1. \u5f15\u8a00\uff1a\u4e3a\u4ec0\u4e48\u9700\u8981UMAT\uff1f<\/h2>\n
\u5728\u5de5\u7a0b\u4eff\u771f\u5b9e\u8df5\u4e2d\uff0cAbaqus\u5185\u7f6e\u7684\u6750\u6599\u5e93\u5df2\u7ecf\u8986\u76d6\u4e86\u7ebf\u5f39\u6027\u3001\u91d1\u5c5e\u5851\u6027\u3001\u8d85\u5f39\u6027\u3001\u7c98\u5f39\u6027\u7b49\u5e38\u89c1\u672c\u6784\u6a21\u578b\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u9762\u5bf9\u4ee5\u4e0b\u573a\u666f\u65f6\uff0c\u5185\u7f6e\u6a21\u578b\u5f80\u5f80\u529b\u4e0d\u4ece\u5fc3\uff1a<\/p>\n
- \n
- \u65b0\u578b\u6750\u6599\u672c\u6784<\/strong>\uff1a\u5982\u5f62\u72b6\u8bb0\u5fc6\u5408\u91d1\u3001\u81ea\u6108\u5408\u805a\u5408\u7269\u3001\u68af\u5ea6\u529f\u80fd\u6750\u6599\u7b49\u524d\u6cbf\u6750\u6599\uff1b<\/li>\n
- \u591a\u7269\u7406\u573a\u8026\u5408<\/strong>\uff1a\u70ed-\u529b-\u5316\u5b66\u8026\u5408\u3001\u8f90\u7167\u635f\u4f24\u6f14\u5316\u7b49\u590d\u6742\u4ea4\u4e92\u884c\u4e3a\uff1b<\/li>\n
- \u81ea\u5b9a\u4e49\u635f\u4f24\u4e0e\u5931\u6548\u51c6\u5219<\/strong>\uff1a\u590d\u5408\u6750\u6599\u6e10\u8fdb\u635f\u4f24\u3001\u75b2\u52b3\u5bff\u547d\u9884\u6d4b\u7b49\uff1b<\/li>\n
- \u5df2\u6709\u79d1\u7814\u6210\u679c\u7684\u5de5\u7a0b\u5316<\/strong>\uff1a\u5c06\u8bba\u6587\u4e2d\u7684\u672c\u6784\u65b9\u7a0b\u8f6c\u5316\u4e3a\u53ef\u8ba1\u7b97\u7684\u6570\u503c\u5b9e\u73b0\u3002<\/li>\n<\/ul>\n
UMAT\u6b63\u662f\u4e3a\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u800c\u8bbe\u8ba1\u7684\u3002\u5b83\u8d4b\u4e88\u7528\u6237\u5b8c\u5168\u7684\u672c\u6784\u5b9a\u4e49\u81ea\u7531\u5ea6\u2014\u2014\u53ea\u8981\u4f60\u80fd\u5199\u51fa\u5e94\u529b\u66f4\u65b0\u7b97\u6cd5\u548c\u5207\u7ebf\u521a\u5ea6\u77e9\u9635\uff0cAbaqus\u5c31\u80fd\u5c06\u5176\u5d4c\u5165\u6709\u9650\u5143\u6c42\u89e3\u6d41\u7a0b\u3002<\/p>\n
\u56fe1 UMAT\u5728\u6750\u6599\u529b\u5b66\u884c\u4e3a\u7814\u7a76\u4e2d\u7684\u5b9a\u4f4d<\/figcaption><\/figure>\n 2. \u7406\u8bba\u57fa\u7840\uff1a\u672c\u6784\u79ef\u5206\u4e0eNewton\u8fed\u4ee3<\/h2>\n
2.1 \u7387\u5f62\u5f0f\u672c\u6784\u65b9\u7a0b<\/h3>\n
\u56fa\u4f53\u529b\u5b66\u4e2d\uff0c\u6750\u6599\u7684\u529b\u5b66\u884c\u4e3a\u901a\u5e38\u4ee5\u7387\u5f62\u5f0f\uff08rate form\uff09\u63cf\u8ff0\uff1a<\/p>\n
d\u03c3 = C : d\u03b5<\/em><\/p>\n
\u5176\u4e2d C<\/em> \u4e3a\u56db\u9636\u672c\u6784\u5f20\u91cf\u3002\u5bf9\u4e8e\u5f39\u5851\u6027\u6750\u6599\uff0c\u91c7\u7528\u52a0\u6cd5\u5206\u89e3\uff1a<\/p>\n
d\u03b5 = d\u03b5e<\/sup> + d\u03b5p<\/sup><\/em><\/p>\n
\u5f39\u6027\u90e8\u5206\u6ee1\u8db3\u5e7f\u4e49Hooke\u5b9a\u5f8b d\u03c3 = Ce<\/sup> : d\u03b5e<\/sup><\/em>\uff0c\u5851\u6027\u90e8\u5206\u7531\u6d41\u52a8\u6cd5\u5219\u548c\u786c\u5316\u5f8b\u63a7\u5236\u3002<\/p>\n
2.2 J2\u5851\u6027\u7406\u8bba<\/h3>\n
J2\uff08Von Mises\uff09\u5851\u6027\u662f\u91d1\u5c5e\u6750\u6599\u7684\u7ecf\u5178\u672c\u6784\u6a21\u578b\uff0c\u5176\u6838\u5fc3\u65b9\u7a0b\u5305\u62ec\uff1a<\/p>\n
\u5c48\u670d\u51fd\u6570<\/strong>\uff1a<\/p>\n
f(\u03c3, \u03ba) = \u03c3eq<\/sub> – \u03c3y<\/sub>(\u03ba) = 0<\/em><\/p>\n
\u5176\u4e2d\u7b49\u6548\u5e94\u529b \u03c3eq<\/sub> = \u221a(3\/2 \u00b7 s:s)<\/em>\uff0cs<\/em> \u4e3a\u504f\u5e94\u529b\u5f20\u91cf\uff0c\u03ba<\/em> \u4e3a\u7b49\u6548\u5851\u6027\u5e94\u53d8\uff08\u786c\u5316\u5185\u53d8\u91cf\uff09\u3002<\/p>\n
\u6d41\u52a8\u6cd5\u5219<\/strong>\uff08\u5173\u8054\u6d41\u52a8\uff09\uff1a<\/p>\n
d\u03b5p<\/sup> = d\u03b3 \u00b7 \u2202f\/\u2202\u03c3 = d\u03b3 \u00b7 3s\/(2\u03c3eq<\/sub>)<\/em><\/p>\n
\u786c\u5316\u5f8b<\/strong>\uff08\u7b49\u5411\u786c\u5316\uff09\uff1a<\/p>\n
\u03c3y<\/sub>(\u03ba) = \u03c3y0<\/sub> + H\u00b7\u03ba<\/em><\/p>\n
2.3 \u56de\u6620\u7b97\u6cd5\uff08Return Mapping\uff09<\/h3>\n
\u5728\u6709\u9650\u5143\u589e\u91cf\u6b65\u4e2d\uff0c\u672c\u6784\u79ef\u5206\u91c7\u7528”\u5f39\u6027\u9884\u6d4b-\u5851\u6027\u4fee\u6b63”\u7b56\u7565\uff1a<\/p>\n
- \n
- \u5f39\u6027\u9884\u6d4b<\/strong>\uff1a\u5047\u8bbe\u589e\u91cf\u6b65\u4e3a\u7eaf\u5f39\u6027\uff0c\u8ba1\u7b97\u8bd5\u5e94\u529b \u03c3trial<\/sub> = \u03c3n<\/sub> + Ce<\/sup> : \u0394\u03b5<\/em>\uff1b<\/li>\n
- \u5c48\u670d\u5224\u65ad<\/strong>\uff1a\u82e5 f(\u03c3trial<\/sub>) \u2264 0<\/em>\uff0c\u63a5\u53d7\u5f39\u6027\u6b65\uff1b\u5426\u5219\u8fdb\u5165\u5851\u6027\u4fee\u6b63\uff1b<\/li>\n
- \u5851\u6027\u4fee\u6b63<\/strong>\uff1a\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b f(\u03c3trial<\/sub> – 2G\u00b7\u0394\u03b3\u00b7n) = 0<\/em>\uff0c\u5f97\u5230\u5851\u6027\u4e58\u5b50 \u0394\u03b3<\/em>\uff1b<\/li>\n
- \u5e94\u529b\u66f4\u65b0<\/strong>\uff1a\u03c3n+1<\/sub> = \u03c3trial<\/sub> – 2G\u00b7\u0394\u03b3\u00b7n<\/em>\uff0c\u66f4\u65b0\u5185\u53d8\u91cf \u03ban+1<\/sub> = \u03ban<\/sub> + \u0394\u03b3<\/em>\u3002<\/li>\n<\/ol>\n
\u56fe2 J2\u5f39\u5851\u6027\u672c\u6784\u5e94\u529b\u66f4\u65b0\u4e0e\u56de\u6620\u7b97\u6cd5\u793a\u610f<\/figcaption><\/figure>\n 3. \u5b98\u65b9\u6587\u6863\u89e3\u8bfb\uff1aUMAT\u63a5\u53e3\u89c4\u8303<\/h2>\n
\u6587\u6863\u6765\u6e90<\/strong>\uff1aAbaqus Analysis User’s Guide \u2192 User Subroutines \u2192 UMAT
\n\u6587\u6863\u8def\u5f84<\/strong>\uff1aSIMACAESUBRefMap\/simasub-c-umat.htm
\n\u9002\u7528\u4ea7\u54c1<\/strong>\uff1aAbaqus\/Standard\uff08\u9690\u5f0f\u6c42\u89e3\u5668\uff09<\/div>\n3.1 \u5b98\u65b9\u5b9a\u4e49\u4e0e\u8b66\u544a<\/h3>\n
Abaqus\u5b98\u65b9\u6587\u6863\u5bf9UMAT\u7684\u5b9a\u4e49\u4e3a\uff1a“User subroutine to define a material’s mechanical behavior”<\/em>\u3002\u540c\u65f6\u7ed9\u51fa\u4e86\u660e\u786e\u8b66\u544a\uff1a<\/p>\n
Warning<\/strong>: The use of this subroutine generally requires considerable expertise. Initial testing on a single-element model with prescribed traction loading is strongly recommended.<\/div>\n\u8fd9\u6bb5\u8bdd\u7684\u6838\u5fc3\u4fe1\u606f\u662f\uff1a\u52a1\u5fc5\u5148\u7528\u5355\u5355\u5143\u6a21\u578b\u9a8c\u8bc1\u4f60\u7684UMAT<\/strong>\uff0c\u518d\u4e0a\u590d\u6742\u6a21\u578b\u3002\u8fd9\u662f\u591a\u5e74\u5b9e\u6218\u4e2d\u6700\u91cd\u8981\u7684\u7ecf\u9a8c\u4e4b\u4e00\u3002<\/p>\n
3.2 \u5fc5\u987b\u5b9a\u4e49\u7684\u53d8\u91cf<\/h3>\n
\n\n
\n \u53d8\u91cf<\/th>\n \u7ef4\u5ea6<\/th>\n \u8bf4\u660e<\/th>\n<\/tr>\n \n DDSDDE(NTENS,NTENS)<\/td>\n \u77e9\u9635<\/td>\n \u672c\u6784Jacobian\u77e9\u9635\uff0c\u5373\u4e00\u81f4\u5207\u7ebf\u521a\u5ea6 \u2202\u0394\u03c3\/\u2202\u0394\u03b5<\/td>\n<\/tr>\n \n STRESS(NTENS)<\/td>\n \u6570\u7ec4<\/td>\n \u4f20\u5165\u4e3a\u589e\u91cf\u6b65\u5f00\u59cb\u5e94\u529b\uff0c\u5fc5\u987b\u66f4\u65b0\u4e3a\u589e\u91cf\u6b65\u7ed3\u675f\u5e94\u529b\uff08Cauchy\u5e94\u529b\uff09<\/td>\n<\/tr>\n \n STATEV(NSTATV)<\/td>\n \u6570\u7ec4<\/td>\n \u72b6\u6001\u53d8\u91cf\uff08\u5982\u7b49\u6548\u5851\u6027\u5e94\u53d8\u3001\u80cc\u5e94\u529b\u7b49\uff09\uff0c\u4f20\u5165\u4e3a\u6b65\u521d\u503c\uff0c\u8fd4\u56de\u6b65\u672b\u503c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 3.3 \u5173\u952e\u4f20\u5165\u53d8\u91cf<\/h3>\n
\n\n
\n \u53d8\u91cf<\/th>\n \u8bf4\u660e<\/th>\n<\/tr>\n \n STRAN(NTENS)<\/td>\n \u589e\u91cf\u6b65\u5f00\u59cb\u65f6\u7684\u603b\u5e94\u53d8<\/td>\n<\/tr>\n \n DSTRAN(NTENS)<\/td>\n \u672c\u589e\u91cf\u6b65\u7684\u5e94\u53d8\u589e\u91cf<\/td>\n<\/tr>\n \n DTIME<\/td>\n \u65f6\u95f4\u589e\u91cf<\/td>\n<\/tr>\n \n NTENS<\/td>\n \u5e94\u529b\/\u5e94\u53d8\u5206\u91cf\u603b\u6570 = NDI + NSHR<\/td>\n<\/tr>\n \n PROPS(NPROPS)<\/td>\n \u6750\u6599\u5e38\u6570\u6570\u7ec4\uff08\u6765\u81ea*USER MATERIAL\u8f93\u5165\uff09<\/td>\n<\/tr>\n \n DFGRD0\/DFGRD1(3,3)<\/td>\n \u589e\u91cf\u6b65\u5f00\u59cb\/\u7ed3\u675f\u65f6\u7684\u53d8\u5f62\u68af\u5ea6\uff08\u6709\u9650\u5e94\u53d8\u5206\u6790\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 3.4 \u6536\u655b\u6027\u8981\u70b9<\/h3>\n
\u5b98\u65b9\u6587\u6863\u660e\u786e\u6307\u51fa\uff1a<\/p>\n
- \n
- DDSDDE\u5fc5\u987b\u51c6\u786e\u5b9a\u4e49\u624d\u80fd\u5b9e\u73b0\u5feb\u901fNewton\u6536\u655b\uff1b<\/li>\n
- \u4e0d\u6b63\u786e\u7684Jacobian\u53ea\u5f71\u54cd\u6536\u655b\u901f\u5ea6\uff0c\u4e0d\u5f71\u54cd\u6700\u7ec8\u7ed3\u679c\uff08\u5982\u679c\u80fd\u6536\u655b\u7684\u8bdd\uff09\uff1b<\/li>\n
- \u975e\u5bf9\u79f0Jacobian\u7684\u6c42\u89e3\u4ee3\u4ef7\u662f\u5bf9\u79f0\u7cfb\u7edf\u76844\u500d<\/strong>\uff1b<\/li>\n
- \u5bf9\u4e8e\u8f7b\u5fae\u975e\u5bf9\u79f0\u60c5\u51b5\uff08\u5982\u5c0f\u6469\u64e6\u89d2\uff09\uff0c\u53ef\u4f7f\u7528\u5bf9\u79f0\u8fd1\u4f3c\u4ee5\u964d\u4f4e\u8ba1\u7b97\u6210\u672c\u3002<\/li>\n<\/ul>\n
\u56fe3 UMAT\u5b50\u7a0b\u5e8f\u8c03\u7528\u6d41\u7a0b\u4e0e\u5e94\u529b\u66f4\u65b0\u7b97\u6cd5<\/figcaption><\/figure>\n 4. \u5b9e\u6218\u8981\u70b9\uff1a\u591a\u5e74\u7ecf\u9a8c\u603b\u7ed3<\/h2>\n
4.1 \u5f00\u53d1\u6d41\u7a0b\u5efa\u8bae<\/h3>\n
- \n
- \u5148\u5199\u6570\u5b66\uff0c\u540e\u5199\u4ee3\u7801<\/strong>\uff1a\u5728\u7eb8\u4e0a\u63a8\u5bfc\u5b8c\u6574\u7684\u5e94\u529b\u66f4\u65b0\u516c\u5f0f\u548c\u4e00\u81f4\u5207\u7ebf\u521a\u5ea6\uff0c\u786e\u8ba4\u65e0\u8bef\u540e\u518d\u8f6cFortran\uff1b<\/li>\n
- \u5355\u5355\u5143\u9a8c\u8bc1<\/strong>\uff1a\u7528C3D8R\u5355\u5355\u5143\u65bd\u52a0\u4f4d\u79fb\u8f7d\u8377\uff0c\u5bf9\u6bd4UMAT\u8f93\u51fa\u4e0e\u7406\u8bba\u89e3\/\u5185\u7f6e\u6a21\u578b\u7ed3\u679c\uff1b<\/li>\n
- \u9010\u6b65\u590d\u6742\u5316<\/strong>\uff1a\u5f39\u6027\u2192\u5f39\u5851\u6027\u2192\u786c\u5316\u2192\u591a\u8f74\u2192\u6709\u9650\u5e94\u53d8\uff0c\u6bcf\u4e00\u6b65\u90fd\u9a8c\u8bc1\uff1b<\/li>\n
- \u5584\u7528STATEV<\/strong>\uff1a\u5c06\u4e2d\u95f4\u53d8\u91cf\uff08\u5982\u8bd5\u5e94\u529b\u3001\u5851\u6027\u4e58\u5b50\uff09\u5b58\u5165STATEV\uff0c\u65b9\u4fbf\u540e\u5904\u7406\u8c03\u8bd5\u3002<\/li>\n<\/ol>\n
4.2 \u5e38\u89c1\u9677\u9631<\/h3>\n
- \n
- \u5e94\u529b\u5b58\u50a8\u987a\u5e8f<\/strong>\uff1aAbaqus\u4e2d\u76f4\u63a5\u5206\u91cf\u5728\u524d\uff0811,22,33\uff09\uff0c\u526a\u5207\u5206\u91cf\u5728\u540e\uff0812,13,23\uff09\uff0c\u4e14\u4e3a\u5de5\u7a0b\u526a\u5e94\u53d8\uff08\u03b3=2\u03b512<\/sub>\uff09\uff1b<\/li>\n
- \u5e73\u9762\u5e94\u529b\/\u5e94\u53d8<\/strong>\uff1aNTENS\u5728\u4e0d\u540c\u5355\u5143\u7c7b\u578b\u4e0b\u4e0d\u540c\uff083D\u5b9e\u4f53=6\uff0c\u5e73\u9762\u5e94\u53d8=4\uff0c\u5e73\u9762\u5e94\u529b=3\uff09\uff0c\u4ee3\u7801\u5fc5\u987b\u517c\u5bb9\uff1b<\/li>\n
- \u6709\u9650\u5e94\u53d8\u65cb\u8f6c<\/strong>\uff1aAbaqus\u5728\u8c03\u7528UMAT\u524d\u5df2\u5b8c\u6210\u5e94\u529b\u7684\u521a\u4f53\u65cb\u8f6c\uff0cUMAT\u4e2d\u53ea\u9700\u505acorotational\u5e94\u529b\u79ef\u5206\uff1b<\/li>\n
- \u521d\u59cb\u8c03\u7528<\/strong>\uff1a\u7b2c\u4e00\u4e2a\u589e\u91cf\u6b65\u5f00\u59cb\u65f6STRESS\u548cSTATEV\u5747\u4e3a\u96f6\uff08\u9664\u975e\u7528SDVINI\u521d\u59cb\u5316\uff09\uff0c\u4e0d\u8981\u5047\u8bbe\u5b83\u4eec\u6709\u503c\u3002<\/li>\n<\/ul>\n
4.3 \u8c03\u8bd5\u6280\u5de7<\/h3>\n
- \n
- \u4f7f\u7528
WRITE(*,*)<\/code> \u6216CALL XIT<\/code> \u8fdb\u884c\u65ad\u70b9\u8c03\u8bd5\uff08\u9700\u5728\u4ea4\u4e92\u6a21\u5f0f\u8fd0\u884c\uff09\uff1b<\/li>\n- \u5c06\u5173\u952e\u53d8\u91cf\u5199\u5165STATEV\uff0c\u5728Viewer\u4e2d\u67e5\u770b\u4e91\u56fe\u5206\u5e03\uff1b<\/li>\n
- \u5bf9\u6bd4\u5185\u7f6eMises\u5851\u6027\uff08*PLASTIC\uff09\u7ed3\u679c\uff0c\u9a8c\u8bc1UMAT\u5b9e\u73b0\u7684\u6b63\u786e\u6027\u3002<\/li>\n<\/ul>\n
\u56fe4 Abaqus\u5b98\u65b9\u6587\u6863\u4e2d\u7ebf\u6027\u7c98\u5f39\u6027UMAT\u793a\u4f8b\u7684\u5e94\u529b-\u65f6\u95f4\u54cd\u5e94\u66f2\u7ebf<\/figcaption><\/figure>\n 5. Abaqus\u5b9e\u73b0\uff1aJ2\u5f39\u5851\u6027UMAT\u5b8c\u6574\u4ee3\u7801<\/h2>\n
5.1 \u8f93\u5165\u6587\u4ef6\uff08INP\uff09\u5173\u952e\u7247\u6bb5<\/h3>\n
*MATERIAL, NAME=J2_PLASTIC\n*USER MATERIAL, CONSTANTS=5\n210000., 0.3, 350., 5000., 0.\n** E, nu, sigma_y0, H(isotropic), gamma(kinematic)\n*DEPVAR\n4\n** STATEV: 1-3=plastic strain components, 4=equivalent plastic strain<\/code><\/pre>\n5.2 UMAT Fortran\u4ee3\u7801\uff08\u6838\u5fc3\u90e8\u5206\uff09<\/h3>\n
SUBROUTINE UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,\n 1 RPL,DDSDDT,DRPLDE,DRPLDT,STRAN,DSTRAN,TIME,DTIME,\n 2 TEMP,DTEMP,PREDEF,DPRED,CMNAME,NDI,NSHR,NTENS,\n 3 NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,CELENT,\n 4 DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,JSTEP,KINC)\nC\n INCLUDE 'ABA_PARAM.INC'\n CHARACTER*80 CMNAME\n DIMENSION STRESS(NTENS),STATEV(NSTATV),\n 1 DDSDDE(NTENS,NTENS),DDSDDT(NTENS),DRPLDE(NTENS),\n 2 STRAN(NTENS),DSTRAN(NTENS),TIME(2),PREDEF(1),\n 3 DPRED(1),PROPS(NPROPS),COORDS(3),DROT(3,3),\n 4 DFGRD0(3,3),DFGRD1(3,3),JSTEP(4)\nC\nC --- \u8bfb\u53d6\u6750\u6599\u5e38\u6570 ---\n E = PROPS(1) ! \u5f39\u6027\u6a21\u91cf\n ANU = PROPS(2) ! \u6cca\u677e\u6bd4\n SIGY0 = PROPS(3) ! \u521d\u59cb\u5c48\u670d\u5e94\u529b\n HARD = PROPS(4) ! \u7b49\u5411\u786c\u5316\u6a21\u91cf\nC\nC --- \u5f39\u6027\u5e38\u6570 ---\n EG = E\/(2.*(1.+ANU)) ! \u526a\u5207\u6a21\u91cf G\n EK = E\/(3.*(1.-2.*ANU)) ! \u4f53\u79ef\u6a21\u91cf K\n ELAM = (EK - 2.*EG\/3.) ! Lame\u5e38\u6570 lambda\nC\nC --- \u521d\u59cb\u5316DDSDDE\u4e3a\u96f6 ---\n DO I=1,NTENS\n DO J=1,NTENS\n DDSDDE(I,J) = 0.\n END DO\n END DO\nC\nC --- \u5f39\u6027Jacobian ---\n DO I=1,NDI\n DO J=1,NDI\n DDSDDE(I,J) = ELAM\n END DO\n DDSDDE(I,I) = ELAM + 2.*EG\n END DO\n DO I=NDI+1,NTENS\n DDSDDE(I,I) = EG\n END DO\nC\nC --- \u5f39\u6027\u9884\u6d4b: \u66f4\u65b0\u5e94\u529b ---\n DO I=1,NTENS\n DO J=1,NTENS\n STRESS(I) = STRESS(I) + DDSDDE(I,J)*DSTRAN(J)\n END DO\n END DO\nC\nC --- \u8ba1\u7b97\u504f\u5e94\u529b\u548c\u7b49\u6548\u5e94\u529b ---\n SMISES = (STRESS(1)-STRESS(2))**2\n 1 + (STRESS(2)-STRESS(3))**2\n 2 + (STRESS(3)-STRESS(1))**2\n DO I=NDI+1,NTENS\n SMISES = SMISES + 6.*STRESS(I)**2\n END DO\n SMISES = SQRT(SMISES\/2.)\nC\nC --- \u5c48\u670d\u5224\u65ad ---\n EQPLAS = STATEV(4) ! \u7b49\u6548\u5851\u6027\u5e94\u53d8\n SYIELD = SIGY0 + HARD*EQPLAS ! \u5f53\u524d\u5c48\u670d\u5e94\u529b\nC\n IF (SMISES .GT. SYIELD) THEN\nC --- \u5851\u6027\u4fee\u6b63 (Return Mapping) ---\n DGMULT = (SMISES - SYIELD)\/(3.*EG + HARD)\n EQPLAS = EQPLAS + DGMULT\nC\nC \u66f4\u65b0\u5e94\u529b\n SHYDRO = (STRESS(1)+STRESS(2)+STRESS(3))\/3.\n DO I=1,NDI\n STRESS(I) = STRESS(I) - 3.*EG*DGMULT\n 1 *(STRESS(I)-SHYDRO)\/SMISES\n END DO\n DO I=NDI+1,NTENS\n STRESS(I) = STRESS(I) - 3.*EG*DGMULT\n 1 *STRESS(I)\/SMISES\n END DO\nC\nC \u66f4\u65b0\u72b6\u6001\u53d8\u91cf\n STATEV(4) = EQPLAS\nC\nC --- \u4e00\u81f4\u5207\u7ebf\u521a\u5ea6 (Consistent Tangent) ---\n EFFG = EG*(1. - 3.*EG*DGMULT\/SMISES)\n EFFG2 = 2.*EFFG\n EFFG3 = 1.5*EFFG2\n EFFHRD = 3.*EG*HARD\/(3.*EG+HARD) - EFFG3\nC (\u6b64\u5904\u7701\u7565\u5b8c\u6574\u7684DDSDDE\u66f4\u65b0\uff0c\u9700\u6309NTENS\u7ef4\u5ea6\u586b\u5145)\n END IF\nC\n RETURN\n END<\/code><\/pre>\n\u6ce8\u610f<\/strong>\uff1a\u4ee5\u4e0a\u4e3a\u6838\u5fc3\u903b\u8f91\u6846\u67b6\u3002\u5b8c\u6574\u751f\u4ea7\u4ee3\u7801\u9700\u8981\u5904\u7406NTENS=3\/4\/6\u7684\u5404\u79cd\u60c5\u51b5\u3001\u6b63\u786e\u5b9e\u73b0\u77e9\u9635\u4e58\u6cd5\u5faa\u73af\u3001\u4ee5\u53ca\u5b8c\u6574\u7684\u4e00\u81f4\u5207\u7ebf\u521a\u5ea6\u77e9\u9635\u3002\u5efa\u8bae\u53c2\u8003Abaqus Verification Manual\u4e2d\u7684UMAT\u9a8c\u8bc1\u7b97\u4f8b\uff08umatmst3.inp \/ umatmst3.f\uff09\u3002<\/div>\n5.3 \u9a8c\u8bc1\u6a21\u578b\u8bbe\u7f6e<\/h3>\n
\u6309\u7167\u5b98\u65b9\u6587\u6863\u5efa\u8bae\uff0c\u4f7f\u7528\u5355\u5355\u5143\u6a21\u578b\u8fdb\u884c\u9a8c\u8bc1\uff1a<\/p>\n
*HEADING\n UMAT J2 Plasticity - Single Element Verification\n*NODE\n1, 0., 0., 0.\n2, 1., 0., 0.\n3, 1., 1., 0.\n4, 0., 1., 0.\n5, 0., 0., 1.\n6, 1., 0., 1.\n7, 1., 1., 1.\n8, 0., 1., 1.\n*ELEMENT, TYPE=C3D8R\n1, 1,2,3,4,5,6,7,8\n*NSET, NSET=BOTTOM\n1,2,3,4\n*NSET, NSET=TOP\n5,6,7,8\n*BOUNDARY\nBOTTOM, 3, 3, 0.\nBOTTOM, 1, 1, 0.\nBOTTOM, 2, 2, 0.\n*MATERIAL, NAME=J2_PLASTIC\n*USER MATERIAL, CONSTANTS=4\n210000., 0.3, 350., 5000.\n*DEPVAR\n4\n*STEP\n*STATIC\n0.01, 1., 1e-8, 0.05\n*BOUNDARY\nTOP, 3, 3, 0.02\n*OUTPUT, FIELD\n*ELEMENT OUTPUT\nS, E, PEEQ\n*END STEP<\/code><\/pre>\n6. \u7ed3\u679c\u9a8c\u8bc1<\/h2>\n
\u5c06UMAT\u8ba1\u7b97\u7ed3\u679c\u4e0e\u7406\u8bba\u89e3\u5bf9\u6bd4\uff1a<\/p>\n
- \n
- \u5f39\u6027\u9636\u6bb5<\/strong>\uff08\u03b5 < \u03c3y<\/sub>\/E = 0.00167\uff09\uff1a\u03c3 = E\u00b7\u03b5 = 210000\u00d7\u03b5\uff0cUMAT\u8f93\u51fa\u5e94\u4e0e\u7406\u8bba\u5b8c\u5168\u4e00\u81f4\uff1b<\/li>\n
- \u5851\u6027\u9636\u6bb5<\/strong>\uff1a\u03c3 = \u03c3y<\/sub> + H\u00b7(\u03b5 – \u03c3y<\/sub>\/E)\uff0c\u5207\u7ebf\u6a21\u91cf\u4e3a Et<\/sub> = E\u00b7H\/(E+H) \u2248 4884 MPa\uff1b<\/li>\n
- \u5bf9\u6bd4\u5185\u7f6e\u6a21\u578b<\/strong>\uff1a\u5efa\u7acb\u76f8\u540c\u53c2\u6570\u7684*PLASTIC\u6a21\u578b\uff0c\u4e24\u8005\u5e94\u529b-\u5e94\u53d8\u66f2\u7ebf\u5e94\u5b8c\u5168\u91cd\u5408\u3002<\/li>\n<\/ul>\n
\u56fe5 UMAT\u5b9e\u9645\u5de5\u7a0b\u5e94\u7528\uff1a\u542b\u949d\u7f3a\u53e3\u7684\u7ea4\u7ef4\u91d1\u5c5e\u5c42\u5408\u677f\u635f\u4f24\u6a21\u578b\uff08\u6765\u6e90\uff1aAbaqus Example Problems Guide, SIMACAEEXARefMap\/simaexa-c-damagefailfml.htm\uff09<\/figcaption><\/figure>\n \u9a8c\u8bc1\u901a\u8fc7\u540e\uff0c\u5373\u53ef\u5c06UMAT\u5e94\u7528\u4e8e\u5b9e\u9645\u5de5\u7a0b\u6a21\u578b\u3002\u4e0a\u56fe\u5c55\u793a\u4e86Abaqus\u5b98\u65b9\u793a\u4f8b\u4e2d\u4f7f\u7528UMAT\u5b9e\u73b0\u7684\u7ea4\u7ef4\u91d1\u5c5e\u5c42\u5408\u677f\u6e10\u8fdb\u635f\u4f24\u5206\u6790\uff0c\u4f53\u73b0\u4e86UMAT\u5728\u5904\u7406\u590d\u6742\u6750\u6599\u5931\u6548\u884c\u4e3a\u65b9\u9762\u7684\u5f3a\u5927\u80fd\u529b\u3002<\/p>\n
7. \u603b\u7ed3<\/h2>\n
UMAT\u5b50\u7a0b\u5e8f\u5f00\u53d1\u7684\u6838\u5fc3\u8981\u70b9\u56de\u987e\uff1a<\/p>\n
- \n
- \u7406\u89e3\u8c03\u7528\u673a\u5236<\/strong>\uff1aUMAT\u5728\u6bcf\u4e2a\u6750\u6599\u79ef\u5206\u70b9\u88ab\u8c03\u7528\uff0c\u5fc5\u987b\u8fd4\u56de\u66f4\u65b0\u540e\u7684\u5e94\u529b\u3001\u72b6\u6001\u53d8\u91cf\u548cJacobian\u77e9\u9635\uff1b<\/li>\n
- \u638c\u63e1\u5e94\u529b\u66f4\u65b0\u7b97\u6cd5<\/strong>\uff1a\u5f39\u6027\u9884\u6d4b-\u5851\u6027\u4fee\u6b63\uff08Return Mapping\uff09\u662f\u6700\u7ecf\u5178\u7684\u6846\u67b6\uff1b<\/li>\n
- \u4e00\u81f4\u5207\u7ebf\u521a\u5ea6\u662f\u5173\u952e<\/strong>\uff1aDDSDDE\u7684\u51c6\u786e\u6027\u76f4\u63a5\u51b3\u5b9aNewton\u8fed\u4ee3\u6536\u655b\u901f\u5ea6\uff1b<\/li>\n
- \u5355\u5355\u5143\u9a8c\u8bc1\u4e0d\u53ef\u7701\u7565<\/strong>\uff1a\u8fd9\u662f\u5b98\u65b9\u6587\u6863\u7684\u5f3a\u70c8\u5efa\u8bae\uff0c\u4e5f\u662f\u5b9e\u6218\u4e2d\u7684\u94c1\u5f8b\uff1b<\/li>\n
- \u6ce8\u610f\u5b58\u50a8\u7ea6\u5b9a<\/strong>\uff1a\u5e94\u529b\/\u5e94\u53d8\u5206\u91cf\u987a\u5e8f\u3001\u5de5\u7a0b\u526a\u5e94\u53d8\u3001NTENS\u968f\u5355\u5143\u7c7b\u578b\u53d8\u5316\u3002<\/li>\n<\/ol>\n
UMAT\u7684\u5b66\u4e60\u66f2\u7ebf\u786e\u5b9e\u9661\u5ced\uff0c\u4f46\u4e00\u65e6\u638c\u63e1\uff0c\u5b83\u5c06\u6781\u5927\u5730\u6269\u5c55\u4f60\u7684\u4eff\u771f\u80fd\u529b\u8fb9\u754c\u3002\u4ece\u91d1\u5c5e\u6210\u5f62\u5230\u590d\u5408\u6750\u6599\u635f\u4f24\uff0c\u4ece\u751f\u7269\u529b\u5b66\u5230\u5730\u8d28\u6750\u6599\uff0c\u51e0\u4e4e\u6240\u6709\u524d\u6cbf\u4eff\u771f\u7814\u7a76\u90fd\u79bb\u4e0d\u5f00\u7528\u6237\u5b50\u7a0b\u5e8f\u3002<\/p>\n
\u53c2\u8003\u6587\u732e<\/h2>\n
[1] Abaqus Analysis User’s Guide, “UMAT – User subroutine to define a material’s mechanical behavior”, SIMACAESUBRefMap\/simasub-c-umat.htm.[2] Abaqus Verification Manual, “UMAT and UHYPER verification problems”, SIMACAEVERRefMap\/simaver-c-umatuhyper.htm.<\/p>\n[3] \u9ec4\u6d74\u7b49, “\u57fa\u4e8eABAQUS\u7684\u5f39\u5851\u6027\u6750\u6599UMAT\u5b50\u7a0b\u5e8f\u5f00\u53d1\u4e0e\u9a8c\u8bc1”, CSDN Blog, 2025. \u4ecb\u7ecd\u4e86J2\u5f39\u5851\u6027UMAT\u7684\u5b8c\u6574\u5b9e\u73b0\u6d41\u7a0b\u548c\u5e94\u529b\u66f4\u65b0\u7b97\u6cd5\u3002<\/p>\n
[4] jjyxy, “\u8c08\u6750\u6599\u529b\u5b66\u884c\u4e3a\u7814\u7a76\u7684\u6807\u914d\u2014ABAQUS UMAT”, CSDN Blog. \u7efc\u8ff0\u4e86UMAT\u5728\u6750\u6599\u529b\u5b66\u7814\u7a76\u4e2d\u7684\u5b9a\u4f4d\u548c\u5e94\u7528\u573a\u666f\u3002<\/p>\n
[5] Simo J C, Hughes T J R. “Computational Inelasticity”, Springer, 1998. \u8ba1\u7b97\u5851\u6027\u529b\u5b66\u7684\u7ecf\u5178\u6559\u6750\uff0c\u7cfb\u7edf\u9610\u8ff0\u4e86Return Mapping\u7b97\u6cd5\u7684\u6570\u5b66\u57fa\u7840\u3002<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
Abaqus UMAT\u5b50\u7a0b\u5e8f\u5f00\u53d1\u5165\u95e8\uff1a\u4ece\u7406\u8bba\u5230J2\u5f39\u5851\u6027\u672c\u6784\u5b9e\u73b0 \u6458\u8981\uff1aUMAT\uff08User Material\uff09 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-381","post","type-post","status-publish","format-standard","hentry","category-abaqus"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/numsimlab.com\/index.php?rest_route=\/wp\/v2\/posts\/381","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/numsimlab.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/numsimlab.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/numsimlab.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/numsimlab.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=381"}],"version-history":[{"count":1,"href":"https:\/\/numsimlab.com\/index.php?rest_route=\/wp\/v2\/posts\/381\/revisions"}],"predecessor-version":[{"id":382,"href":"https:\/\/numsimlab.com\/index.php?rest_route=\/wp\/v2\/posts\/381\/revisions\/382"}],"wp:attachment":[{"href":"https:\/\/numsimlab.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numsimlab.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numsimlab.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- \u638c\u63e1\u5e94\u529b\u66f4\u65b0\u7b97\u6cd5<\/strong>\uff1a\u5f39\u6027\u9884\u6d4b-\u5851\u6027\u4fee\u6b63\uff08Return Mapping\uff09\u662f\u6700\u7ecf\u5178\u7684\u6846\u67b6\uff1b<\/li>\n
- \u5851\u6027\u9636\u6bb5<\/strong>\uff1a\u03c3 = \u03c3y<\/sub> + H\u00b7(\u03b5 – \u03c3y<\/sub>\/E)\uff0c\u5207\u7ebf\u6a21\u91cf\u4e3a Et<\/sub> = E\u00b7H\/(E+H) \u2248 4884 MPa\uff1b<\/li>\n
- \u5e73\u9762\u5e94\u529b\/\u5e94\u53d8<\/strong>\uff1aNTENS\u5728\u4e0d\u540c\u5355\u5143\u7c7b\u578b\u4e0b\u4e0d\u540c\uff083D\u5b9e\u4f53=6\uff0c\u5e73\u9762\u5e94\u53d8=4\uff0c\u5e73\u9762\u5e94\u529b=3\uff09\uff0c\u4ee3\u7801\u5fc5\u987b\u517c\u5bb9\uff1b<\/li>\n
- \u5355\u5355\u5143\u9a8c\u8bc1<\/strong>\uff1a\u7528C3D8R\u5355\u5355\u5143\u65bd\u52a0\u4f4d\u79fb\u8f7d\u8377\uff0c\u5bf9\u6bd4UMAT\u8f93\u51fa\u4e0e\u7406\u8bba\u89e3\/\u5185\u7f6e\u6a21\u578b\u7ed3\u679c\uff1b<\/li>\n
- \u5bf9\u4e8e\u8f7b\u5fae\u975e\u5bf9\u79f0\u60c5\u51b5\uff08\u5982\u5c0f\u6469\u64e6\u89d2\uff09\uff0c\u53ef\u4f7f\u7528\u5bf9\u79f0\u8fd1\u4f3c\u4ee5\u964d\u4f4e\u8ba1\u7b97\u6210\u672c\u3002<\/li>\n<\/ul>\n
- \u5c48\u670d\u5224\u65ad<\/strong>\uff1a\u82e5 f(\u03c3trial<\/sub>) \u2264 0<\/em>\uff0c\u63a5\u53d7\u5f39\u6027\u6b65\uff1b\u5426\u5219\u8fdb\u5165\u5851\u6027\u4fee\u6b63\uff1b<\/li>\n
- \u591a\u7269\u7406\u573a\u8026\u5408<\/strong>\uff1a\u70ed-\u529b-\u5316\u5b66\u8026\u5408\u3001\u8f90\u7167\u635f\u4f24\u6f14\u5316\u7b49\u590d\u6742\u4ea4\u4e92\u884c\u4e3a\uff1b<\/li>\n