{"id":43648,"date":"2025-11-13T11:06:29","date_gmt":"2025-11-13T07:36:29","guid":{"rendered":"https:\/\/caeassistant.com\/?p=43648"},"modified":"2026-06-07T15:39:22","modified_gmt":"2026-06-07T12:09:22","slug":"%e7%9b%b8%e5%9c%ba%e6%a8%a1%e5%9e%8b%e6%96%ad%e8%a3%82","status":"publish","type":"post","link":"https:\/\/dev.caeassistant.com\/zh\/%e5%8d%9a%e5%ae%a2\/%e7%9b%b8%e5%9c%ba%e6%a8%a1%e5%9e%8b%e6%96%ad%e8%a3%82\/","title":{"rendered":"\u4ec0\u4e48\u662f\u76f8\u573a\u6a21\u578b\uff1f\u9884\u6d4b\u590d\u6742\u65ad\u88c2\u548c\u754c\u9762\u6f14\u5316\u7684\u5f3a\u5927\u5de5\u5177"},"content":{"rendered":"<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4f60\u662f\u5426\u5c1d\u8bd5\u8fc7\u6a21\u62df\u88c2\u7eb9\u6269\u5c55\u6216\u6750\u6599\u5931\u6548\uff1f\u5982\u679c\u662f\uff0c\u4f60\u53ef\u80fd\u9047\u5230\u8fc7\u4e00\u4e9b\u5c40\u9650\u6027\u3002\u4f20\u7edf\u65b9\u6cd5\u5728\u88c2\u7eb9\u6269\u5c55\u8def\u5f84\u672a\u77e5\u7684\u60c5\u51b5\u4e0b\u96be\u4ee5\u594f\u6548\u3002\u5f53\u591a\u6761\u88c2\u7eb9\u4ee5\u4e0d\u53ef\u9884\u6d4b\u7684\u65b9\u5f0f\u5206\u652f\u548c\u5408\u5e76\u65f6\uff0c\u5b83\u4eec\u4e5f\u540c\u6837\u5931\u6548\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4f20\u7edf\u7684\u6709\u9650\u5143\u6cd5\uff08FEM\uff09\u6216\u6269\u5c55\u6709\u9650\u5143\u6cd5\uff08XFEM\uff09\u7b49\u65b9\u6cd5\u65e0\u6cd5\u6709\u6548\u5904\u7406\u5982\u6b64\u590d\u6742\u7684\u6a21\u578b\u3002\u800c\u76f8\u573a\u6a21\u578b\u5219\u6070\u6070\u5c55\u73b0\u4e86\u5176\u4f18\u52bf\u3002\u6839\u636e\u6211\u4eec\u7684\u7ecf\u9a8c\uff0c\u76f8\u573a\u6a21\u578b\u80fd\u591f\u6a21\u62df\u88c2\u7eb9\u7684\u840c\u751f\u3001\u6269\u5c55\u3001\u5206\u652f\u548c\u5408\u5e76\u7b49\u8fc7\u7a0b\uff0c\u4f7f\u5176\u81ea\u7136\u5730\u53d1\u751f\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6b64\u5916\uff0c\u76f8\u573a\u65ad\u88c2\u6a21\u62df\u65e0\u9700\u663e\u5f0f\u8ffd\u8e2a\u5373\u53ef\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c\u5e76\u80fd\u4e0e\u5176\u4ed6\u7269\u7406\u73b0\u8c61\u65e0\u7f1d\u8026\u5408\u3002\u672c\u535a\u5ba2\u5df2\u8ba8\u8bba\u4e86\u4f7f\u7528 Abaqus \u548c Julia \u4ee3\u7801\u8bed\u8a00\u5b9e\u73b0\u8be5\u6a21\u578b\u7684\u4e24\u79cd\u65b9\u6cd5\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Phase-Field Models for Fracture: Q&amp;A<\/strong><\/p>\n<div class=\"mahour-accordion\"><\/p>\n<div class=\"mahour-accordion-item active\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                \u76f8\u573a\u6a21\u578b\uff08PFM\uff09\u5728\u65ad\u88c2\u529b\u5b66\u4e2d\u7684\u57fa\u672c\u6982\u5ff5\u662f\u4ec0\u4e48\uff1f\u5b83\u4e0e\u6e05\u6670\u754c\u9762\u6a21\u578b\u6709\u4f55\u4e0d\u540c\uff1f            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\n\u76f8\u573a\u6a21\u578b\u5229\u7528\u8fde\u7eed\u6807\u91cf\u53d8\u91cf\u5bf9\u5f25\u6563\u533a\u57df\u5185\u7684\u5c16\u9510\u88c2\u7eb9\u8fdb\u884c\u89c4\u5219\u5316\u5904\u7406\uff0c\u907f\u514d\u4e86\u663e\u5f0f\u8ffd\u8e2a\u590d\u6742\u88c2\u7eb9\u62d3\u6251\u7ed3\u6784\u7684\u9700\u8981\u3002\u8fd9\u4e0e\u5c16\u9510\u754c\u9762\u6a21\u578b\u5f62\u6210\u5bf9\u6bd4\uff0c\u540e\u8005\u5c06\u88c2\u7eb9\u89c6\u4e3a\u4e8c\u7ef4\u66f2\u9762\uff0c\u9700\u8981\u590d\u6742\u7684\u7f51\u683c\u91cd\u5212\u5206\u6216\u589e\u5f3a\u6280\u672f\u6765\u5904\u7406\u88c2\u7eb9\u6269\u5c55\u3002.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                \u4f7f\u7528\u76f8\u573a\u6a21\u578b\u6a21\u62df\u590d\u5408\u6750\u6599\u5c42\u5408\u677f\u5931\u6548\u65f6\uff0c\u4e3b\u8981\u8003\u8651\u54ea\u4e09\u4e2a\u957f\u5ea6\u5c3a\u5ea6\uff1f            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\n\u590d\u5408\u6750\u6599\u5c42\u5408\u677f\u5931\u6548\u5efa\u6a21\u7684\u4e09\u5927\u4e3b\u8981\u957f\u5ea6\u5c3a\u5ea6\u662f\u5fae\u89c2\u5c3a\u5ea6\u3001\u4ecb\u89c2\u5c3a\u5ea6\u548c\u5b8f\u89c2\u5c3a\u5ea6\u3002\u5fae\u89c2\u5c3a\u5ea6\u8003\u8651\u5fae\u89c2\u7ed3\u6784\uff08\u7ea4\u7ef4\u3001\u57fa\u4f53\uff09\uff1b\u4ecb\u89c2\u5c3a\u5ea6\u5c06\u6bcf\u4e00\u5c42\u677f\u5efa\u6a21\u4e3a\u5747\u8d28\u5316\u7684\u5404\u5411\u5f02\u6027\u6750\u6599\uff1b\u5b8f\u89c2\u5c3a\u5ea6\u5219\u5c06\u6574\u4e2a\u5c42\u5408\u677f\u89c6\u4e3a\u5355\u4e00\u7684\u5747\u8d28\u5316\u677f\u3002.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                What is a (degradation function) in the context of PFM, and what are its key properties?            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\n\u9000\u5316\u51fd\u6570\uff0c\u901a\u5e38\u8868\u793a\u4e3a\u03c9(d)\u6216g(\u03c6)\uff0c\u7528\u4e8e\u6a21\u62df\u6750\u6599\u521a\u5ea6\u968f\u635f\u4f24\u4ece\u5b8c\u6574\u72b6\u6001\u6f14\u5316\u81f3\u5b8c\u5168\u65ad\u88c2\u72b6\u6001\u800c\u53d1\u751f\u7684\u635f\u5931\u3002\u5bf9\u4e8e\u5b8c\u6574\u72b6\u6001\uff08\u03c6=0\uff09\uff0c\u5176\u503c\u5fc5\u987b\u4e3a1\uff1b\u5bf9\u4e8e\u65ad\u88c2\u72b6\u6001\uff08\u03c6=1\uff09\uff0c\u5176\u503c\u5fc5\u987b\u4e3a0\u3002\u6b64\u5916\uff0c\u8be5\u51fd\u6570\u5fc5\u987b\u5355\u8c03\u9012\u51cf\uff0c\u4e14\u5728\u5b8c\u5168\u65ad\u88c2\u72b6\u6001\u4e0b\u5176\u5bfc\u6570\u4e3a\u96f6\u3002.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                \u5982\u4f55\u5c06\u5185\u805a\u533a\u6a21\u578b\uff08CZM\uff09\u7eb3\u5165\u76f8\u573a\u6a21\u578b\uff0c\u8fd9\u5e26\u6765\u4e86\u54ea\u4e9b\u4e3b\u8981\u6311\u6218\uff1f            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\nCZMs can be incorporated by using zero-thickness interface elements along potential crack paths or by modifying the PFM&#8217;s degradation function. A key challenge is that the crack surface separation, which is central to a CZM for relating cohesive traction, cannot be calculated directly in a PFM, where the crack is smeared over a region.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                Explain the (staggered solution scheme) used for solving coupled displacement and phase-field problems in finite element software like Abaqus.            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\n\u4ea4\u9519\u5f0f\u7b97\u6cd5\uff0c\u4e5f\u79f0\u4e3a\u4ea4\u66ff\u6700\u5c0f\u5316\uff08AM\uff09\u7b97\u6cd5\uff0c\u53ef\u4ee5\u540c\u65f6\u72ec\u7acb\u4e14\u4f9d\u6b21\u5730\u6c42\u89e3\u8026\u5408\u7684\u4f4d\u79fb\u573a\u548c\u76f8\u573a\u95ee\u9898\u3002\u6bcf\u4e2a\u573a\u7684\u89e3\u90fd\u57fa\u4e8e\u524d\u4e00\u6b21\u8fed\u4ee3\u5f97\u5230\u7684\u53d8\u91cf\uff0c\u8be5\u8fc7\u7a0b\u91cd\u590d\u8fdb\u884c\u76f4\u81f3\u6536\u655b\u3002.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                What is the (heat transfer analogy) and how is it used to implement phase-field fracture models in commercial software packages?            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\n\u70ed\u4f20\u9012\u7c7b\u6bd4\u6cd5\u5229\u7528\u4e86\u7a33\u6001\u70ed\u4f20\u9012\u65b9\u7a0b\u548c\u76f8\u573a\u6f14\u5316\u65b9\u7a0b\u4e4b\u95f4\u7684\u6570\u5b66\u76f8\u4f3c\u6027\u3002\u901a\u8fc7\u5c06\u76f8\u573a\u53d8\u91cf\u5b9a\u4e49\u4e3a\u7c7b\u4f3c\u4e8e\u6e29\u5ea6\uff08T \u2261 \u03c6\uff09\uff0c\u5e76\u5c06\u65ad\u88c2\u9a71\u52a8\u529b\u5b9a\u4e49\u4e3a\u5185\u90e8\u70ed\u6e90\uff0c\u5373\u53ef\u5229\u7528\u5185\u7f6e\u7684\u70ed\u4f20\u9012\u529f\u80fd\uff08\u4f8b\u5982 UMATHT \u5b50\u7a0b\u5e8f\uff09\u5b9e\u73b0 PFM\uff0c\u800c\u65e0\u9700\u81ea\u5b9a\u4e49\u7528\u6237\u5143\u7d20\u3002.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                In the context of piezoresistive composites, how does the presence of cracks, as modeled by the phase-field variable, affect the material&#039;s electrical properties?            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\nThe presence of cracks significantly increases local electrical resistivity, interrupting the flow of electrical current. This is modeled by degrading the material&#8217;s electrical conductivity or permeability using a degradation function, h2(\u03c6), which is dependent on the magnitude of the phase-field variable \u03c6.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                \u63cf\u8ff0\u5386\u53f2\u573a\u53d8\u91cf H \u5728\u76f8\u573a\u88c2\u7f1d\u5efa\u6a21\u4e2d\u7684\u4f5c\u7528\u3002.            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\nThe history field variable H ensures the irreversibility of damage by storing the maximum value of the fracture driving force (e.g., strain energy density) that a material point has experienced over time. This prevents the model from exhibiting non-physical &#8220;self-healing&#8221; behavior if the material is unloaded.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                \u76f8\u573a\u6a21\u578b\u5982\u4f55\u63cf\u8ff0\u91d1\u5c5e\u4e2d\u7684\u6c22\u8106\u73b0\u8c61\uff1f            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\nPhase-field models capture hydrogen embrittlement by defining the material&#8217;s fracture resistance, or toughness (Gc), as a function of the local hydrogen concentration (cH). The model couples the mechanical deformation problem with a hydrogen diffusion problem, where hydrogen accumulation in regions of high hydrostatic stress leads to a local reduction in toughness, promoting crack growth.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<div class=\"mahour-accordion-item\">\r\n\r\n        <button class=\"mahour-accordion-header\" type=\"button\">\r\n\r\n            <span class=\"mahour-accordion-title\">\r\n                \u4f7f\u7528\u76f8\u573a\u6a21\u578b\u8fdb\u884c\u65ad\u88c2\u6a21\u62df\u7684\u4e3b\u8981\u4f18\u70b9\u548c\u7f3a\u70b9\u662f\u4ec0\u4e48\uff1f            <\/span>\r\n\r\n            <span class=\"mahour-accordion-icon\">\r\n              <svg fill=\"#eb5d21\" height=\"16px\" width=\"16px\" version=\"1.1\" id=\"Layer_1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewbox=\"0 0 330.002 330.002\" xml:space=\"preserve\"><g id=\"SVGRepo_bgCarrier\" stroke-width=\"0\"><\/g><g id=\"SVGRepo_tracerCarrier\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><\/g><g id=\"SVGRepo_iconCarrier\"> <path id=\"XMLID_23_\" d=\"M329.155,100.036c-2.108-6.011-7.784-10.035-14.154-10.035h-300c-6.371,0-12.046,4.024-14.154,10.035 c-2.109,6.011-0.19,12.699,4.784,16.678l150.004,120c2.739,2.191,6.055,3.287,9.37,3.287c3.316,0,6.631-1.096,9.371-3.287 l149.996-120C329.346,112.734,331.264,106.047,329.155,100.036z\"><\/path> <\/g><\/svg>\r\n            <\/span>\r\n\r\n        <\/button>\r\n\r\n        <div class=\"mahour-accordion-body\">\r\n\r\n            <div class=\"mahour-accordion-content\">\r\n                <br \/>\n\u5176\u4e3b\u8981\u4f18\u52bf\u5728\u4e8e\u80fd\u591f\u4ee5\u7b80\u4fbf\u7684\u65b9\u5f0f\u81ea\u52a8\u5904\u7406\u4e8c\u7ef4\u548c\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u590d\u6742\u7684\u88c2\u7eb9\u73b0\u8c61\uff0c\u4f8b\u5982\u88c2\u7eb9\u7684\u840c\u751f\u3001\u5206\u652f\u548c\u5408\u5e76\u3002\u4e3b\u8981\u7f3a\u70b9\u5305\u62ec\u8ba1\u7b97\u6210\u672c\u9ad8\u6602\uff08\u56e0\u4e3a\u9700\u8981\u975e\u5e38\u7cbe\u7ec6\u7684\u7f51\u683c\u6765\u89e3\u6790\u635f\u4f24\u533a\u57df\uff09\uff0c\u4ee5\u53ca\u96be\u4ee5\u7cbe\u786e\u5b9a\u4f4d\u88c2\u7eb9\u5c16\u7aef\u4ee5\u8ba1\u7b97\u901f\u5ea6\u7b49\u7269\u7406\u91cf\u3002.<\/p>\n<p>            <\/div>\r\n\r\n        <\/div>\r\n\r\n    <\/div>\n<p><\/div><script type=\"application\/ld+json\">{\n    \"@context\": \"https:\\\/\\\/schema.org\",\n    \"@type\": \"FAQPage\",\n    \"mainEntity\": [\n        {\n            \"@type\": \"Question\",\n            \"name\": \"What is the fundamental concept behind phase-field models (PFM) for fracture, and how do they differ from sharp interface models?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"Phase-field models regularize sharp cracks over a diffuse region using a continuous scalar variable, avoiding the need to explicitly track complex crack topologies. This contrasts with sharp interface models, which treat cracks as two-dimensional surfaces and require complex remeshing or enrichment techniques to handle crack propagation.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"What are the three main length scales for modeling failure in composite laminates using phase-field models?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"The three main length scales for modeling failure in composite laminates are microscopic, mesoscopic, and macroscopic. The microscopic scale considers the microstructure (fibers, matrix); the mesoscopic scale models each lamina as a homogenized anisotropic material; and the macroscopic scale treats the entire laminate as a single homogenized plate.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"What is a (degradation function) in the context of PFM, and what are its key properties?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"A degradation function, often denoted \\u03c9(d) or g(\\u03c6), models the loss of material stiffness as damage evolves from an intact state to a fully broken state. Its value must be 1 for the intact state (\\u03c6=0) and 0 for the broken state (\\u03c6=1), and it must be a monotonically decreasing function, with its derivative being zero at the fully broken state.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"How can Cohesive Zone Models (CZMs) be incorporated into phase-field models, and what is a primary challenge this presents?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"CZMs can be incorporated by using zero-thickness interface elements along potential crack paths or by modifying the PFM&#8217;s degradation function. A key challenge is that the crack surface separation, which is central to a CZM for relating cohesive traction, cannot be calculated directly in a PFM, where the crack is smeared over a region.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Explain the (staggered solution scheme) used for solving coupled displacement and phase-field problems in finite element software like Abaqus.\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"A staggered scheme, also known as an alternating minimization (AM) algorithm, solves the coupled displacement and phase-field problems independently and sequentially at the same time. The solution for each field is based on the variables obtained from the previous iteration, a process that is repeated until convergence is achieved.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"What is the (heat transfer analogy) and how is it used to implement phase-field fracture models in commercial software packages?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"The heat transfer analogy exploits the mathematical similarity between the steady-state heat transfer equation and the phase-field evolution equation. By defining the phase-field variable as analogous to temperature (T \\u2261 \\u03c6) and the fracture driving force as an internal heat source, PFM can be implemented using built-in heat transfer capabilities (like UMATHT subroutines) without needing custom user elements.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"In the context of piezoresistive composites, how does the presence of cracks, as modeled by the phase-field variable, affect the material's electrical properties?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"The presence of cracks significantly increases local electrical resistivity, interrupting the flow of electrical current. This is modeled by degrading the material&#8217;s electrical conductivity or permeability using a degradation function, h2(\\u03c6), which is dependent on the magnitude of the phase-field variable \\u03c6.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Describe the role of the history field variable H in phase-field fracture modeling.\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"The history field variable H ensures the irreversibility of damage by storing the maximum value of the fracture driving force (e.g., strain energy density) that a material point has experienced over time. This prevents the model from exhibiting non-physical &#8220;self-healing&#8221; behavior if the material is unloaded.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"How do phase-field models capture the phenomenon of hydrogen embrittlement in metals?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"Phase-field models capture hydrogen embrittlement by defining the material&#8217;s fracture resistance, or toughness (Gc), as a function of the local hydrogen concentration (cH). The model couples the mechanical deformation problem with a hydrogen diffusion problem, where hydrogen accumulation in regions of high hydrostatic stress leads to a local reduction in toughness, promoting crack growth.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"What are the main advantages and disadvantages of using phase-field models for fracture simulation?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"The main advantages are the ability to automatically handle complex crack phenomena like nucleation, branching, and coalescence in both 2D and 3D with a straightforward implementation. The primary disadvantages include high computational cost, due to the need for very fine meshes to resolve the damage zone, and ambiguities in precisely locating the crack tip for calculating quantities like velocity.\"\n            }\n        }\n    ]\n}<\/script>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-43649\" src=\"https:\/\/caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-scaled.png\" alt=\"\u76f8\u573a\u6a21\u578b\" width=\"1021\" height=\"903\" srcset=\"https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-scaled.png 1600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-300x265.png 300w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-1024x905.png 1024w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-430x380.png 430w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-768x679.png 768w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-1536x1358.png 1536w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-2048x1810.png 2048w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-14x12.png 14w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-62x55.png 62w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-600x530.png 600w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-725x641.png 725w, https:\/\/dev.caeassistant.com\/wp-content\/uploads\/2025\/11\/NotebookLM-Mind-Map-150x133.png 150w\" sizes=\"(max-width: 1021px) 100vw, 1021px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #ff6600;\">\u76f8\u573a\u6a21\u578b\u5728\u6750\u6599\u79d1\u5b66\u4e2d\u626e\u6f14\u7740\u600e\u6837\u7684\u89d2\u8272\uff1f<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u76f8\u573a\u6a21\u578b\uff08PFM\uff09\u89e3\u51b3\u4e86\u4f20\u7edf\u65ad\u88c2\u529b\u5b66\u7684\u5173\u952e\u5c40\u9650\u6027\u3002\u5f53\u88c2\u7eb9\u8def\u5f84\u4e8b\u5148\u672a\u77e5\u65f6\uff0c\u8bf8\u5982\u6709\u9650\u5143\u6cd5\uff08FEM\uff09\u4e4b\u7c7b\u7684\u7ecf\u5178\u65b9\u6cd5\u96be\u4ee5\u594f\u6548\uff1b\u800c\u5f53\u591a\u4e2a\u88c2\u7eb9\u76f8\u4e92\u4f5c\u7528\u3001\u5206\u652f\u6216\u5408\u5e76\u65f6\uff0c\u8bf8\u5982\u6269\u5c55\u6709\u9650\u5143\u6cd5\uff08XFEM\uff09\u4e4b\u7c7b\u7684\u65b9\u6cd5\u4e5f\u9762\u4e34\u6311\u6218\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">PFM\u901a\u8fc7\u5c06\u88c2\u7eb9\u89c6\u4e3a\u53d7\u70ed\u529b\u5b66\u539f\u7406\u63a7\u5236\u7684\u6f14\u5316\u6269\u6563\u754c\u9762\u6765\u514b\u670d\u8fd9\u4e9b\u969c\u788d\uff0c\u65e0\u9700\u590d\u6742\u7684\u51e0\u4f55\u8ffd\u8e2a\uff0c\u5373\u53ef\u81ea\u7136\u5730\u6355\u6349\u4efb\u610f\u88c2\u7eb9\u62d3\u6251\u7ed3\u6784\u3002\u5176\u6838\u5fc3\u601d\u60f3\u7b80\u6d01\u800c\u5de7\u5999\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8be5\u65b9\u6cd5\u5e76\u975e\u663e\u5f0f\u5730\u8ffd\u8e2a\u6e05\u6670\u7684\u8fb9\u754c\uff0c\u800c\u662f\u5c06\u754c\u9762\u5b9a\u4e49\u4e3a\u5f25\u6563\u533a\u57df\u3002\u4f8b\u5982\uff0c\u8003\u8651\u4e00\u4e2a\u88c2\u7eb9\u8868\u9762\uff0c\u5b83\u5c06\u5b8c\u6574\u6750\u6599\u4e0e\u65ad\u88c2\u6750\u6599\u5206\u9694\u5f00\u6765\u3002\u76f8\u573a\u6a21\u578b\u4f1a\u5c06\u8be5\u754c\u9762\u6269\u6563\u5230\u4e00\u4e2a\u6709\u9650\u4f53\u79ef\u5185\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u8f85\u52a9\u573a\u53d8\u91cf\u03c6\u6765\u5b9e\u73b0\u8fd9\u79cd\u6269\u6563\u3002\u79d1\u5b66\u5bb6\u901a\u5e38\u79f0\u4e4b\u4e3a\u76f8\u573a\u6216\u5e8f\u53c2\u91cf\u3002\u8be5\u53d8\u91cf\u53ef\u4ee5\u5728\u4e0d\u540c\u7684\u6750\u6599\u72b6\u6001\u4e4b\u95f4\u5e73\u6ed1\u8fc7\u6e21\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5728 <strong>\u76f8\u573a\u6cd5<\/strong>, \uff0c\u4e00\u4e2a <strong>\u5f25\u6563\u533a<\/strong> \uff08\u4e5f\u79f0\u4e3a <em>\u6269\u6563\u754c\u9762<\/em>\uff09\u662f <strong>\u4e24\u79cd\u4e0d\u540c\u76f8\u4e4b\u95f4\u7684\u8fc7\u6e21\u533a<\/strong> \u2014 \u4f8b\u5982\uff0c\u56fa\u4f53\u548c\u6db2\u4f53\u4e4b\u95f4\uff0c\u6216\u8005\u4e24\u4e2a\u6676\u4f53\u9897\u7c92\u4e4b\u95f4\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4f60\u53ef\u4ee5\u628a\u6f2b\u5c04\u533a\u60f3\u8c61\u6210\u4e00\u4e2a <strong>\u201c\u6a21\u7cca\u7684\u8fb9\u754c\u201d<\/strong> \u5b83\u4ee5\u7b26\u5408\u7269\u7406\u5b9e\u9645\u4e14\u8ba1\u7b97\u7a33\u5b9a\u7684\u65b9\u5f0f\u8fde\u63a5\u4e24\u4e2a\u4e0d\u540c\u7684\u76f8\u3002\u5b83\u5728\u7edf\u4e00\u7684\u6846\u67b6\u5185\u6355\u6349\u754c\u9762\u8fd0\u52a8\u3001\u66f2\u7387\u6548\u5e94\u548c\u754c\u9762\u80fd\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #ff6600;\">\u76f8\u573a\u65b9\u6cd5\u80cc\u540e\u7684\u7406\u8bba\u80cc\u666f\u662f\u4ec0\u4e48\uff1f<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u76f8\u573a\u5bf9\u4e8e\u4e0d\u540c\u7684\u76f8\u5177\u6709\u4e0d\u540c\u7684\u503c\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u03c6 = 0 \u8868\u793a\u5b8c\u6574\u7684\u5757\u72b6\u6750\u6599\u3002\u76f8\u53cd\uff0c\u03c6 = 1 \u8868\u793a\u5b8c\u5168\u7834\u788e\u7684\u6750\u6599\u6216\u88c2\u7eb9\u3002\u5728\u8fd9\u4e24\u4e2a\u503c\u4e4b\u95f4\uff0c\u76f8\u573a\u5728\u754c\u9762\u9644\u8fd1\u5448\u73b0\u5e73\u6ed1\u8fde\u7eed\u7684\u53d8\u5316\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u03c6 \u7684\u6f14\u5316\u9075\u5faa\u504f\u5fae\u5206\u65b9\u7a0b (PDE)\u3002\u8be5\u65b9\u7a0b\u6e90\u4e8e\u4e0d\u53ef\u9006\u70ed\u529b\u5b66\u539f\u7406\u3002\u5728\u65ad\u88c2\u529b\u5b66\u4e2d\uff0c\u538b\u7535\u529b\u529b\u5b66 (PFM) \u6210\u529f\u5730\u878d\u5165\u4e86\u683c\u91cc\u83f2\u65af\u7684\u70ed\u529b\u5b66\u6846\u67b6\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8be5\u65b9\u6cd5\u5229\u7528\u5185\u90e8\u957f\u5ea6\u5c3a\u5ea6 l\u2080 \u6765\u89c4\u8303\u5c16\u9510\u88c2\u7eb9\u3002\u8be5\u53c2\u6570\u63a7\u5236\u7740\u6269\u6563\u88c2\u7eb9\u533a\u57df\u7684\u5bbd\u5ea6\uff0c\u4ece\u800c\u786e\u4fdd\u7f51\u683c\u7684\u5ba2\u89c2\u6027\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u635f\u4f24\u89e3\u91ca\u4e3a\u4e00\u4e2a\u6807\u91cf\u53d8\u91cf\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8fd9\u79cd\u8303\u5f0f\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f3a\u5927\u7684\u6570\u503c\u5e73\u53f0\uff0c\u80fd\u591f\u6709\u6548\u5730\u9884\u6d4b\u9ad8\u5ea6\u590d\u6742\u7684\u88c2\u7eb9\u6269\u5c55\u884c\u4e3a\uff0c\u5305\u62ec\u88c2\u7eb9\u5206\u652f\u3001\u504f\u8f6c\u3001\u5408\u5e76\u548c\u6210\u6838\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u5b83\u9002\u7528\u4e8e\u4efb\u610f\u51e0\u4f55\u5f62\u72b6\u548c\u5c3a\u5bf8\u3002\u6700\u91cd\u8981\u7684\u662f\uff0c\u5b83\u65e0\u9700\u4efb\u4f55\u7279\u5b9a\u7684\u88c2\u7eb9\u6269\u5c55\u51c6\u5219\u6216\u624b\u52a8\u7f51\u683c\u8c03\u6574\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #ff6600;\">\u76f8\u573a\u6cd5\u7684\u4e3b\u8981\u5e94\u7528\u6709\u54ea\u4e9b\uff1f<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u76f8\u573a\u5efa\u6a21\u7684\u901a\u7528\u6027\u4f7f\u5176\u80fd\u591f\u5e94\u7528\u4e8e\u591a\u79cd\u6750\u6599\uff0c\u5e76\u80fd\u89e3\u51b3\u590d\u6742\u7684\u7269\u7406\u95ee\u9898\u3002\u8fd9\u4e9b\u95ee\u9898\u901a\u5e38\u6d89\u53ca\u8026\u5408\u7684\u591a\u573a\u73b0\u8c61\u3002.<\/span><\/p>\n<h3>\u57fa\u672c\u9aa8\u6298\u7c7b\u578b<\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6839\u636e\u76f8\u573a\u6a21\u578b\u6240\u8981\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u53ef\u4ee5\u91c7\u7528\u4e0d\u540c\u7684\u88c2\u7f1d\u6a21\u578b\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u53ef\u4ee5\u4f7f\u7528\u7684\u88c2\u7f1d\u7c7b\u578b\u3002.<\/span><\/p>\n<h4>\u8106\u6027\u65ad\u88c2<\/h4>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u7814\u7a76\u4eba\u5458\u5e7f\u6cdb\u4f7f\u7528\u538b\u7535\u529b\u663e\u5fae\u955c\uff08PFM\uff09\u6765\u7814\u7a76\u51c6\u9759\u6001\u548c\u52a8\u6001\u8106\u6027\u65ad\u88c2\u95ee\u9898\uff0c\u8fd9\u9002\u7528\u4e8e\u4e8c\u7ef4\u548c\u4e09\u7ef4\u573a\u666f\u3002\u8be5\u65b9\u6cd5\u5c24\u5176\u64c5\u957f\u6355\u6349\u9676\u74f7\u6750\u6599\u548c\u73bb\u7483\u4e2d\u88c2\u7eb9\u7684\u7a81\u7136\u6269\u5c55\u3002.<\/span><\/p>\n<h4>\u97e7\u6027\u9aa8\u6298<\/h4>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u79d1\u5b66\u5bb6\u5df2\u6210\u529f\u5c06\u76f8\u573a\u6a21\u578b\u5e94\u7528\u4e8e\u5ef6\u6027\u635f\u4f24\u573a\u666f\uff0c\u5305\u62ec\u5f39\u5851\u6027\u56fa\u4f53\u3002\u8fd9\u4e9b\u5e94\u7528\u901a\u5e38\u6d89\u53ca\u5851\u6027\u9000\u5316\u51fd\u6570\uff0c\u5e76\u8003\u8651\u4e86\u5851\u6027\u6548\u5e94\u5bf9\u52a8\u6001\u88c2\u7eb9\u6269\u5c55\u7684\u5f71\u54cd\u3002.<\/span><\/p>\n<h4>\u75b2\u52b3\u6027\u9aa8\u6298<\/h4>\n<p><span style=\"font-size: 14pt;\">\u73b0\u4ee3\u538b\u88c2\u75b2\u52b3\uff08PFM\uff09\u65b9\u6cd5\u5df2\u5c06\u75b2\u52b3\u9000\u5316\u51fd\u6570\u7eb3\u5165\u8003\u91cf\u3002\u56e0\u6b64\uff0c\u5b83\u4eec\u80fd\u591f\u9884\u6d4b\u91d1\u5c5e\u5728\u5faa\u73af\u8f7d\u8377\u4f5c\u7528\u4e0b\u7684\u88c2\u7eb9\u6269\u5c55\uff0c\u6709\u6548\u6db5\u76d6\u9ad8\u5468\u75b2\u52b3\u3001\u4f4e\u5468\u75b2\u52b3\u548c\u6781\u4f4e\u5468\u75b2\u52b3\u533a\u57df\u3002.<\/span><\/p>\n<h3>\u8026\u5408\u591a\u7269\u7406\u573a\u95ee\u9898<\/h3>\n<p><span style=\"font-size: 14pt;\">PFM\u7684\u53d8\u5206\u7279\u6027\u4f7f\u5176\u6210\u4e3a\u8026\u5408\u7684\u7406\u60f3\u9009\u62e9\u3002\u5177\u4f53\u800c\u8a00\uff0c\u5b83\u53ef\u4ee5\u5c06\u88c2\u7eb9\u6f14\u5316\u4e0e\u5176\u4ed6\u7269\u7406\u573a\u65e0\u7f1d\u8fde\u63a5\u8d77\u6765\u3002.<\/span><\/p>\n<h4>\u6c22\u8f85\u52a9\u88c2\u89e3<\/h4>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u672c\u5e94\u7528\u7814\u7a76\u6c22\u5411\u65ad\u88c2\u8fc7\u7a0b\u533a\u7684\u4f20\u8f93\u3002\u968f\u540e\uff0c\u5b83\u901a\u8fc7\u8026\u5408\u6846\u67b6\u6a21\u62df\u88c2\u7eb9\u6269\u5c55\u3002\u8be5\u6846\u67b6\u6574\u5408\u4e86\u529b\u5b66\u3001\u6269\u6563\u548c\u76f8\u573a\u4e09\u4e2a\u7ec4\u6210\u90e8\u5206\u3002.<\/span><\/p>\n<h4>\u5e94\u529b\u8150\u8680\u5f00\u88c2<\/h4>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5de5\u7a0b\u5e08\u5229\u7528PFM\u65b9\u6cd5\u6a21\u62df\u6eb6\u89e3\u9a71\u52a8\u7684\u5e94\u529b\u8150\u8680\u5f00\u88c2\u3002\u8be5\u65b9\u6cd5\u4e5f\u80fd\u6709\u6548\u5904\u7406\u70b9\u8680\u3002\u6b64\u5916\uff0c\u5b83\u8fd8\u5305\u542b\u4e86\u819c\u7834\u88c2-\u6eb6\u89e3-\u518d\u949d\u5316\uff08FRDR\uff09\u8fc7\u7a0b\u3002.<\/span><\/p>\n<h4>\u70ed\u673a\u68b0\u65ad\u88c2<\/h4>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u7814\u7a76\u4eba\u5458\u5206\u6790\u70ed\u65ad\u88c2\u573a\u666f\uff0c\u4f8b\u5982\u9676\u74f7\u6750\u6599\u7684\u6dec\u706b\u8fc7\u7a0b\u3002\u4ed6\u4eec\u901a\u8fc7\u5c06\u6e29\u5ea6\u573a\u4e0e\u673a\u68b0\u53d8\u5f62\u548c\u635f\u4f24\u6f14\u5316\u76f8\u7ed3\u5408\u6765\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\u3002.<\/span><\/p>\n<h4>\u6c34\u529b\u538b\u88c2<\/h4>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u76f8\u573a\u6a21\u578b\u6a21\u62df\u591a\u5b54\u4ecb\u8d28\u4e2d\u6d41\u4f53\u9a71\u52a8\u88c2\u7f1d\u7684\u6f14\u5316\u3002\u5b83\u5c06\u76f8\u573a\u6f14\u5316\u4e0e\u6d41\u4f53\u6d41\u52a8\u548c\u538b\u529b\u573a\u8026\u5408\u8d77\u6765\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u77f3\u6cb9\u548c\u5730\u70ed\u5de5\u7a0b\u9886\u57df\u5177\u6709\u91cd\u8981\u4ef7\u503c\u3002.<\/span><\/p>\n<h4>\u7535\u673a\u68b0\u65ad\u88c2<\/h4>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u79d1\u5b66\u5bb6\u5229\u7528\u8fd9\u79cd\u6280\u672f\u5bf9\u538b\u963b\u5f0f\u78b3\u7eb3\u7c73\u7ba1\u590d\u5408\u6750\u6599\u8fdb\u884c\u5efa\u6a21\u3002\u8be5\u65b9\u6cd5\u5c06\u5f62\u53d8\u3001\u7535\u52bf\u548c\u76f8\u573a\u65ad\u88c2\u53d8\u91cf\u8026\u5408\u8d77\u6765\uff0c\u4ece\u800c\u80fd\u591f\u7cbe\u786e\u9884\u6d4b\u7535\u8026\u5408\u5931\u6548\u6a21\u5f0f\u3002.<\/span><\/p>\n<h4>\u9502\u79bb\u5b50\u7535\u6c60\u8870\u51cf<\/h4>\n<p><span style=\"font-size: 14pt;\">\u5de5\u7a0b\u5e08\u4eec\u5bf9\u7535\u6c60\u7535\u6781\u9897\u7c92\u4e2d\u5316\u5b66\u673a\u68b0\u4f5c\u7528\u5f15\u8d77\u7684\u65ad\u88c2\u8fdb\u884c\u5efa\u6a21\u3002\u8fd9\u9879\u5e94\u7528\u6709\u52a9\u4e8e\u9884\u6d4b\u7535\u6c60\u5bff\u547d\u548c\u6027\u80fd\u8870\u51cf\u3002.<\/span><\/p>\n<h3>\u5177\u4f53\u6750\u6599\u548c\u7ed3\u6784<\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u76f8\u573a\u6cd5\u80fd\u591f\u6210\u529f\u5904\u7406\u5404\u79cd\u7279\u6b8a\u6750\u6599\uff1a<\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff08\u5c42\u5185\u65ad\u88c2\u548c\u5c42\u95f4\u65ad\u88c2\uff09<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u529f\u80fd\u68af\u5ea6\u6750\u6599\uff08FGMs\uff09<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u7c7b\u5ca9\u77f3\u6750\u6599\uff08\u5305\u62ec\u538b\u526a\u88c2\u7f1d\uff09<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5f62\u72b6\u8bb0\u5fc6\u5408\u91d1\uff08SMA\uff09<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #ff6600;\">\u6709\u54ea\u4e9b\u53ef\u7528\u7684\u76f8\u573a\u6a21\u578b\uff08\u672c\u6784\u9009\u62e9\uff09\uff1f<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u76f8\u573a\u5efa\u6a21\u4e2d\u7684\u7b2c\u4e00\u4e2a\u51b3\u7b56\u662f <strong>\u9009\u62e9\u5408\u9002\u7684\u6784\u6210\u6a21\u578b<\/strong> \u57fa\u4e8e\u60a8\u60f3\u8981\u6355\u6349\u7684\u6750\u6599\u884c\u4e3a\u548c\u5931\u6548\u673a\u5236\u3002\u201c\u672c\u6784\u201d\u4e00\u8bcd\u6307\u7684\u662f\u6750\u6599\u7684\u672c\u6784\u5b9a\u5f8b\u6216\u672c\u6784\u5173\u7cfb\u2014\u2014\u672c\u8d28\u4e0a\uff0c\u5b83\u662f\u5bf9\u6750\u6599\u5728\u8f7d\u8377\u4f5c\u7528\u4e0b\u884c\u4e3a\u7684\u6570\u5b66\u63cf\u8ff0\u3002\u5728\u76f8\u573a\u65ad\u88c2\u5efa\u6a21\u4e2d\uff0c\u672c\u6784\u6a21\u578b\u5b9a\u4e49\u4e86\uff1a<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\">\u635f\u4f24\u5982\u4f55\u4ece\u5b8c\u597d\u65e0\u635f\uff08\u03c6 = 0\uff09\u6f14\u53d8\u4e3a\u5b8c\u5168\u7834\u635f\uff08\u03c6 = 1\uff09<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u6750\u6599\u521a\u5ea6\u5982\u4f55\u968f\u635f\u4f24\u589e\u52a0\u800c\u964d\u4f4e\uff08\u901a\u8fc7\u9000\u5316\u51fd\u6570\uff09<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u88c2\u7eb9\u6269\u5c55\u7684\u9a71\u52a8\u56e0\u7d20\uff08\u5e94\u53d8\u80fd\u3001\u6bd4\u80fd\u5206\u91cf\uff09<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u88c2\u7f1d\u4f55\u65f6\u4f55\u5730\u5f00\u59cb\u4ea7\u751f\u548c\u6269\u5c55<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6211\u4eec\u5728\u4e0b\u8868\u4e2d\u63d0\u4f9b\u4e86\u76f8\u573a\u672c\u6784\u6a21\u578b\u7684\u66f4\u591a\u8be6\u7ec6\u4fe1\u606f\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"border-collapse: collapse; width: 100%; text-align: right;\" border=\"1\" cellspacing=\"0\" cellpadding=\"8\">\n<thead>\n<tr>\n<th>\u6a21\u578b<\/th>\n<th>\u63cf\u8ff0<\/th>\n<th>Suitability\/Purpose<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">AT2 Model (Standard PFM)<\/td>\n<td style=\"text-align: right;\">The standard formulation, typically based on a crack density function \\( \\omega(\\phi) \\).<\/td>\n<td style=\"text-align: right;\">Brittle fracture; damage initiates immediately upon loading.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">AT1 Model<\/td>\n<td style=\"text-align: right;\">Uses \\( \\omega(\\phi) = \\phi \\).<\/td>\n<td style=\"text-align: right;\">Suitable for materials that exhibit a linear elastic regime before the onset of damage (i.e., it includes a minimum fracture driving force \\( H_{min} \\)).<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">PF-CZM (Phase-Field Cohesive Zone Model)<\/td>\n<td style=\"text-align: right;\">Provides an explicit link to material strength.<\/td>\n<td style=\"text-align: right;\">Quasi-brittle failure and matching analytical\/experimental softening curves.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">Strain Energy Splits<\/td>\n<td style=\"text-align: right;\">Necessary extensions to prevent damage under compression (e.g., rock-like or concrete materials).<\/td>\n<td style=\"text-align: right;\">Includes the spectral split (Miehe et al.), volumetric-deviatoric split (Amor et al.), and the Drucker-Prager based split (suited for rock materials).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span style=\"color: #ff6600;\"><strong>\u5982\u4f55\u6c42\u89e3\u76f8\u573a\u6a21\u578b\u7684\u8026\u5408\u65b9\u7a0b\u7ec4\uff1f\uff08\u6c42\u89e3\u65b9\u6848\uff09<\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4e00\u65e6\u9009\u5b9a\u4e86\u6784\u6210\u6a21\u578b\uff0c\u4e0b\u4e00\u6b65\u5c31\u662f\u51b3\u5b9a <strong>\u5982\u4f55\u6c42\u89e3\u8026\u5408\u65b9\u7a0b\u7ec4<\/strong> \u6570\u503c\u65b9\u6cd5\u4e0a\uff0c\u76f8\u573a\u65ad\u88c2\u95ee\u9898\u6d89\u53ca\u4e24\u4e2a\u8026\u5408\u7684\u504f\u5fae\u5206\u65b9\u7a0b\uff08PDE\uff09\uff1a<\/span><\/p>\n<ol style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\"><strong>\u673a\u68b0\u5e73\u8861\u65b9\u7a0b<\/strong> \uff08\u5bf9\u4e8e\u4f4d\u79fb\u573a\uff0c, <strong>\u4f60<\/strong>)<\/span><\/li>\n<li><span style=\"font-size: 14pt;\"><strong>\u76f8\u573a\u6f14\u5316\u65b9\u7a0b<\/strong> \uff08\u5bf9\u4e8e\u635f\u4f24\u573a\uff0c, <strong>\u03c6<\/strong>)<\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8fd9\u4e9b\u65b9\u7a0b\u5f0f\u662f <strong>\u76f8\u4e92\u4f9d\u5b58<\/strong>:<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 14pt;\">\u4f4d\u79fb\u573a\u5f71\u54cd\u5e94\u53d8\u80fd\uff0c\u8fdb\u800c\u9a71\u52a8\u635f\u4f24\u6f14\u5316\u3002<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">\u635f\u4f24\u573a\u4f1a\u964d\u4f4e\u6750\u6599\u521a\u5ea6\uff0c\u4ece\u800c\u5f71\u54cd\u5176\u529b\u5b66\u54cd\u5e94\u3002<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u6311\u6218\uff1a<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4f60\u4e0d\u80fd\u5728\u4e0d\u77e5\u9053\u53e6\u4e00\u4e2a\u95ee\u9898\u7684\u60c5\u51b5\u4e0b\u89e3\u51b3\u5176\u4e2d\u4e00\u4e2a\u95ee\u9898\u3002\u5b83\u4eec\u5fc5\u987b\u4e00\u8d77\u89e3\u51b3\u3002 <strong>\u4e00\u8d77<\/strong>, \u4f46\u662f\u5982\u4f55\u505a\u5230\u5462\uff1f<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u5de5\u7a0b\u5e08\u53ef\u4ee5\u4f7f\u7528Abaqus\u4e2d\u7684\u4e24\u79cd\u4e3b\u8981\u7b56\u7565\u6765\u6c42\u89e3\u76f8\u573a\u6a21\u578b\u3002\u4e0b\u8868\u5217\u51fa\u4e86\u8fd9\u4e9b\u65b9\u6cd5\uff1a<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"border-collapse: collapse; width: 100%; text-align: right;\" border=\"1\" cellspacing=\"0\" cellpadding=\"8\">\n<thead>\n<tr>\n<th>\u65b9\u6cd5<\/th>\n<th>\u63cf\u8ff0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">Staggered (Alternate Minimization)<\/td>\n<td style=\"text-align: right;\">Solves displacement and phase field equations separately in alternating steps. Widely used but computationally intensive.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">Monolithic<\/td>\n<td style=\"text-align: right;\">Solves both equations simultaneously. More robust and efficient, especially with quasi-Newton methods.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #ff6600;\">\u5982\u4f55\u5728Abaqus\u4e2d\u5b9e\u73b0\u76f8\u573a\u65ad\u88c2\u6a21\u578b<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u9009\u5b9a\u6a21\u578b\u548c\u6c42\u89e3\u7b56\u7565\u540e\uff0c\u6211\u4eec\u9700\u8981\u5728Abaqus\u7b49\u8f6f\u4ef6\u4e2d\u5b9e\u73b0\u5b83\u4eec\u3002\u76f8\u573a\u65ad\u88c2\u6a21\u578b\u5e76\u975eAbaqus\u7b49\u5546\u4e1a\u6709\u9650\u5143\u8f6f\u4ef6\u7684\u5185\u7f6e\u529f\u80fd\u3002\u56e0\u6b64\uff0c\u5de5\u7a0b\u5e08\u5fc5\u987b\u4f7f\u7528\u5404\u79cd\u7528\u6237\u81ea\u5b9a\u4e49\u5b50\u7a0b\u5e8f\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8fd9\u4e9b\u5b50\u7a0b\u5e8f\u662f\u7528 Fortran \u8bed\u8a00\u7f16\u5199\u7684\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u5b9e\u73b0\u65b9\u5f0f\u5206\u4e3a\u4e24\u7c7b\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3>\u57fa\u4e8eUEL\u7684\u5b9e\u73b0<\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6700\u65e9\u7684\u5b9e\u73b0\u65b9\u5f0f\u4f7f\u7528\u7528\u6237\u5355\u5143 (UEL) \u5b50\u7a0b\u5e8f\u3002\u8fd9\u79cd\u65b9\u6cd5\u5c06\u76f8\u4f4d\u573a (\u03c6) \u5b9a\u4e49\u4e3a\u4e00\u4e2a\u989d\u5916\u7684\u8282\u70b9\u81ea\u7531\u5ea6\uff0c\u4e0e\u4f4d\u79fb (u) \u5e76\u5217\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u8fc7\u7a0b\uff1a <\/strong>UEL \u5b50\u7a0b\u5e8f\u5141\u8bb8\u7528\u6237\u624b\u52a8\u5b9a\u4e49\u5355\u5143\u5207\u7ebf\u521a\u5ea6\u77e9\u9635\uff0c\u8fd8\u53ef\u4ee5\u663e\u5f0f\u5b9a\u4e49\u8282\u70b9\u529b\u5411\u91cf\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u9000\u7a0e\uff1a <\/strong>\u8fd9\u79cd\u65b9\u6cd5\u4ec5\u5c06 Abaqus \u7528\u4f5c\u6c42\u89e3\u5668\uff0c\u56e0\u6b64\u727a\u7272\u4e86\u8bb8\u591a\u5185\u7f6e\u529f\u80fd\u3002\u6b64\u5916\uff0c\u5b83\u8fd8\u4f7f\u7f51\u683c\u751f\u6210\u548c\u53ef\u89c6\u5316\u53d8\u5f97\u590d\u6742\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u8026\u5408\u95ee\u9898\uff1a <\/strong>\u5bf9\u4e8e\u590d\u6742\u7684\u591a\u7269\u7406\u573a\u95ee\u9898\uff0c\u975e\u5f39\u6027\u8026\u5408\u5c42\uff08UEL\uff09\u662f\u5fc5\u4e0d\u53ef\u5c11\u7684\u3002\u8fd9\u4e9b\u95ee\u9898\u6d89\u53ca\u591a\u4e2a\u8026\u5408\u573a\uff0c\u4f8b\u5982\u5f62\u53d8\u573a\uff08u\uff09\u3001\u6c22\u6d53\u5ea6\u573a\uff08C\uff09\u548c\u76f8\u573a\uff08\u03c6\uff09\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6709\u4e9b\u5b9e\u73b0\u65b9\u5f0f\u91c7\u7528\u5206\u5c42\u6709\u9650\u5143\u7cfb\u7edf\u6765\u6784\u5efa\u6a21\u578b\u3002\u4f8b\u5982\uff0c\u7531\u4f4d\u79fb\u5355\u5143\u3001\u76f8\u573a\u5355\u5143\u548c\u7528\u4e8e\u540e\u5904\u7406\u7684UMAT\u5355\u5143\u7ec4\u6210\u7684\u4e09\u5c42\u7ed3\u6784\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3>\u96c6\u6210\u70b9\u7ea7\u5b9e\u73b0<\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4e00\u79cd\u66f4\u7b80\u5355\u3001\u66f4\u7a33\u5065\u7684\u65b9\u6cd5\u662f\u5229\u7528\u7c7b\u6bd4\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u5229\u7528\u4e86\u76f8\u573a\u6f14\u5316\u65b9\u7a0b\u548c\u70ed\u4f20\u9012\u65b9\u7a0b\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u673a\u5236\uff1a <\/strong>\u76f8\u573a\u6620\u5c04\u5230\u6e29\u5ea6\u81ea\u7531\u5ea6\uff08\u03c6 \u2192 \u03b8\uff09\u3002\u8fd9\u4f7f\u5f97\u53ef\u4ee5\u4f7f\u7528 Abaqus \u5185\u7f6e\u7684\u8026\u5408\u6e29\u5ea6-\u4f4d\u79fb\u5355\u5143\u3002\u4f8b\u5982 CPE4T\u3002.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\"><strong>\u5b50\u7a0b\u5e8f\uff1a <\/strong>\u5de5\u7a0b\u5e08\u4e3b\u8981\u5728\u96c6\u6210\u70b9\u7ea7\u522b\u5b9e\u73b0\u6b64\u529f\u80fd\u3002\u4ed6\u4eec\u4f7f\u7528\u7528\u6237\u6750\u6599\uff08UMAT\uff09\u548c\u7528\u6237\u6750\u6599\u70ed\u4f20\u9012\uff08UMATHT\/HETVAL\uff09\u5b50\u7a0b\u5e8f\u3002.<\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5bf9\u4e8e Abaqus 2020 \u6216\u66f4\u9ad8\u7248\u672c\uff1a\u4ec5\u9700\u4e00\u4e2a UMAT \u5b50\u7a0b\u5e8f\u3002\u8be5\u5b50\u7a0b\u5e8f\u5b9a\u4e49\u4e86\u4f53\u79ef\u70ed\u6e90 (r) \u53ca\u5176\u5bfc\u6570\u3002\u6700\u7b80\u5355\u7684\u5b9e\u73b0\u65b9\u5f0f\u4ec5\u9700 33 \u884c\u4ee3\u7801\u3002.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5bf9\u4e8e 2020 \u5e74\u4e4b\u524d\u7684 Abaqus \u7248\u672c\uff1a\u901a\u5e38\u9700\u8981\u5c06 UMAT \u51fd\u6570\u4e0e HETVAL \u5b50\u7a0b\u5e8f\u7ed3\u5408\u4f7f\u7528\u3002\u8fd9\u4e9b\u51fd\u6570\u7528\u4e8e\u5b9a\u4e49\u70ed\u6e90\u9879\u3002.<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5bf9\u4e8e\u591a\u91cd\u6269\u6563\u65b9\u7a0b\uff0c\u901a\u7528\u6846\u67b6\u901a\u5e38\u4f7f\u7528 UMAT \u548c UMATHT \u5b50\u7a0b\u5e8f\u3002\u4f8b\u5982\uff0c\u76f8\u573a\u548c\u6c22\u8f93\u8fd0\u65b9\u7a0b\u3002\u8fd9\u53ef\u80fd\u9700\u8981\u201c\u53cc\u90e8\u5206\u65b9\u6cd5\u201d\u6765\u5b9a\u4e49\u989d\u5916\u7684\u7c7b\u6e29\u5ea6\u81ea\u7531\u5ea6\u3002.<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #ff6600;\">\u60a8\u662f\u5426\u9700\u8981\u5f00\u6e90\u7684 Abaqus \u76f8\u573a\u6a21\u578b\uff1f\u8bf7\u67e5\u770b\u4e0b\u8868\u3002<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u6709\u5927\u91cf\u7684\u5f00\u6e90\u4ee3\u7801\u53ef\u4f9b\u4f7f\u7528\u3002\u8fd9\u4e9b\u8d44\u6e90\u5b9e\u73b0\u4e86\u5404\u79cd\u76f8\u573a\u6a21\u578b\u3002\u5b83\u4eec\u4e3b\u8981\u5229\u7528 Abaqus \u7528\u6237\u5b50\u7a0b\u5e8f\uff08Fortran\uff09\u6216\u901a\u7528\u6709\u9650\u5143\u6846\u67b6\uff08Python\uff09\u3002.<\/span><\/p>\n<h3>Abaqus\u5b9e\u73b0<\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u4ee5\u4e0b\u5927\u90e8\u5206\u4ee3\u7801\u5747\u53ef\u5728\u4ee5\u4e0b\u7f51\u5740\u4e0b\u8f7d\uff1a <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.empaneda.com\/codes\/\" target=\"_blank\" rel=\"nofollow noopener\">https:\/\/www.empaneda.com\/codes\/<\/a><\/span><\/span><span style=\"font-size: 14pt;\">,<span style=\"color: #0000ff;\"> <a style=\"color: #0000ff;\" href=\"https:\/\/molnar-research.com\/tutorials_PH.html\" target=\"_blank\" rel=\"nofollow noopener\">https:\/\/molnar-research.com\/tutorials_PH.html<\/a><\/span><\/span><span style=\"font-size: 14pt;\">, \uff0c \u6216\u8005 <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/mechmat.web.ox.ac.uk\/codes\" target=\"_blank\" rel=\"nofollow noopener\">https:\/\/mechmat.web.ox.ac.uk\/codes<\/a><\/span><\/span><span style=\"font-size: 14pt;\">. \u66f4\u591a\u53c2\u8003\u6587\u732e\u8bf7\u53c2\u89c1\u4e0b\u8868\u3002.<\/span><\/p>\n<table style=\"border-collapse: collapse; width: 100%; text-align: right;\" border=\"1\" cellspacing=\"0\" cellpadding=\"8\">\n<thead>\n<tr>\n<th>IMPLEMENTATION TYPE<\/th>\n<th>MODELS &amp; PURPOSE<\/th>\n<th>CODE\/SUBROUTINES<\/th>\n<th>SOURCE\/CONTRIBUTOR<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">UMAT\/HETVAL<\/td>\n<td style=\"text-align: right;\">\u79ef\u5206\u70b9\u7ea7\u522b\uff08\u7b80\u5355\u3001\u901a\u7528 PFM\uff09\u3002\u7edf\u4e00\u5b9e\u73b0 AT1\u3001AT2\u3001PF-CZM \u6a21\u578b\uff0c\u5305\u62ec\u5404\u79cd\u5e94\u53d8\u80fd\u5206\u88c2\uff08\u8c31\u3001\u4f53\u79ef-\u504f\u91cf\u3001Drucker-Prager\uff09\u3002.<\/td>\n<td style=\"text-align: right;\">PFF-UMAT.f (Abaqus 2020+ UMAT only) and PFF-HETVAL.f (UMAT + HETVAL for older versions). Simple versions: UMATs.f \/ HETVALs.f. AT1 model: UMAT and UEL (PhaseFieldUMAT.zip, Tutorial_9_AT1.zip)<\/td>\n<td style=\"text-align: right;\">Y. Navidnehrani, E. Mart\u00ednez-Pa\u00f1eda.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\u8026\u5408\u5f0f HE\/HAC \u7684 UEL<\/td>\n<td style=\"text-align: right;\">\u91c7\u7528 8 \u8282\u70b9\u4e8c\u6b21 UEL \u5355\u5143\u8026\u5408\u53d8\u5f62-\u6c22\u6269\u6563-\u76f8\u573a\u65ad\u88c2\u3002.<\/td>\n<td style=\"text-align: right;\">PhaseFieldH.for\uff08UEL \u5b50\u7a0b\u5e8f\uff09<\/td>\n<td style=\"text-align: right;\">E. Mart\u00ednez-Pa\u00f1eda\u3002.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\u52a8\u6001\/\u97e7\u6027\u65ad\u88c2\u7684UEL<\/td>\n<td style=\"text-align: right;\">\u5f39\u5851\u6027\u76f8\u573a\u65b9\u6cd5\u7528\u4e8e\u8106\u6027\u548c\u97e7\u6027\u9759\u6001\u548c\u52a8\u6001\u65ad\u88c2\uff1b\u5e7f\u6cdb\u4f7f\u7528\u7684\u7a33\u5065\u4ea4\u9519\u6c42\u89e3\u65b9\u6848\u3002.<\/td>\n<td style=\"text-align: right;\">\u5f00\u6e90 UEL \u5b50\u7a0b\u5e8f\uff08\u4e4b\u524d\u4f7f\u7528\u7684\u5206\u5c42\u7cfb\u7edf\uff09<\/td>\n<td style=\"text-align: right;\">G. Moln\u00e1r\uff0cA. Gravouil\u3002.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">SCC\/\u8150\u8680\u7684UEL<\/td>\n<td style=\"text-align: right;\">\u5229\u7528 UEL \u5b50\u7a0b\u5e8f\u5b9e\u73b0\u7684\u6eb6\u89e3\u9a71\u52a8\u5e94\u529b\u8150\u8680\u5f00\u88c2\u548c\u70b9\u8680\u76f8\u573a\u6a21\u578b\u3002.<\/td>\n<td style=\"text-align: right;\">UEL \u5b50\u7a0b\u5e8f\u6587\u4ef6\uff08Fortran\uff09<\/td>\n<td style=\"text-align: right;\">C. Cui\uff0cE. Mart\u00ednez-Pa\u00f1eda\u3002.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\u62df\u725b\u987f\u6c42\u89e3\u5668\u7684 UEL<\/td>\n<td style=\"text-align: right;\">\u91c7\u7528\u9ad8\u6548\u51c6\u725b\u987f\uff08BFGS\uff09\u6574\u4f53\u6c42\u89e3\u65b9\u6848\u7684\u76f8\u573a\u6a21\u578b\uff08\u7528\u4e8e\u65ad\u88c2\u548c\u75b2\u52b3\uff09\u3002.<\/td>\n<td style=\"text-align: right;\">FatigueQN.f\uff08UEL \u5b50\u7a0b\u5e8f\uff09<\/td>\n<td style=\"text-align: right;\">PK \u514b\u91cc\u65af\u6ed5\u68ee\uff0cE. \u9a6c\u4e01\u5185\u65af-\u5e15\u6d85\u8fbe\u3002.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\u673a\u7535\u5f0fPFM\u7684UEL<\/td>\n<td style=\"text-align: right;\">\u8026\u5408\u5f62\u53d8-\u7535\u573a-\u76f8\u573a\u6a21\u578b\uff0c\u4e13\u95e8\u7528\u4e8e\u538b\u963b\u6750\u6599\uff08\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u6bcf\u4e2a\u8282\u70b9 5 \u4e2a\u81ea\u7531\u5ea6\uff09\u3002.<\/td>\n<td style=\"text-align: right;\">UEL\u538b\u963b\u76f8\u573a\uff08UEL\u5b50\u7a0b\u5e8f\uff09<\/td>\n<td style=\"text-align: right;\">L. Quinteros\uff0cE. Mart\u00ednez-Pa\u00f1eda\u3002.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">PF-CZM\u5b9e\u65bd<\/td>\n<td style=\"text-align: right;\">\u5c06\u76f8\u573a\u6b63\u5219\u5316\u5185\u805a\u533a\u6a21\u578b\uff08PF-CZM\uff09\u5b9e\u73b0\u5230 ABAQUS \u4e2d\u3002.<\/td>\n<td style=\"text-align: right;\">pfczm_bfgs.for\uff08\u7528\u4e8e PF-CZM \u7684 BFGS \u6574\u4f53\u6c42\u89e3\u5668\uff09<\/td>\n<td style=\"text-align: right;\">\u5434\u5efa\u52c7\uff0c\u9ec4\u5b87\u3002.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">UEL\/UMAT \u7528\u4e8e\u5f39\u5851\u6027\u65ad\u88c2<\/td>\n<td style=\"text-align: right;\">\u4f7f\u7528\u4ea4\u9519\u7b97\u6cd5\u5bf9\u5f39\u5851\u6027\u56fa\u4f53\u65ad\u88c2\u8fdb\u884c\u76f8\u573a\u5efa\u6a21\u7684 2D \u548c 3D UEL\/UMAT\u3002.<\/td>\n<td style=\"text-align: right;\">UEL \u548c UMAT \u5b50\u7a0b\u5e8f<\/td>\n<td style=\"text-align: right;\">\u65b9\u6770.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\u8106\u6027\/\u97e7\u6027\u65ad\u88c2\u7684 UEL\uff08\u6b8b\u4f59\u63a7\u5236\uff09<\/td>\n<td style=\"text-align: right;\">\u4f7f\u7528\u57fa\u4e8e\u6b8b\u4f59\u8303\u6570\u7684\u4ea4\u9519\u65b9\u6848\uff082D\/3D \u7ebf\u6027\u5355\u5143\uff09\u7684 UEL\/UMAT \u6765\u5206\u6790\u8106\u6027\u548c\u97e7\u6027\u65ad\u88c2\u3002.<\/td>\n<td style=\"text-align: right;\">UEL \u548c UMAT \u5b50\u4f8b\u7a0b (Fortran)<\/td>\n<td style=\"text-align: right;\">K. Seles.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\u51c6\u8106\u6027\u6750\u6599\u4e2d\u7684\u75b2\u52b3\u88c2\u7eb9\u6269\u5c55<\/td>\n<td style=\"text-align: right;\">\u76f8\u573a\u5185\u805a\u533a\u65b9\u6cd5\u7528\u4e8e\u8106\u6027\u6750\u6599\u75b2\u52b3\u88c2\u7eb9\u6a21\u62df\u3002.<\/td>\n<td style=\"text-align: right;\">HETVAL \u548c UMAT \u5b50\u7a0b\u5e8f<\/td>\n<td style=\"text-align: right;\">Abedulqader Bakthere.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\u52a8\u6001\u76f8\u573a\u6a21\u62df<\/td>\n<td style=\"text-align: right;\">\u5f39\u5851\u6027\u56fa\u4f53\uff08\u52a8\u6001\u76f8\u573a\u65ad\u88c2\u6a21\u62df\uff09\u3002.<\/td>\n<td style=\"text-align: right;\">UMAT \u548c UEL<\/td>\n<td style=\"text-align: right;\">Molnar\u7814\u7a76\u5c0f\u7ec4\u3002.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #ff6600;\">\u5982\u4f55\u5728 Julia \u8bed\u8a00\u4ee3\u7801\u4e2d\u5b9e\u73b0\u76f8\u573a\u6a21\u578b\uff1f<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8bb8\u591a\u4eba\u9762\u4e34\u7684\u6311\u6218\u4e4b\u4e00\u662f\uff0c\u4ed6\u4eec\u53ef\u80fd\u65e0\u6cd5\u83b7\u5f97\u50cf Abaqus \u8fd9\u6837\u7684\u5546\u4e1a\u6709\u9650\u5143\u8f6f\u4ef6\u6765\u6a21\u62df\u76f8\u573a\u95ee\u9898\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u8fd1\u5e74\u6765\uff0c\u4f7f\u7528\u514d\u8d39\u8f6f\u4ef6\u548c\u7f16\u7a0b\u8bed\u8a00\u5f15\u8d77\u4e86\u5e7f\u6cdb\u5173\u6ce8\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">Julia \u662f\u4e00\u79cd\u53ef\u7528\u4e8e\u6a21\u62df\u76f8\u573a\u95ee\u9898\u7684\u5f00\u6e90\u514d\u8d39\u7f16\u7a0b\u8bed\u8a00\u3002\u5982\u4eca\uff0cJulia \u8bed\u8a00\u56e0\u5176\u5f00\u6e90\u7279\u6027\u548c\u76f8\u6bd4\u5176\u4ed6\u7f16\u7a0b\u8bed\u8a00\u66f4\u5f3a\u5927\u7684\u529f\u80fd\u800c\u5e7f\u53d7\u6b22\u8fce\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u60a8\u53ef\u4ee5\u8bbf\u95ee <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.empaneda.com\/wp-content\/uploads\/2023\/04\/JuliaPhaseField.zip\" target=\"_blank\" rel=\"nofollow noopener\">\u514d\u8d39\u5f00\u6e90\u7684 Julia \u4ee3\u7801\u8bed\u8a00\u6e90\u4ee3\u7801<\/a><\/span><\/span><span style=\"font-size: 14pt;\"> \u7528\u4e8e\u5206\u6790\u76f8\u573a\u95ee\u9898\u7684 Julia \u7f16\u7a0b\u8bed\u8a00\u53ef\u4ee5\u514d\u8d39\u4e0b\u8f7d\u548c\u4f7f\u7528\u3002\u4e0e\u5546\u4e1a\u8f6f\u4ef6\u4e0d\u540c\uff0cJulia \u4ee3\u7801\u8bed\u8a00\u65e0\u9700\u4efb\u4f55\u8bb8\u53ef\u6216\u8d2d\u4e70\uff0c\u60a8\u53ef\u4ee5\u5b8c\u5168\u514d\u8d39\u4f7f\u7528\u3002. <\/span><span style=\"font-size: 14pt;\">\u8be5 Julia \u4ee3\u7801\u8bed\u8a00\u6e90\u4ee3\u7801\u53ef\u7528\u4e8e\u65ad\u88c2\u548c\u75b2\u52b3\u95ee\u9898\u7684\u76f8\u573a\u5efa\u6a21\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #ff6600;\">\u7ed3\u8bba<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u76f8\u573a\u6a21\u578b\u6280\u672f\u5df2\u5728\u8ba1\u7b97\u529b\u5b66\u9886\u57df\u786e\u7acb\u4e86\u5176\u5730\u4f4d\u3002\u5b83\u4e3a\u6a21\u62df\u6750\u6599\u5931\u6548\u63d0\u4f9b\u4e86\u4e00\u79cd\u7a33\u5065\u3001\u7b80\u6d01\u4e14\u901a\u7528\u7684\u8303\u5f0f\u3002\u76f8\u573a\u6a21\u578b\u5728\u6a21\u62df\u754c\u9762\u6f14\u5316\u65b9\u9762\u4e5f\u8868\u73b0\u51fa\u8272\u3002\u901a\u8fc7\u5c06\u5c16\u9510\u7684\u4e0d\u8fde\u7eed\u6027\u89c4\u5219\u5316\u4e3a\u5f25\u6563\u7684\u635f\u4f24\u5e26\uff0c\u76f8\u573a\u6a21\u578b\u80fd\u591f\u81ea\u7136\u5730\u6355\u6349\u590d\u6742\u7684\u73b0\u8c61\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8fd9\u4e9b\u8fc7\u7a0b\u5305\u62ec\u88c2\u7eb9\u7684\u840c\u751f\u3001\u6269\u5c55\u3001\u5408\u5e76\u548c\u5206\u652f\u3002\u8be5\u65b9\u6cd5\u9002\u7528\u4e8e\u4efb\u610f\u4e8c\u7ef4\u548c\u4e09\u7ef4\u51e0\u4f55\u5f62\u72b6\uff0c\u56e0\u6b64\u6709\u6548\u5730\u907f\u514d\u4e86\u5bf9\u7279\u5b9a\u65ad\u88c2\u51c6\u5219\u7684\u9700\u6c42\u3002\u56e0\u6b64\uff0c\u5b83\u975e\u5e38\u9002\u7528\u4e8e\u591a\u573a\u8026\u5408\u3002\u8fd9\u79cd\u56fa\u6709\u7684\u53d8\u5206\u7ed3\u6784\u4fc3\u8fdb\u4e86\u5176\u5728\u5404\u79cd\u6750\u6599\u4e2d\u7684\u6210\u529f\u5e94\u7528\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u5e94\u7528\u8303\u56f4\u8fdc\u4e0d\u6b62\u7b80\u5355\u7684\u8106\u6027\u65ad\u88c2\u3002\u4f8b\u5982\uff0c\u6c22\u81f4\u5f00\u88c2\u3001\u5e94\u529b\u8150\u8680\u5f00\u88c2\u548c\u70ed\u673a\u68b0\u65ad\u88c2\u7b49\u3002\u5728 Abaqus \u7b49\u5546\u4e1a\u8f6f\u4ef6\u4e2d\u7684\u5b9e\u73b0\u4e3b\u8981\u4f9d\u8d56\u4e8e\u4e24\u79cd\u7b56\u7565\u3002\u6bcf\u79cd\u7b56\u7565\u5404\u6709\u4f18\u52bf\uff1a1\uff09\u7528\u6237\u5143\u7d20\u7ea7\u5b9e\u73b0\uff1b2\uff09\u96c6\u6210\u70b9\u7ea7\u5b9e\u73b0\u3002. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u7136\u800c\uff0c\u76f8\u573a\u65ad\u88c2\u5efa\u6a21\u662f\u4e00\u4e2a\u9ad8\u7ea7\u8bfe\u9898\uff0c\u9700\u8981Abaqus\u4eff\u771f\u8f6f\u4ef6\u5177\u5907\u4e00\u5b9a\u7684\u4e13\u4e1a\u6c34\u5e73\u3002\u4f5c\u4e3a\u5b9e\u73b0\u76f8\u573a\u6a21\u578b\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\uff0c\u6709\u4eba\u5efa\u8bae\u4f7f\u7528Julia\u8bed\u8a00\u4ee3\u7801\u3002.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">\u8fd9\u00a0<a href=\"https:\/\/caeassistant.com\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\">CAE \u52a9\u624b<\/span><\/a><\/span><span style=\"font-size: 14pt;\">\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<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><\/span><span style=\"font-size: 14pt;\"> \u73b0\u5728\uff01<\/span><\/p>\n<p>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>Have you ever tried to model crack growth or material failure? If so, you may have faced limitations. Traditional methods struggle when crack paths are unknown in advance. They also fail when multiple cracks branch and merge unpredictably. Classical approaches like FEM or XFEM cannot handle such complexity effectively. This is where the Phase Field [&hellip;]<\/p>","protected":false},"author":250,"featured_media":45224,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[67],"tags":[],"class_list":["post-43648","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\/43648","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=43648"}],"version-history":[{"count":13,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/posts\/43648\/revisions"}],"predecessor-version":[{"id":49491,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/posts\/43648\/revisions\/49491"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/media\/45224"}],"wp:attachment":[{"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/media?parent=43648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/categories?post=43648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dev.caeassistant.com\/zh\/wp-json\/wp\/v2\/tags?post=43648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}