{"id":8888,"date":"2023-05-26T03:32:36","date_gmt":"2023-05-25T19:32:36","guid":{"rendered":"https:\/\/www.andrewsun.net\/panta_rhei\/?p=8888"},"modified":"2023-06-02T02:24:12","modified_gmt":"2023-06-01T18:24:12","slug":"%e5%85%b3%e4%ba%8e%e6%9c%ac%e6%9e%84%e5%85%b3%e7%b3%bb","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8888","title":{"rendered":"\u5173\u4e8e\u201c\u672c\u6784\u5173\u7cfb\u201d"},"content":{"rendered":"<div class=\"kcite-section\" 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class=\"wp-block-heading\">1. 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Ferry\u7684\u7ecf\u5178\u6559\u6750\u3002\u4ed6\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cthe relations between stress, strain, and their time dependences\u201d\u3002\u8fd9\u6bd4\u76f4\u63a5\u8bf4\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u591a\u4e86\u4e2a\u65f6\u95f4\u4f9d\u8d56\u6027\u3002\u8fd9\u5e76\u4e0d\u662f\u4e3a\u66f4\u51c6\u786e\u5730\u63cf\u8ff0\u672c\u6784\u5173\u7cfb\u7684\u610f\u4e49\u672c\u8eab\u4f5c\u51fa\u7684\u9650\u5b9a\uff0c\u800c\u662f\u4e3a\u4e86\u5f3a\u8c03\u6750\u6599\u7c98\u5f39\u6027\u7684\u53ef\u80fd\u6027\u3002\u6240\u4ee5\u5f52\u6839\u7ed3\u5e95\uff0c\u5728\u201c\u4f55\u8c13\u672c\u6784\u5173\u7cfb\u201d\u8fd9\u4ef6\u4e8b\u4e0a\uff0c Ferry\u76f8\u5f53\u4e8e\u7b80\u5355\u8bf4\u4e86\u53e5\u201c\u5c31\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u201d\u3002<\/p>\n\n\n\n<p>Ferry\u7684\u4e66\u662f\u6d41\u4f20\u975e\u5e38\u5e7f\u7684\u3001\u53e3\u7891\u7ecf\u4e45\u4e0d\u8870\u7684\uff0c\u7ecf\u5178\u4e2d\u7684\u7ecf\u5178\u3002\u4f46\u662f\u4ed6\u5173\u4e8e\u672c\u6784\u5173\u7cfb\u7684\u7b80\u5355\u63cf\u8ff0\uff0c\u867d\u7136\u5fc5\u4e0d\u4ee3\u8868\u4ed6\u672c\u4eba\u7406\u89e3\u5c31\u771f\u8fd9\u4e48\u7b80\u5355\uff0c\u5374\u88ab\u8bb8\u591a\u4e5f\u8bb8\u53ea\u770b\u4e00\u672c\u4e66\u5b66\u6d41\u53d8\u5b66\uff0c\u8fd8\u5f88\u8ba4\u771f\u5b66\u7684\u5b66\u751f\u8bb0\u4e3a\u6559\u6761\u3002\u4f8b\u5982\uff0cM. Rao\u5199\u7684\u4e66\uff0c\u5c31\u539f\u6837\u7167\u642cFerry\u7684\u8bf4\u6cd5\uff0c\u5e76\u6807\u6ce8\u4e86\u5bf9Ferry\u7684\u4e66\u7684\u5f15\u7528\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u975e\u8981\u4fdd\u6301\u201c\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u201d\u8fd9\u79cd\u53d9\u8ff0\u6846\u67b6\u6765\u8bb2\u201c\u4f55\u8c13\u672c\u6784\u5173\u7cfb\u201d\u90a3\u81f3\u5c11\u5e94\u8be5\u52a0\u4ec0\u4e48\u6837\u7684\u9650\u5b9a\u6027\u8bf4\u660e\u5462\uff1f\u4e24\u65b9\u9762\u3002\u4e00\u662f\uff0c\u6240\u8c13\u5e94\u529b\u548c\u5e94\u53d8\u90fd\u662f\u5f20\u91cf\uff0c\u5b83\u4eec\u6bcf\u4e2a\u67099\u4e2a\u91cf\u3002\u4f46\u8fd9\u4ef6\u4e8b\u8981\u4ee5\u4e0d\u51fa\u73b0\u201c\u5f20\u91cf\u201d\u8fd9\u4e2a\u6982\u5ff5\u7684\u65b9\u5f0f\u8bf4\u51fa\u6765\uff0c\u8ba9\u4eba\u4e00\u4e0b\u5b50\u5c31\u660e\u767d\u4e3a\u4ec0\u4e48\u5b83\u4eec\u662f\u8fd9\u79cd\u91cf\uff0c\u81f3\u5c11\u53cd\u6b63\u4e0d\u662f\u6807\u91cf\uff08\u5f88\u96be\uff09\uff1b\u4e8c\u662f\uff0c\u5e94\u529b\u548c\u5e94\u53d8\u90fd\u662f\u573a\uff0c\u5b83\u4eec\u7684\u201c\u53d6\u503c\u201d\u65e2\u4f9d\u8d56\u7a7a\u95f4\u4f4d\u7f6e\u53c8\u4f9d\u8d56\u65f6\u95f4\u3002\u8fd9\u5012\u4e0d\u662f\u4ec0\u4e48\u5f88\u96be\u7406\u89e3\u7684\u70b9\u3002\u5982\u679c\u8fd9\u4e24\u4e2a\u90fd\u660e\u786e\u4e86\uff0c\u90a3\u5c31\u53ef\u4ee5\u6210\u529f\u7684\u8ba9\u4eba\u5bf9\u201c\u65cb\u8f6c\u6d41\u53d8\u4eea\u8f6f\u4ef6\u6240\u8f93\u51fa\u7ed9\u4f60\u7684\u6807\u91cf\u503c\u5e94\u529b\u548c\u5e94\u53d8\u5230\u5e95\u662f\u5565\u201d\u4ea7\u751f\u8d28\u7591\uff1b\u8fd9\u4e2a\u8d28\u7591\u624d\u662f\u6b63\u5f0f\u5b66\u4e60\u6d41\u53d8\u5b66\u7684\u5f00\u7aef\u2014\u2014\u5982\u679c\u4f60\u6070\u5de7\u5c31\u662f\u90a3\u79cd\u6ca1\u5b66\u6d41\u53d8\u5b66\u5c31\u7167\u7740\u6587\u732e\u6216\u5e08\u5144\u5e08\u59d0\u7684\u201c\u6307\u5bfc\u201d\u505a\u4e86\u5927\u91cf\u65cb\u8f6c\u6d41\u53d8\u4eea\u5b66\u6d4b\u8bd5\u7684\u5b66\u751f\u7684\u8bdd\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.1 \u5e94\u529b\u3001\u5e94\u53d8\u90fd\u662f\u573a\u51fd\u6570<\/h4>\n\n\n\n<p>\u6211\u4eec\u5148\u770b\u6697\u793a\u4e86\u7b2c\u4e8c\u4e2a\u70b9\u7684\u8bf4\u6cd5\u3002<\/p>\n\n\n\n<p>\u6709\u672c\u4e66Yamaguchi (2008)\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cthe relationship between the internal stress and the applied strain\u201d\uff0c\u8fd9\u4e2a\u201cinternal\u201d\u5c31\u5f88\u9e21\u8d3c\u3002\u4e0d\u5c31\u662f\u60f3\u6697\u6233\u6233\u5730\u5f3a\u8c03\u4e00\u4e0b\u201c\u5b83\u4eec\u90fd\u662f\u573a\u54e6\u201d\u5417\uff1f<\/p>\n\n\n\n<p>\u8fd8\u6709\u4e00\u672c\u4e66Mewis &amp; Wagner (2012)\u8bf4\uff0c\u672c\u6784\u5173\u7cfb\u662f\u201cintrinsic relation between the stresses and kinematics\u201d\u3002\u5728\u672c\u5173\u6ce8\u7126\u70b9\u4e0b\uff0c\u8fd9\u53e5\u8bdd\u65e0\u975e\u7ed9\u4f60\u6765\u4e86\u4e2a\u201ckinematics\u201d\u8fd9\u8bcd\uff0c\u597d\u50cf\u8bf4\u5f97\u60ac\u4e00\u70b9\u513f\uff0c\u80fd\u8ba9\u4f60\u4e0d\u6562\u786e\u5b9a\u4f5c\u8005\u662f\u4e0d\u662f\u80a4\u6d45\u7684\u3002<\/p>\n\n\n\n<p>\u7c7b\u4f3c\u4e0a\u8ff0\u8fd9\u822c\u7684\u201c\u514d\u8d23\u5f0f\u201d\u7684\u4fee\u9970\u9650\u5b9a\uff0c\u5bf9\u521d\u5b66\u8005\u66f4\u51c6\u786e\u5730\u7406\u89e3\u4e00\u70b9\u7528\u5904\u90fd\u6ca1\u6709\uff1b\u5728\u521d\u5b66\u8005\u90a3\u91cc\u4e0a\u8ff0\u8fd9\u79cd\u505a\u6cd5\u76f8\u5f53\u4e8e\u7b80\u5355\u8bf4\u672c\u6784\u5173\u7cfb\u5c31\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.2 \u5e94\u529b\u3001\u5e94\u53d8\u662f\u5f20\u91cf\uff08\u4f46\u4e0d\u660e\u8bf4\uff09<\/h4>\n\n\n\n<p>\u5728\u4e00\u53e5\u8bdd\u4e2d\u4e0d\u660e\u8bf4\u5f20\u91cf\u53c8\u5f3a\u8c03\u51fa\u8fd9\u4e00\u610f\u4e49\u7684\u96be\u5ea6\u786e\u5b9e\u6709\u70b9\u513f\u5927\u3002\u6211\u53cd\u6b63\u662f\u505a\u4e0d\u5230\u7684\u3002\u6211\u7ffb\u7684\u4e66\uff0c\u6709\u5f88\u591a\u4e5f\u505a\u4e0d\u5230\u3002\u6240\u4ee5\u5b9e\u9645\u4e0a\u5f88\u591a\u4e66\u5e72\u8106\u5728\u53e5\u5b50\u4e2d\u51fa\u73b0\u201c\u5f20\u91cf\u201d\u8fd9\u8bcd\u4e86\u3002\u5728\u8fd9\u4e9b\u4e66\u5f53\u4e2d\uff0c\u6709\u4e9b\u662f\u5728\u4ecb\u7ecd\u5b8c\u5e94\u529b\u5f20\u91cf\u4e4b\u524d\u5c31\u8bb2\u672c\u6784\u5173\u7cfb\u662f\u4ec0\u4e48\u7684\u8bdd\uff0c\u6240\u4ee5\u201c\u5f20\u91cf\u201d\u4e00\u8bcd\u7684\u51fa\u73b0\u662f\u63d0\u524d\u7684\u3002\u800c\u4e14\u4e00\u4e9b\u5c31\u662f\u5230\u4e86\u8bb2\u672c\u6784\u65b9\u7a0b\u7684\u90e8\u5206\u624d\u8bf4\u4ec0\u4e48\u662f\u672c\u6784\u5173\u7cfb\uff0c\u4f46\u8fd9\u79cd\u60c5\u51b5\u4e0b\u672c\u6587\u5173\u6ce8\u7684\u95ee\u9898\u5c31\u4e0d\u5b58\u5728\u4e86\uff0c\u56e0\u4e3a\u90fd\u5230\u4e86\u8bb2\u672c\u6784\u65b9\u7a0b\u7684\u7ae0\u8282\u4e86\uff0c\u90a3\u5e94\u529b\u5f20\u91cf\u3001\u8fd0\u52a8\u5b66\u3001\u5b88\u6052\u5f8b\u3001\u8fd0\u52a8\u65b9\u7a0b\u7b49\u77e5\u8bc6\u5e94\u8be5\u90fd\u8bb2\u8fc7\u4e86\u3002<\/p>\n\n\n\n<p>\u4e00\u672c\u6d41\u53d8\u5b66\u7684\u5de8\u7ecf\u5178\u7684\u6559\u6750Barnes, Hutton and Walters (1989)\u8bf4\uff0c\u672c\u6784\u5173\u7cfb\u8054\u7cfb\u7684\u662f\u201csuitably defined stress and deformation variables\u201d\u3002\u8fd9\u91cc\u7684suitably defined\uff0c\u80fd\u4e0d\u80fd\u88ab\u8bdf\u75c5\u4e3a\u201c\u5bf9\u521d\u5b66\u8005\u5b8c\u5168\u65e0\u7528\u7684\u514d\u8d23\u5f0f\u4fee\u9970\u201d\u5462\uff1f\u6211\u89c9\u5f97\u4e0d\u80fd\u8fd9\u4e48\u8bf4\u3002\u56e0\u4e3a\u5b83\u51c6\u786e\u63d0\u51fa\u4e86\u4e00\u4e2a\u6709\u6559\u5b66\u6548\u679c\u7684\u7591\u95ee\uff1a\u600e\u6837define\u624d\u53ebsuitably define\uff1f\u5e26\u7740\u8fd9\u4e2a\u7591\u95ee\u53bb\u5b66\u4e60\u5e94\u529b\u5f20\u91cf\u548c\u5e94\u53d8\u5f20\u91cf\uff0c\u80fd\u81ea\u7136\u5730\u7406\u89e3\u4e3a\u5565\u5b83\u4eec\u662f\u5f20\u91cf\uff0c\u800c\u4e0d\u662f\u5929\u6389\u4e0b\u6765\u6211\u5c31\u662f\u8981\u7528\u5f20\u91cf\u53bb\u63cf\u8ff0\u5b83\u4eec\u3002\u8fd9\u662f\u6211\u627e\u5230\u7684\uff0c\u552f\u4e00\u4e00\u4e2a\uff0c\u60f3\u5f3a\u8c03\u5e94\u529b\u548c\u5e94\u53d8\u662f\u5f20\u91cf\uff0c\u5374\u4e0d\u7528\u51fa\u73b0\u5f20\u91cf\u4e00\u8bcd\u7684\u6210\u529f\u53d9\u8ff0\uff01\u5b83\u4e5f\u9884\u5148\u56de\u7b54\u4e86\u201c\u4e3a\u5565\u975e\u8981\u662f\u5f20\u91cf\u5462\u201d\u2014\u2014\u56e0\u4e3a\u8fd9\u6837define\u624dsuitable\uff01<\/p>\n\n\n\n<p>\u53e6\u4e00\u4e2a\u4e5f\u6ca1\u51fa\u73b0\u5f20\u91cf\u4e00\u8bcd\uff0c\u4f46\u4e0d\u592a\u6210\u529f\u7684\u53d9\u8ff0\uff0c\u6765\u81ea\u4e00\u4e2a\u4e5f\u5f88\u91cd\u91cf\u7ea7\u7684\u4f5c\u8005Tschoegl (1989)\u3002\u4ed6\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201crelation between a general deformation and a general set of forces\u201d\u3002\u8fd9\u5c31\u771f\u5730\u53ef\u4ee5\u88ab\u8bdf\u75c5\u4e3a\u201c\u5bf9\u521d\u5b66\u8005\u5b8c\u5168\u65e0\u7528\u7684\u514d\u8d23\u5f0f\u4fee\u9970\u201d\u4e86\u3002\u4f46\u662f\u8fd9\u672c\u4e66\u5728\u540e\u9762\u4ecd\u7136\u5f88\u5b8c\u6574\u5730\u7ed9\u8bfb\u8005\u5448\u73b0\u4e86\u201c\u672c\u6784\u5173\u7cfb\u201d\u7684\u51c6\u786e\u610f\u4e49\uff1b\u5b83\u53ea\u662f\u6ca1\u5728\u201c\u4e00\u53e5\u8bdd\u201d\u95ee\u9898\u4e0a\u7cbe\u76ca\u6c42\u7cbe\u800c\u5df2\u3002\u8fd9\u672c\u4e66\u5728\u5c55\u793a\u201c\u672c\u6784\u5173\u7cfb\u4e2d\u7684\u5e94\u529b\u548c\u5e94\u53d8\u4e3a\u4f55\u975e\u5f97\u662f\u5f20\u91cf\u201d\u8fd9\u4e00\u4efb\u52a1\u4e0a\u505a\u4e86\u4e00\u4e2a\u7ecf\u5178\u7684\u4e3e\u4f8b\u8bf4\u660e\u3002\u8fd9\u79cd\u4e3e\u4f8b\u8bf4\u660e\u65b9\u5f0f\u88ab\u591a\u4e2a\u6559\u79d1\u4e66\u91c7\u7528\uff0c\u6bd4\u5982Riande et al. (2000)\u3002<\/p>\n\n\n\n<p>\u5176\u4ed6\u4e66\u4e2d\u7684\u53d9\u8ff0\u5c31\u662f\u90fd\u51fa\u73b0\u4e86tensor\u4e00\u8bcd\u7684\u3002\u6bd4\u5982\u53e6\u4e00\u4e2a\u4f17\u4eba\u53e3\u4e2d\u7684\u5de8\u578b\u7ecf\u5178Bird, Armstrong &amp; Hassager (1987)\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cexpression of the stress tensor in terms of some kinematic tensors\u201d\u3002<\/p>\n\n\n\n<p>\u518d\u53e6\u4e00\u4e2a\u5de8\u578b\u7ecf\u5178Truesdell &amp; Noll (2004)\u8bf4\u672c\u6784\u65b9\u7a0b\u201crelate the stress tensor and the heat-flux vector to the motion\u201d\u3002\u8fd9\u91cc\u4f5c\u8005\u4e0d\u9650\u4e8e\u529b\u5b66\u672c\u6784\u65b9\u7a0b\uff0c\u4e14\u201c\u5e94\u53d8\u201d\u8fd9\u4ef6\u4e8b\u76f4\u63a5\u7528\u4e00\u4e2a\u201cthe motion\u201d\u6307\u4ee3\u4e86\uff0c\u6709\u591fgeneral\u3002\u8fd9\u91cc\u8ddf\u524d\u6587\u6307\u51fa\u53d1\u7684Malkin\u53ea\u660e\u786e\u5e94\u529b\u4f5c\u4e3a\u573a\u662f\u201cat a point\u201d\uff0c\u5374\u4e0d\u660e\u8bf4\u8fd0\u52a8\u5b66\u4e0a\u7684at a point\u662f\u5f02\u66f2\u540c\u5de5\u4e4b\u5999\uff0c\u4f46\u8fd9\u91cc\u6211\u4ecd\u5148\u4e0d\u8be6\u7ec6\u89e3\u91ca\u8fd9\u4ef6\u4e8b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.3 \u672c\u6784\u5173\u7cfb\u662f\u6750\u6599\u5bf9\u5916\u573a\u7684\u54cd\u5e94<\/h4>\n\n\n\n<p>\u672c\u6784\u5173\u7cfb\u7684\u6982\u5ff5\u8fd8\u6709\u4e00\u4e2a\u4e00\u822c\u6027\u7684\u601d\u60f3\u5c31\u662f\uff0c\u5b83\u5f3a\u8c03\u4e00\u4e2a\u6750\u6599\u4f5c\u4e3a\u4f53\u7cfb\uff0c\u5b83\u5bf9\u73af\u5883\u53d8\u5316\u7684\u54cd\u5e94\uff0c\u7c7b\u4f3c\u4e8e\u201c\u4fe1\u53f7\u4e0e\u7cfb\u7edf\u201d\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u4f5c\u51fa\u8fd9\u79cd\u5f3a\u8c03\u7684\u53d9\u8ff0\u4e5f\u5f88\u591a\u3002Findley, Lai &amp; Onaran (1976)\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201creaction to the external excitations\u201d\u3002Truesdell (1968)\u8bf4\u672c\u6784\u5173\u7cfb\u201cspecify the nature of their response to their surroundings\u201d\u3002<\/p>\n\n\n\n<p>\u8fd9\u79cd\u523a\u6fc0-\u54cd\u5e94\u7684\u7ed3\u6784\uff0c\u6bd4\u4ec5\u8bf4\u662f\u201c\u4ec0\u4e48\u4e0e\u4ec0\u4e48\u7684\u5173\u7cfb\u201d\u66f4\u8d34\u8fd1\u201c\u672c\u6784\u5173\u7cfb\u201d\u7684\u539f\u59cb\u601d\u60f3\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u672c\u6784\u5173\u7cfb\u7684\u7279\u6b8a\u4e0e\u666e\u9002<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">2.1 \u672c\u6784\u5173\u7cfb\u662f\u63cf\u8ff0\u6750\u6599\u7684\u7279\u6b8a\u6027\u7684<\/h4>\n\n\n\n<p>\u8fd9\u4e00\u70b9\u5f88\u591a\u4e66\u90fd\u80fd\u987a\u5229\u5730\u5730\u4f20\u8fbe\u3002<\/p>\n\n\n\n<p>\u4f46\u5f88\u591a\u662f\u662f\u8fd9\u4e48\u8bf4\u7684\uff1a\u5b88\u6052\u65b9\u7a0b\u5217\u5b8c\u4e86\uff0c\u65b9\u7a0b\u4e0d\u5c01\u95ed\uff0c\u6240\u4ee5\u9700\u8981\u672c\u6784\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u7136\u540e\u7ffb\u904d\u5168\u4e66\u597d\u50cf\u4e5f\u5c31\u53ea\u8fd9\u4e48\u8bf4\u4e86\uff0c\u6ca1\u6709\u518d\u4ece\u7269\u7406\u4e0a\u8bf4\u8fd9\u4ef6\u4e8b\u3002\u597d\u50cf\u8bf4\u672c\u6784\u5173\u7cfb\u7684\u610f\u4e49\u5c31\u53ea\u662f\u6570\u5b66\u4e0a\u610f\u4e49\uff1b\u4e00\u5207\u662f\u201c\u4e3a\u4e86\u9898\u76ee\u80fd\u505a\u5f97\u51fa\u6765\u201d\uff0c\u5f97\u5206\u5c31\u884c\uff0c\u95ee\u90a3\u4e48\u591a\u5e72\u4ec0\u4e48\uff0c\u4e00\u79cd\u505a\u9898\u5bb6\u601d\u7ef4\u3002<\/p>\n\n\n\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u5b88\u6052\u5f8b\u548c\u8fd0\u52a8\u65b9\u7a0b\u4e5f\u662f\u4eba\u5bf9\u81ea\u7136\u7684\u5047\u8bf4\u6027\u516c\u8bbe\uff0c\u662f\u53ef\u9519\u7684\u3002\u65e2\u7136\u73b0\u5728\u6211\u4eec\u9ed8\u8ba4\u5b83\u6b63\u786e\u4e86\uff0c\u90a3\u53ea\u80fd\u8bf4\u5217\u5b8c\u4e86\u4e4b\u540e\u65b9\u7a0b\u90fd\u4e0d\u5c01\u95ed\u662f\u4e0d\u662f\u76f8\u5f53\u4e8e\u6b63\u9762\u5730\u8868\u8fbe\u4e86\u8fd9\u5957\u7269\u7406\u7406\u8bba\u7684\u4e00\u79cd\u4e3b\u89c2\u7684\u89c2\u70b9\uff1f\u76f4\u8bf4\u4e86\u5427\uff1a\u5149\u77e5\u9053\u5b88\u6052\u5f8b\u9884\u6d4b\u4e0d\u4e86\u8fd0\u52a8\uff0c\u8fd9\u662f\u8fd9\u5957\u7269\u7406\u7406\u8bba\u672c\u8eab\u5c31\u8ba4\u4e3a\u7684\u3002\u6570\u5b66\u4e0a\u65b9\u7a0b\u5c01\u95ed\u4e0d\u4e86\uff0c\u53ea\u80fd\u8bf4\u4f60\u7528\u5bf9\u4e86\u6570\u5b66\u53bb\u63cf\u8ff0\u4f60\u7684\u7269\u7406\u89c2\u70b9\uff0c\u6570\u5b66\u4e0a\u7684\u6548\u679c\u4e0e\u4f60\u7269\u7406\u89c2\u70b9\u76f8\u7b26\u4e86\u800c\u5df2\u3002\u800c\u4e0d\u662f\u8bf4\u6211\u975e\u8981\u5728\u6570\u5b66\u4e0a\u8fd9\u4e48\u5217\u5f0f\u5b50\uff0c\u7136\u540e\u53d1\u73b0\u8bf4\u54ce\u54df\u4e0d\u5c01\u95ed\uff0c\u4e4b\u524d\u8fd8\u6ca1\u60f3\u5230\uff0c\u6240\u4ee5\u53ea\u597d\u8ba4\u4e3a\u8fd9\u5c31\u662f\u5c01\u95ed\u4e0d\u4e86\u7684\u3002\u5dee\u52b2\u7684\u6559\u79d1\u4e66\uff0c\u5c31\u662f\u5728\u8fd9\u79cd\u5c42\u9762\u4e0a\u8bb2\u8bdd\u4e0d\u5c0f\u5fc3\u3002<\/p>\n\n\n\n<p>\u5728\u8fd9\u4e00\u70b9\u4e0a\u6bd4\u8f83\u6e05\u6670\u7684\u8868\u8ff0\u6709Tschoegl (1989)\u3002\u4ed6\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cindependent of the size or shape (i.e. geometry) of the body\u201d\/\u201cdepend only on its material nature\u201d\u3002<\/p>\n\n\n\n<p>\u66f4\u9732\u9aa8\u7684\u8868\u8ff0\u8981\u6570Truesdell (1980)\uff1aThe essence of a constitutive relation is that it defines a material. Whatever else happens to a body of that material, it cannot get away from that relation, which cleaves to it like a Doppelganger. That is a difference between a constitutive relation, which is a theoretical concept, and an empirical formula developed by measurement.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.2 \u672c\u6784\u5173\u7cfb\u7684\u4e00\u822c\u6027\u662f\u6307\u5b83\u63cf\u8ff0\u7684\u662f\u6750\u6599\u5728\u4efb\u610f\u6d41\u52a8\u7684\u54cd\u5e94<\/h4>\n\n\n\n<p>\u8fd9\u662f\u6211\u89c9\u5f97\u503c\u5f97\u66f4\u591a\u5730\u5f3a\u8c03\u7684\u4e00\u70b9\u3002\u6211\u4eec\u5e0c\u671b\u62e5\u6709\u7684\u662f\u63cf\u8ff0\u6750\u6599\u5728\u4efb\u610f\u6d41\u573a\u4e2d\u7684\u5e94\u529b\u72b6\u6001\u7684\u4e00\u6761\u5173\u7cfb\u3002\u8fd9\u662f\u66f4\u539f\u59cb\u7684\u52a8\u673a\u3002\u524d\u9762\u8bf4\u5230\u5e94\u529b\u548c\u5e94\u53d8\u4e4b\u6240\u4ee5\u8981\u7528\u5f20\u91cf\u5b9a\u4e49\u662f\u4e3a\u4e86\u66f4suitable\u3002\u4f46\u4e3a\u5565\u975e\u8981\u8fd9\u4e48suitable\uff1f\u56e0\u4e3a\u60f3\u5b9e\u73b0\u73b0\u5728\u8bf4\u7684\u8fd9\u4e2a\u4efb\u610f\u6027\u3002<\/p>\n\n\n\n<p>\u5173\u4e8e\u8fd9\u4e00\u70b9\uff0cLarson\u3001Dealy\u8fd9\u4e24\u4e2a\u4eba\u7684\u4e00\u4e9b\u4e66\u90fd\u6709\u6240\u5f3a\u8c03\u3002\u6bd4\u5982Larson\u90a3\u672c\u8bb2\u672c\u6784\u5173\u7cfb\u7684\u4e66\u8bf4\u672c\u6784\u5173\u7cfb\u8981\u201callow one to calculate the stresses in a liquid, provided the flow history\u201d\u3002\u5728Dealy\u4e0eLarson\u5408\u8457\u7684\u4e66\uff0c\u4ee5\u53ca\u524d\u8005\u4e0e\u53e6\u4e00\u4eba\u5408\u8457\u7684\u4e66\uff0c\u90fd\u8bf4\u672c\u6784\u5173\u7cfb\u8981\u7ed9\u51fa\u201crheological response of a viscoelastic material to any type of deformation\u201d\/\u201cnonlinear viscoelastic stresses in arbitrary flows\/any type of deformations\u201d\u2026\u2026\u7b49\u7b49\u3002\u201c\u4efb\u610f\u201d\u662f\u5173\u952e\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u786e\u5b9a\u6750\u6599\u7684\u672c\u6784\u5173\u7cfb\u662f\u6d41\u53d8\u5b66\u7684\u4e2d\u5fc3\u4efb\u52a1<\/h3>\n\n\n\n<p>\u672c\u6765\u5c31\u5f88\u6015\u6570\u5b66\u7684\u4eba\uff0c\u5f88\u4e0d\u559c\u6b22\u542c\u5230\u4f60\u628a\u4ed6\u6700\u6015\u7684\u4e1c\u897f\u4f5c\u4e3a\u4ed6\u8eb2\u4e0d\u5f00\u7684\u5b66\u95ee\u7684\u91cd\u70b9\u3002\u6240\u4ee5\u8fd9\u4e2a\u89c2\u70b9\u662f\u5929\u7136\u60f9\u4eba\u8d28\u7591\u7684\u3002\u4e4b\u6240\u4ee5\u8bf4\u786e\u5b9a\u6750\u6599\u7684\u672c\u6784\u5173\u7cfb\u662f\u6d41\u53d8\u5b66\u7814\u7a76\u7684\u4e2d\u5fc3\u4efb\u52a1\uff0c\u662f\u6709\u5176\u5185\u5728\u903b\u8f91\u7684\uff0c\u4f46\u5728\u4e2a\u6587\u7ae0\u91cc\u6211\u4e0d\u5c55\u5f00\u4e86\uff0c\u9ed8\u8ba4\u5b83\u6709\u5185\u5728\u7406\u7531\u3002\u6211\u53ea\u5217\u51fa\u201c\u4eba\u5bb6\u4e5f\u6709\u8fd9\u4e48\u8bf4\u201d\uff0c\u4ee5\u56de\u9988\u90a3\u4e9b\uff0c\u660e\u660e\u5df2\u7ecf\u627f\u8ba4\u6709\u7406\uff0c\u4e5f\u4ecd\u9700\u8981\u6743\u5a01\u80cc\u4e66\u624d\u6709\u5b89\u5168\u611f\u7684\u5b66\u751f\u3002<\/p>\n\n\n\n<p>\u8bb8\u5143\u6cfd (1988)\u8bf4\u201c\u5efa\u7acb\u672c\u6784\u65b9\u7a0b\u662f\u6d41\u53d8\u5b66\u7684\u4e2d\u5fc3\u4efb\u52a1\u201d\u3002\u738b\u7389\u5fe0 &amp; \u90d1\u957f\u4e49 (1993)\u5927\u91cf\u53c2\u8003\u4e86\u524d\u8005\uff0c\u4e5f\u51fa\u73b0\u4e86\u4e00\u6a21\u4e00\u6837\u7684\u8bdd\u3002<\/p>\n\n\n\n<p>Malkin (1994)\u8bf4\u786e\u5b9a\u672c\u6784\u5173\u7cfb\u201coccupies the central position in modern rheology\u201d<\/p>\n\n\n\n<p>Gupta (2000)\u8bf4\u662f\u201cone of the major goals\u201d\u3002<\/p>\n\n\n\n<p>\u4f60\u95ee\uff0c\u90a3\u5fae\u89c2\u7ed3\u6784\u7684\u8054\u7cfb\u4e0d\u7ba1\u4e86\u5417\uff1f<\/p>\n\n\n\n<p>Malkin &amp; Isayev (2006)\u4e2d\u8bf4\u786e\u5b9a\u672c\u6784\u5173\u7cfb\u662f\u201cthe first main goal\u201d\uff0c\u81f3\u4e8e\u8ba4\u8bc6\u5fae\u89c2\u7ed3\u6784\u8054\u7cfb\u5c5e\u4e8e\u201cthe second goal\u201d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. \u8d5e\u8d4f\u51e0\u4e2a\u4f5c\u8005<\/h3>\n\n\n\n<p>\u6211\u5f88\u559c\u6b22\u7684\u4e00\u4e2a\u4f5c\u8005<a rel=\"noreferrer noopener\" href=\"https:\/\/www.rheology.org\/sor\/fellowship\/MalkinA\" target=\"_blank\">Alexander Ya. Malkin<\/a>\uff0c\u57281994\u5e74\u7684\u6559\u6750\u8bf4\uff0c\u672c\u6784\u5173\u7cfb\u63cf\u8ff0\u201cstresses acting at a point and deformations occurring as a result of their action\u201d\u3002\u8fd9\u4e2a\u8868\u8ff0\u5e94\u8be5\u523b\u5728\u77f3\u7891\u4e0a\u3002<\/p>\n\n\n\n<p>\u9996\u5148\uff0c\u5173\u4e8e\u201c\u5e94\u529b\u662f\u573a\u201d\u8fd9\u4ef6\u4e8b\uff0c\u4ed6\u5f88\u660e\u786e\u5730\u8bf4\u51fa\u4e86\u5b9e\u8d28\u610f\u4e49\uff0c\u5373\u201cacting at a point\u201d\u3002\u6839\u636e\u8fd9\u53e5\u8bdd\u7684\u63aa\u8f9e\uff0c\u4f60\u4f1a\u6b63\u786e\u65e0\u8bef\u7684\u6d6e\u73b0\u51fa\u4e00\u79cd\u201c\u672c\u6784\u5173\u7cfb\u5c31\u662f\u67d0\u70b9\u4e0a\u7684\u5173\u7cfb\u201d\u7684\u5370\u8c61\u3002\u8fd9\u79cd\u5370\u8c61\u80fd\u987a\u5229\u8ba9\u4f60\u4ea7\u751f\u7591\u95ee\uff1a\u624d\u544a\u8bc9\u6211\u4e00\u70b9\u4e0a\u7684\u5173\u7cfb\uff0c\u8fd9\u6709\u5565\u7528\uff1f\u2014\u2014\u8fd9\u80fd\u4f7f\u4f60\u6b63\u786e\u5730\u6c42\u7d22\u5230\uff0c\u539f\u6765\u4f60\u9700\u8981\u6c42\u89e3\u5b8c\u8fd0\u52a8\u65b9\u7a0b\u4e4b\u540e\uff0c\u624d\u7b97\u5f97\u5230\u4f60\u4f1a\u8ba4\u4e3a\u6709\u7528\u7684\u7ed3\u8bba\u3002<\/p>\n\n\n\n<p>Malkin\u786e\u5b9e\u5728\u4e66\u540e\u6070\u5f53\u7684\u4f4d\u7f6e\u660e\u786e\u4e86\u8fd9\u4e00\u70b9\uff1aThe transition from rheological equation of state (or consitutive equation) of a liquid to a hydrodynamic problem is equivalent to the transition from discussing the situation &#8220;at a point&#8221; to considering flow of a liquid in a volume.<\/p>\n\n\n\n<p>\u4ed6\u7ee7\u7eed\u5217\u51fa\uff0c\u8981\u60f3\u8fbe\u5230\u8fd9\u4e00\u76ee\u7684\uff1aIt requires one to combine the following elements:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>rheological equation of state<\/li>\n\n\n\n<li>equilibrium (balance) equations; in the isothermal case, it is an equation of force balance only<\/li>\n\n\n\n<li>boundary conditions<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u6bb5\u4ecb\u7ecd\u53c8\u4f5c\u51fa\u4e86\u5f88\u597d\u7684\u903b\u8f91\u6697\u793a\uff1a\u5982\u679c\u4e24\u4e2a\u6d41\u4f53\u7684\u6d41\u52a8\u884c\u4e3a\u4e0d\u540c\uff0c\u90a3\u4e48\u6709\u4e09\u79cd\u60c5\u51b5\uff1a1. \u5b83\u4eec\u7684\u672c\u6784\u5173\u7cfb\u7684\u5f62\u5f0f\u4e0d\u540c\uff0c\u53ef\u79f0\u4e3a\u4e0d\u540c\u7c7b\u522b\u7684\u6d41\u4f53\uff1b2. \u5177\u6709\u76f8\u540c\u5f62\u5f0f\u7684\u672c\u6784\u5173\u7cfb\uff0c\u4f46\u7cfb\u6570\u4e0d\u540c\uff0c\u53ef\u79f0\u4e3a\u540c\u7c7b\u578b\u7684\u4e0d\u540c\u6d41\u4f53\u6837\u54c1; 3.  \u5177\u6709\u76f8\u540c\u7684\u672c\u6784\u5173\u7cfb\uff0c\u4f46\u6d41\u52a8\u7684\u8fb9\u754c\u6761\u4ef6\u4e0d\u540c\u3002<\/p>\n\n\n\n<p>\u4e3a\u5565\u8bf4\u8fd9\u662f\u903b\u8f91\u6697\u793a\u5462\uff1f\u56e0\u4e3a\u65e2\u7136\u5b88\u6052\u5f8b\u662f\u6240\u6709\u6d41\u4f53\u90fd\u8981\u6ee1\u8db3\u7684\uff0c\u90a3\u4e0a\u8ff0\u5217\u51fa\u7684\u4e09\u6761\uff0c\u53ea\u6709\u7b2c\u4e00\u6761\u548c\u7b2c\u4e09\u6761\u53ef\u4ee5\u4e0d\u540c\u3002\u7b2c\u4e00\u6761\u4f5c\u4e3a\u65b9\u7a0b\uff0c\u5b83\u5f53\u7136\u53ef\u4ee5\u6709\u5f62\u5f0f\u7684\u4e0d\u540c\u548c\u7cfb\u6570\u7684\u4e0d\u540c\u4e24\u4e2a\u5c42\u6b21\u3002\u52a0\u8d77\u6765\u4f60\u5c31\u80fd\u60f3\u51fa\u6d41\u4f53\u884c\u4e3a\u533a\u522b\u7684\u4e09\u79cd\u5c42\u6b21\u3002<\/p>\n\n\n\n<p>\u201cstresses acting at a point and deformations occurring as a result of their action\u201d\u8fd9\u4e2a\u8868\u8ff0\u8fd8\u6709\u4e00\u4e2a\u5f88\u5999\u7684\u5730\u65b9\uff1a\u5173\u4e8e\u8fd0\u52a8\u5b66\u8fd9\u4e00\u5934\uff0c\u4f5c\u8005\u6ca1\u6709\u4e5f\u7528\u201cat a point\u201d\u8fd9\u79cd\u63cf\u8ff0\u6765\u5f3a\u8c03\u5b83\u662f\u573a\u51fd\u6570\uff0c\u800c\u4ec5\u4ec5\u8bf4\u662f\u7531\u4e00\u70b9\u7684\u5e94\u529b\u72b6\u6001\u5f15\u8d77\u7684\u3002\u4e5f\u5c31\u662f\u4e0d\u6392\u9664\uff0c\u4e00\u70b9\u7684\u5e94\u529b\uff0c\u672a\u5fc5\u53ea\u5f15\u8d77\u4e00\u70b9\u7684\u6d41\u573a\u540e\u679c\uff01\u8fd9\u4e2a\u7559\u767d\u592a\u777f\u667a\u4e86\u3002<\/p>\n\n\n\n<p>\u5728\u8fd9\u672c\u4e66\u4e2d\uff0c\u4f5c\u8005\u8fd8\u7528\u5b9e\u4f8b\u8bf4\u660e\uff1aresults of different experiments can be considered as consequences of the same rheological equation of state if formulated in a generalized (tensor) form\uff0c\u5f3a\u8c03\u4e86\u5e94\u529b\u548c\u5e94\u53d8\u5f97\u662f\u5f20\u91cf\u5f62\u5f0f\u3002\u4ed6\u6bd4Tschoegl (1989)\u53ea\u7528\u4e00\u4e2ageneralized\u597d\uff0c\u5728\u4e8e\u8fdb\u4e00\u6b65\u70b9\u51fa\u662ftensor\u3002<\/p>\n\n\n\n<p>\u4f5c\u8005\u8fd8\u5728\u53e6\u4e00\u5904\u8bf4\uff0c\u672c\u6784\u5173\u7cfb\u201cdetermins all mechanical phenomena which can be expected in the observation of &#8230;\u201d\uff0c\u628a\u672c\u6784\u5173\u7cfb\u7684\u4e00\u822c\u6027\u610f\u4e49\u4e5f\u8bf4\u5230\u4e86\u3002<\/p>\n\n\n\n<p>\u518d\u52a0\u4e0a\u524d\u9762\u8bf4\u8fc7\u7684\uff0c\u4ed6\u5728\u4e66\u4e2d\u53c8\u8bf4\u4e86\u786e\u5b9a\u672c\u6784\u5173\u7cfb\u662f\u6d41\u53d8\u5b66\u7814\u7a76\u7684\u4e2d\u5fc3\u4efb\u52a1\uff0c\u4e8e\u662fMalkin\u5728\u8fd9\u672c\u4e66\u4e2d\uff0c\u975e\u5e38\u5168\u9762\u5730\u628a\u8bf4\u5230\u201c\u4f55\u8c13\u672c\u6784\u65b9\u7a0b\u201d\u65f6\u8be5\u8bb2\u5230\u7684\u4e8b\u60c5\u5168\u8bb2\u5b8c\u4e86\u3002<\/p>\n\n\n\n<p>\u53e6\u4e00\u672c\u6211\u8981\u8d5e\u8d4f\u7684\u4e66\u662f\u8bb8\u5143\u6cfd (1988)\u3002\u8bb8\u8001\u5e08\u662f\u9f13\u52b1\u6211\u9009\u62e9\u6d41\u53d8\u5b66\u4f5c\u4e3a\u4e00\u751f\u5b66\u95ee\u7684\u5e08\u957f\u3002\u4f46\u6211\u4e0d\u57fa\u4e8e\u79c1\u4eba\u7684\u5c0a\u656c\u53bb\u63a8\u5d07\u4e66\u3002\u4ece\u672c\u6587\u4e4b\u524d\u7684\u8ba8\u8bba\u53ef\u89c1\u6211\u5bf9\u4e66\u7684\u8981\u6c42\u662f\u4e0d\u4f4e\u7684\u3002\u6211\u535a\u58eb\u5bfc\u5e08\u7684\u4e66\u300a\u9ad8\u5206\u5b50\u6eb6\u6db2\u70ed\u529b\u5b66\u300b\u548c\u8bb8\u8001\u5e08\u7684\u4e66\u300a\u9ad8\u5206\u5b50\u7ed3\u6784\u6d41\u53d8\u5b66\u300b\u6070\u597d\u662f\u975e\u5e38\u597d\u7684\u4e66\uff0c\u8fd9\u662f\u6211\u7684\u5e78\u8fd0\uff0c\u4f7f\u6211\u4e0d\u7528\u9876\u7740\u4e0d\u656c\u7684\u98ce\u9669\u53bb\u6279\u5224\u3002<\/p>\n\n\n\n<p>\u8bb8\u8001\u5e08\u7684\u4e66\u4e3b\u8981\u89e3\u51b3\u201csecond goal\u201d\u3002\u53e6\u4e00\u672c\u4e2d\u6587\u7684\u4e66\uff0c\u4e5f\u662f\u6211\u4e00\u5411\u63a8\u8350\u7684\u9996\u9009\u662f\u738b\u7389\u5fe0 &amp; \u90d1\u957f\u4e49 (1994)\uff0c\u53ef\u89e3\u51b3\u201cfirst goal\u201d\u3002\u5b83\u867d\u7136\u5927\u91cf\u53c2\u8003\u4e86\u8bb8\u8001\u5e08\u7684\u4e66\uff0c\u4f46\u4e5f\u5927\u91cf\u53c2\u8003\u4e86\u8bb8\u591a\u5f53\u65f6\u56fd\u5185\u80fd\u591f\u83b7\u53d6\u7684\u56fd\u5916\u7ecf\u5178\u8d44\u6599\u3002\u6211\u4eb2\u81ea\u9a8c\u8bc1\u8fc7\uff0c\u8fd9\u672c\u4e66\u7684\u5185\u5bb9\u662f\u771f\u6b63\u53c2\u8003\u8fc7\u5b83\u58f0\u79f0\u5f15\u7528\u4e86\u7684\u8d44\u6599\u7684\uff1b\u8fd9\u4e9b\u8d44\u6599\u672c\u8eab\u4e5f\u786e\u5b9e\u90fd\u662f\u7ecf\u5178\u3002\u800c\u4e14\u4e66\u7684\u53d9\u8ff0\u8d28\u91cf\u8bc1\u660e\u4f5c\u8005\u770b\u61c2\u4e86\u6240\u6709\u7684\u8fd9\u4e9b\u8d44\u6599\uff0c\u5e76\u8fdb\u884c\u4e86\u6b63\u786e\u7684\u51dd\u70bc\u3002\u6709\u5f88\u591a\u53d9\u8ff0\u662f\u5f88\u7cbe\u5f69\u7684\uff0c\u6211\u5374\u96be\u4ee5\u627e\u5230\u5176\u4ed6\u51fa\u5904\uff0c\u4e0d\u5f97\u4e0d\u6000\u7591\u6765\u81ea\u8be5\u4e66\u4f5c\u8005\u3002\u6211\u5728\u4e2a\u4eba\u5b66\u4e60\u7684\u751f\u6daf\u4e2d\uff0c\u6bcf\u52a0\u6df1\u4e86\u4e00\u4ef6\u4e8b\u60c5\u7684\u7406\u89e3\u540e\uff0c\u56de\u8fc7\u5934\u6765\u770b\u8fd9\u672c\u4e66\u76f8\u5173\u90e8\u5206\u7684\u8bb2\u8ff0\u6389\u4e0d\u6389\u4ef7\uff0c\u90fd\u53d1\u73b0\u5b83\u4e0d\u4ec5\u7ecf\u53d7\u4e86\u8fd9\u79cd\u8003\u9a8c\u8fd8\u7ed9\u6211\u4e00\u4e2a\u66f4\u7b80\u660e\u7684\u6587\u5b57\u8868\u8ff0\u3002<\/p>\n\n\n\n<p>\u5173\u4e8e\u672c\u6784\u65b9\u7a0b\u95ee\u9898\uff0c\u8fd9\u672c\u4e66\u867d\u7136\u662f\u4ece\u6570\u5b66\u4e0a\u65b9\u7a0b\u7684\u4e0d\u5c01\u95ed\u6027\u5f15\u5165\u7684\uff08\u5728\u8bb2\u8fd0\u52a8\u65b9\u7a0b\u7684\u65f6\u5019\uff09\uff0c\u4f46\u5230\u4e86\u6b63\u5f0f\u4ecb\u7ecd\u672c\u6784\u5173\u7cfb\u7684\u65f6\u5019\uff0c\u5b83\u63a5\u8fc7\u8fd9\u4e00\u8bdd\u9898\uff0c\u7528\u4e86\u4e00\u6bb5\u6211\u89c9\u5f97\u8d28\u91cf\u4e0d\u4f4e\u7684\u8ba8\u8bba\u53bb\u8bc6\u522b\u4e3a\u5c01\u95ed\u800c\u5fc5\u987b\u7684\u672c\u6784\u5173\u7cfb\u7684\u7269\u7406\u89d2\u8272\uff0c\u4ece\u800c\u5f97\u51fa\u201c\u5efa\u7acb\u672c\u6784\u65b9\u7a0b\u662f\u6d41\u53d8\u5b66\u7684\u4e2d\u5fc3\u4efb\u52a1\u201d\u3002<\/p>\n\n\n\n<p>\u53e6\u5916\uff0c\u6c5f\u4f53\u4e7e\u5148\u751f\u4e5f\u662f\u4e00\u4f4d\u503c\u5f97\u4fe1\u8d56\u7684\u6d41\u53d8\u5b66\u4f5c\u8005\uff0c\u53ea\u662f\u5728\u672c\u6587\u7684\u8bdd\u9898\u4e0b\u4ed6\u7684\u4e66\u4e5f\u4e0d\u6210\u4e3a\u4f8b\u5b50\uff0c\u6240\u4ee5\u53ea\u5728\u8fd9\u91cc\u63d0\u4e00\u4e0b\u3002<\/p>\n\n\n\n<p>\u5f88\u591a\u672c\u6587\u6ca1\u6709\u63d0\u5230\u7684\u4f17\u4eba\u53e3\u4e2d\u7684\u6d41\u53d8\u5b66\u7ecf\u5178\uff0c\u90e8\u5206\u5c5e\u4e8e\u4ee5\u4e0b\u4e24\u79cd\u60c5\u51b5\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6211\u8ba4\u4e3a\u662f\u5f88\u597d\u7684\u4e66\uff0c\u4f46\u5173\u4e8e\u672c\u6784\u5173\u7cfb\u8fd9\u4e2a\u6982\u5ff5\uff0c\u6ca1\u6709\u6b63\u9762\u9610\u8ff0\uff0c\u5c5e\u4e8e\u8bf4\u7740\u8bf4\u7740\u5c31\u6e10\u6e10\u7528\u8fd9\u8bcd\u4e86\uff1b<\/li>\n\n\n\n<li>\u6211\u8ba4\u4e3a\u662f\u5f88\u70c2\u7684\u4e66\uff0c\u4e0d\u60f3\u5f97\u7f6a\u4eba\u5c31\u4e0d\u62ff\u51fa\u6765\u8bb2\u4e86\u3002<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Barnes, H., Hutton, J. &amp; Walters, K. (1989), An Introduction to Rheology, Elsevier<\/li>\n\n\n\n<li>Bird, R., Armstrong, R. &amp; Hassager, O. (1989), Dynamics of Polymeric Liquids, 2nd ed., vol. 1, John Wiley &amp; sons<\/li>\n\n\n\n<li>Ferry, J. (1980), Viscoelastic Properties of Polymers, 3rd, ed., John Wiley &amp; Sons<\/li>\n\n\n\n<li>Findley, W., Lai, J. &amp; Onaran, K. (1976), Creep and Relaxation of Nonlinear Viscoelastic Materials, North-Holland Publishing Company<\/li>\n\n\n\n<li>Gupta, R. (2000), Polymer and Composite Rheology, 2nd ed., Marcel Dekker<\/li>\n\n\n\n<li>Malkin, A. (1994), Rheology Fundamentals, ChemTec<\/li>\n\n\n\n<li>Malkin, A. &amp; Isayev, A. (2006), Rheology: Concept, Methods, &amp; Applications, ChemTec<\/li>\n\n\n\n<li>Mewis, J. &amp; Wagner, N. (2012), Colloidal Suspension Rheology, Cambridge University Press<\/li>\n\n\n\n<li>Rao, M. (2014), Rheology of Fluid, Semisolid, and Solid Foods, 3rd ed., Springer<\/li>\n\n\n\n<li>Riande, E. et al. (2000), Polymer Viscoelasticity, Marcel Dekker<\/li>\n\n\n\n<li>Truesdell, C. (1980), Sketch for a History of Constitutive Relations, In: G. Astarita, G. Marrucci &amp; L. Nicolais eds., Rheology, vol.1, Plenum Press<\/li>\n\n\n\n<li>Truesdell, C. &amp; Noll, W. (2004), The Non-Linear Field Theories of Mechanics.<\/li>\n\n\n\n<li>Tschoegl, N. (1989), The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction, Springer<\/li>\n\n\n\n<li>\u738b\u7389\u5fe0 &amp; \u90d1\u957f\u4e49 (1993), \u9ad8\u805a\u7269\u6d41\u53d8\u5b66\u5bfc\u8bba, \u56db\u5ddd\u5927\u5b66\u51fa\u7248\u793e<\/li>\n\n\n\n<li>\u8bb8\u5143\u6cfd (1988), \u9ad8\u5206\u5b50\u7ed3\u6784\u6d41\u53d8\u5b66, \u56db\u5ddd\u6559\u80b2\u51fa\u7248\u793e<\/li>\n\n\n\n<li>Yamaguchi, H. (2008), Engineering Fluid Mechanics, Springer<\/li>\n<\/ul>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 8888 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\u8fd9\u65f6\u5982\u679c\u4ed6\u4eec\u518d\u7ffb\u4e00\u4e9b\u6d41\u53d8\u5b66\u6559\u6750\uff0c\u53d1\u73b0\u5e94\u529b\u662f\u5f20\u91cf\u3001\u5e94\u53d8\u662f\u5f20\u91cf\u4e4b\u7c7b\u7684\u5185\u5bb9\uff0c\u5c31\u4f1a\u89c9\u5f97\u591a\u4f59\u3002\u6570\u5b66\u6574\u90a3\u4e48\u590d\u6742\u5e72\u4ec0\u4e48\uff1f\u201c\u6d41\u53d8\u5b66\u96be\u201d\u3001\u201c\u6570\u5b66\u5f88\u591a\u201d\u4e4b\u7c7b\u7684\u4e89\u8bae\u6709\u76f8\u5f53\u4e00\u90e8\u5206\u662f\u6d6e\u5728\u8fd9\u79cd\u8ba4\u8bc6\u5c42\u9762\u4e0a\u7684\uff0c\u4e25\u91cd\u5e72\u6270\u4e86\u771f\u6b63\u8ba8\u8bba\u6d41\u53d8\u5b66\u7406\u8bba\u7684\u4e25\u683c\u7b80\u5316\uff08\u5982\u6d4b\u7c98\u6d41\u7406\u8bba\uff09\u7684\u5b66\u672f\u58f0\u97f3\u3002 \u6240\u4ee5\u7b2c\u4e00\u4e2a\u5174\u8da3\u70b9\u5c31\u662f\uff0c\u90a3\u4e9b\u8fd1\u4e4e\u7b80\u5355\u8bf4\u201c\u672c\u6784\u5173\u7cfb\u5c31\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u201d\u7684\u6559\u79d1\u4e66\u4e2d\uff0c\u52a0\u4e0a\u4e86\u54ea\u4e9b\u770b\u4f3c\u65e0\u7528\u4f46\u5374\u9632\u6b62\u4e86\u4e0a\u8ff0\u6253\u8138\u7684\u9650\u5b9a\u6027\u4fee\u9970\u3002 \u5148\u770bJ. Ferry\u7684\u7ecf\u5178\u6559\u6750\u3002\u4ed6\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cthe relations between stress, strain, and their time dependences\u201d\u3002\u8fd9\u6bd4\u76f4\u63a5\u8bf4\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u591a\u4e86\u4e2a\u65f6\u95f4\u4f9d\u8d56\u6027\u3002\u8fd9\u5e76\u4e0d\u662f\u4e3a\u66f4\u51c6\u786e\u5730\u63cf\u8ff0\u672c\u6784\u5173\u7cfb\u7684\u610f\u4e49\u672c\u8eab\u4f5c\u51fa\u7684\u9650\u5b9a\uff0c\u800c\u662f\u4e3a\u4e86\u5f3a\u8c03\u6750\u6599\u7c98\u5f39\u6027\u7684\u53ef\u80fd\u6027\u3002\u6240\u4ee5\u5f52\u6839\u7ed3\u5e95\uff0c\u5728\u201c\u4f55\u8c13\u672c\u6784\u5173\u7cfb\u201d\u8fd9\u4ef6\u4e8b\u4e0a\uff0c Ferry\u76f8\u5f53\u4e8e\u7b80\u5355\u8bf4\u4e86\u53e5\u201c\u5c31\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u201d\u3002 Ferry\u7684\u4e66\u662f\u6d41\u4f20\u975e\u5e38\u5e7f\u7684\u3001\u53e3\u7891\u7ecf\u4e45\u4e0d\u8870\u7684\uff0c\u7ecf\u5178\u4e2d\u7684\u7ecf\u5178\u3002\u4f46\u662f\u4ed6\u5173\u4e8e\u672c\u6784\u5173\u7cfb\u7684\u7b80\u5355\u63cf\u8ff0\uff0c\u867d\u7136\u5fc5\u4e0d\u4ee3\u8868\u4ed6\u672c\u4eba\u7406\u89e3\u5c31\u771f\u8fd9\u4e48\u7b80\u5355\uff0c\u5374\u88ab\u8bb8\u591a\u4e5f\u8bb8\u53ea\u770b\u4e00\u672c\u4e66\u5b66\u6d41\u53d8\u5b66\uff0c\u8fd8\u5f88\u8ba4\u771f\u5b66\u7684\u5b66\u751f\u8bb0\u4e3a\u6559\u6761\u3002\u4f8b\u5982\uff0cM. Rao\u5199\u7684\u4e66\uff0c\u5c31\u539f\u6837\u7167\u642cFerry\u7684\u8bf4\u6cd5\uff0c\u5e76\u6807\u6ce8\u4e86\u5bf9Ferry\u7684\u4e66\u7684\u5f15\u7528\u3002 \u5982\u679c\u975e\u8981\u4fdd\u6301\u201c\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u201d\u8fd9\u79cd\u53d9\u8ff0\u6846\u67b6\u6765\u8bb2\u201c\u4f55\u8c13\u672c\u6784\u5173\u7cfb\u201d\u90a3\u81f3\u5c11\u5e94\u8be5\u52a0\u4ec0\u4e48\u6837\u7684\u9650\u5b9a\u6027\u8bf4\u660e\u5462\uff1f\u4e24\u65b9\u9762\u3002\u4e00\u662f\uff0c\u6240\u8c13\u5e94\u529b\u548c\u5e94\u53d8\u90fd\u662f\u5f20\u91cf\uff0c\u5b83\u4eec\u6bcf\u4e2a\u67099\u4e2a\u91cf\u3002\u4f46\u8fd9\u4ef6\u4e8b\u8981\u4ee5\u4e0d\u51fa\u73b0\u201c\u5f20\u91cf\u201d\u8fd9\u4e2a\u6982\u5ff5\u7684\u65b9\u5f0f\u8bf4\u51fa\u6765\uff0c\u8ba9\u4eba\u4e00\u4e0b\u5b50\u5c31\u660e\u767d\u4e3a\u4ec0\u4e48\u5b83\u4eec\u662f\u8fd9\u79cd\u91cf\uff0c\u81f3\u5c11\u53cd\u6b63\u4e0d\u662f\u6807\u91cf\uff08\u5f88\u96be\uff09\uff1b\u4e8c\u662f\uff0c\u5e94\u529b\u548c\u5e94\u53d8\u90fd\u662f\u573a\uff0c\u5b83\u4eec\u7684\u201c\u53d6\u503c\u201d\u65e2\u4f9d\u8d56\u7a7a\u95f4\u4f4d\u7f6e\u53c8\u4f9d\u8d56\u65f6\u95f4\u3002\u8fd9\u5012\u4e0d\u662f\u4ec0\u4e48\u5f88\u96be\u7406\u89e3\u7684\u70b9\u3002\u5982\u679c\u8fd9\u4e24\u4e2a\u90fd\u660e\u786e\u4e86\uff0c\u90a3\u5c31\u53ef\u4ee5\u6210\u529f\u7684\u8ba9\u4eba\u5bf9\u201c\u65cb\u8f6c\u6d41\u53d8\u4eea\u8f6f\u4ef6\u6240\u8f93\u51fa\u7ed9\u4f60\u7684\u6807\u91cf\u503c\u5e94\u529b\u548c\u5e94\u53d8\u5230\u5e95\u662f\u5565\u201d\u4ea7\u751f\u8d28\u7591\uff1b\u8fd9\u4e2a\u8d28\u7591\u624d\u662f\u6b63\u5f0f\u5b66\u4e60\u6d41\u53d8\u5b66\u7684\u5f00\u7aef\u2014\u2014\u5982\u679c\u4f60\u6070\u5de7\u5c31\u662f\u90a3\u79cd\u6ca1\u5b66\u6d41\u53d8\u5b66\u5c31\u7167\u7740\u6587\u732e\u6216\u5e08\u5144\u5e08\u59d0\u7684\u201c\u6307\u5bfc\u201d\u505a\u4e86\u5927\u91cf\u65cb\u8f6c\u6d41\u53d8\u4eea\u5b66\u6d4b\u8bd5\u7684\u5b66\u751f\u7684\u8bdd\u3002 1.1 \u5e94\u529b\u3001\u5e94\u53d8\u90fd\u662f\u573a\u51fd\u6570 \u6211\u4eec\u5148\u770b\u6697\u793a\u4e86\u7b2c\u4e8c\u4e2a\u70b9\u7684\u8bf4\u6cd5\u3002 \u6709\u672c\u4e66Yamaguchi (2008)\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cthe relationship between the internal stress and the applied strain\u201d\uff0c\u8fd9\u4e2a\u201cinternal\u201d\u5c31\u5f88\u9e21\u8d3c\u3002\u4e0d\u5c31\u662f\u60f3\u6697\u6233\u6233\u5730\u5f3a\u8c03\u4e00\u4e0b\u201c\u5b83\u4eec\u90fd\u662f\u573a\u54e6\u201d\u5417\uff1f \u8fd8\u6709\u4e00\u672c\u4e66Mewis &amp; Wagner (2012)\u8bf4\uff0c\u672c\u6784\u5173\u7cfb\u662f\u201cintrinsic relation between the stresses and kinematics\u201d\u3002\u5728\u672c\u5173\u6ce8\u7126\u70b9\u4e0b\uff0c\u8fd9\u53e5\u8bdd\u65e0\u975e\u7ed9\u4f60\u6765\u4e86\u4e2a\u201ckinematics\u201d\u8fd9\u8bcd\uff0c\u597d\u50cf\u8bf4\u5f97\u60ac\u4e00\u70b9\u513f\uff0c\u80fd\u8ba9\u4f60\u4e0d\u6562\u786e\u5b9a\u4f5c\u8005\u662f\u4e0d\u662f\u80a4\u6d45\u7684\u3002 \u7c7b\u4f3c\u4e0a\u8ff0\u8fd9\u822c\u7684\u201c\u514d\u8d23\u5f0f\u201d\u7684\u4fee\u9970\u9650\u5b9a\uff0c\u5bf9\u521d\u5b66\u8005\u66f4\u51c6\u786e\u5730\u7406\u89e3\u4e00\u70b9\u7528\u5904\u90fd\u6ca1\u6709\uff1b\u5728\u521d\u5b66\u8005\u90a3\u91cc\u4e0a\u8ff0\u8fd9\u79cd\u505a\u6cd5\u76f8\u5f53\u4e8e\u7b80\u5355\u8bf4\u672c\u6784\u5173\u7cfb\u5c31\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u3002 1.2 \u5e94\u529b\u3001\u5e94\u53d8\u662f\u5f20\u91cf\uff08\u4f46\u4e0d\u660e\u8bf4\uff09 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\u4e00\u672c\u6d41\u53d8\u5b66\u7684\u5de8\u7ecf\u5178\u7684\u6559\u6750Barnes, Hutton and Walters (1989)\u8bf4\uff0c\u672c\u6784\u5173\u7cfb\u8054\u7cfb\u7684\u662f\u201csuitably 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equation\uff09\u3002\u8fd9\u4e9b\u90fd\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u9488\u5bf9\u725b\u987f\u6d41\u4f53\u7684\u5e94\u7528\u3002\u7136\u800c\uff0c\u7531\u4e8e\u300a\u5316\u5de5\u539f\u7406\u300b\u7684\u7814\u7a76\u76ee\u6807\u4ec5\u4e3a\u89e3\u51b3\u4f20\u8d28\u4f20\u70ed\u95ee\u9898\uff0c\u52a0\u4e0a\u6570\u5b66\u57fa\u7840\u8bbe\u7f6e\u4e0a\u7684\u9650\u5236\uff0c\u300a\u5316\u5de5\u539f\u7406\u300b\u8bfe\u7a0b\u4e2d\u7684\u5e94\u7528\u4f8b\u9898\u4e00\u822c\u4ec5\u9650\u4e8e\u5c42\u6d41\uff08\u7ebf\u6027\u5316\u7684\u7eb3\u7ef4--\u65af\u6258\u514b\u65af\u65b9\u7a0b\uff09\u3001\u4e00\u7ef4\u3001\u5b9a\u6001\u6d41\u95ee\u9898\uff0c\u751a\u81f3\u53ef\u4ee5\u8d8a\u8fc7\u7eb3\u7ef4--\u65af\u6258\u514b\u65af\u65b9\u7a0b\u7684\u660e\u663e\u5f15\u5165\uff0c\u76f4\u63a5\u91c7\u7528\u5fae\u79ef\u5206\u601d\u60f3\u5217\u51fa\u5fae\u5206\u65b9\u7a0b\u89e3\u9898\uff1b\u5f80\u5f80\u53ea\u5173\u5fc3\u538b\u5dee\u548c\u603b\u6d41\u91cf\u7684\u5173\u7cfb\u95ee\u9898\uff08\u4f8b\u5982Hagen--Poisseuille\u65b9\u7a0b\uff09\uff0c\u907f\u514d\u7ec6\u5316\u5230\u6d41\u901f\u5206\u5e03\u573a\u7b49\u6d89\u53ca\u573a\u51fd\u6570\u5fae\u79ef\u5206\u5b9a\u7406\u7684\u6570\u5b66\u77e5\u8bc6\u7684\u9898\u76ee\uff0c\u4ee5\u4fdd\u6301\u5168\u4e66\u7bc7\u5e45\u5728\u5408\u7406\u7684\u8303\u56f4\u5185\u3002 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