u95ee\u9898\uff0c\u8bf7\u968f\u65f6\u901a\u8fc7\u6211\u4eec\u7684\u793e\u4ea4\u5a92\u4f53\u8d26\u53f7\uff08\u5305\u62ec WhatsApp\uff09\u4e0e\u6211\u4eec\u8054\u7cfb\u3002.<\/span><\/p>\n<h2><span style=\"color: #ff6600;\">Hashin Failure Criterion FAQs<\/span><\/h2>\n<h3><span style=\"font-size: 14pt;\">1. What is the Hashin failure criterion in composite materials?<\/span><\/h3>\n<p><span style=\"font-size: 14pt;\">The Hashin failure criterion is a widely used damage model for fiber-reinforced composites that predicts failure initiation based on stress components and distinguishes between different failure mechanisms in fibers and matrix.<\/span><\/p>\n<h3><span style=\"font-size: 14pt;\">2. What are the failure modes defined by Hashin?<\/span><\/h3>\n<p><span style=\"font-size: 14pt;\">Hashin typically defines four main failure modes: fiber tension, fiber compression, matrix tension, and matrix compression. This mode separation makes it more realistic than many interactive criteria.<\/span><\/p>\n<h3><span style=\"font-size: 14pt;\">3. Why are elements not deleting in Abaqus when using the Hashin damage model?<\/span><\/h3>\n<p><span style=\"font-size: 14pt;\">Elements usually do not delete because only Damage Initiation has been defined. To enable deletion, Damage Evolution and element removal settings must also be properly activated.<\/span><\/p>\n<h3><span style=\"font-size: 14pt;\">4. What is the difference between the 2D and 3D Hashin failure criteria?<\/span><\/h3>\n<p><span style=\"font-size: 14pt;\">The 2D Hashin criterion is mainly used for plane stress laminate models, while the 3D version includes out-of-plane stresses and is more suitable for solid composite elements.<\/span><\/p>\n<h3><span style=\"font-size: 14pt;\">5. Do I need a UMAT or VUMAT subroutine to use the Hashin criterion in Abaqus?<\/span><\/h3>\n<p><span style=\"font-size: 14pt;\">Not always. Abaqus provides a built-in Hashin model for many composite analyses. However, UMAT or VUMAT is needed for advanced custom damage criteria.<\/span><\/p>\n<h3><span style=\"font-size: 14pt;\">6. What is the difference between Damage Initiation and Damage Evolution in Hashin?<\/span><\/h3>\n<p><span style=\"font-size: 14pt;\">Damage Initiation identifies when failure starts, while Damage Evolution controls how stiffness degrades and damage progresses after initiation until final failure.<\/span><\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><iframe title=\"Abaqus Hashin \u4e09\u7ef4\u590d\u5408\u6750\u6599\u635f\u4f24\u6a21\u578b - \u57fa\u7840\u77e5\u8bc6\u3001\u5173\u7cfb\u3001\u4f7f\u7528 VUMAT \u5b50\u7a0b\u5e8f\u7684\u793a\u4f8b\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/ZmB6-ejfTOo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><iframe title=\"\u4f7f\u7528 UMAT\u3001VUMAT \u548c USDFLD \u7684 Abaqus Hashin \u635f\u4f24\u6a21\u578b\u5728\u4e09\u7ef4\u8fde\u7eed\u4f53\u5355\u5143\u4e2d\u5e94\u7528\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/RZaF6uhO0fc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"How do we predict the exact moment a composite material will fail under pressure? The Hashin Failure Criteria offer a powerful answer by breaking down the complex failure behaviors of fiber-reinforced composites, helping engineers foresee how and when damage will occur. The Hashin Damage Criteria are specifically developed for fiber-reinforced composites. It identifies whether failure [...]","protected":false},"author":250,"featured_media":29086,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[67],"tags":[],"class_list":["post-28873","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog"],"_links":{"self":[{"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/posts\/28873","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/users\/250"}],"replies":[{"embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/comments?post=28873"}],"version-history":[{"count":12,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/posts\/28873\/revisions"}],"predecessor-version":[{"id":47680,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/posts\/28873\/revisions\/47680"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/media\/29086"}],"wp:attachment":[{"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/media?parent=28873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/categories?post=28873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/tags?post=28873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}