{"id":5598,"date":"2017-06-04T00:08:03","date_gmt":"2017-06-03T16:08:03","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=5598"},"modified":"2026-02-16T11:41:26","modified_gmt":"2026-02-16T03:41:26","slug":"derivation-of-the-%ce%b5-%ce%b4-identity-%ce%b5-%ce%b4%e7%ad%89%e5%bc%8f%e7%9a%84%e6%8e%a8%e5%af%bc","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=5598","title":{"rendered":"Derivation of the \u03b5-\u03b4 identity [\u03b5-\u03b4\u7b49\u5f0f\u7684\u63a8\u5bfc]"},"content":{"rendered":"<p style=\"padding-left: 30px;\"><span style=\"color: #0000ff;\"><strong>The \u03b5-\u03b4 identity (\u03b5-\u03b4\u7b49\u5f0f), one of the most frequently used identity in solid mechanics. Here is a simple derivation of \u00a0the\u00a0\u03b5-\u03b4 identity.<\/strong><\/span><\/p>\n<p style=\"padding-left: 30px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5605\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/06\/Derivation_1.gif\" alt=\"\" width=\"500\" height=\"166\" \/><\/p>\n<p style=\"padding-left: 30px;\"><strong> Step 1~2:<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5606\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/06\/Derivation_2.gif\" alt=\"\" width=\"500\" height=\"382\" \/><\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 3:<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5607\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/06\/Derivation_3.gif\" alt=\"\" width=\"500\" height=\"178\" \/><\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 4:<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5608\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/06\/Derivation_4.gif\" alt=\"\" width=\"500\" height=\"198\" \/><\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 5:<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5609\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/06\/Derivation_5.gif\" alt=\"\" width=\"500\" height=\"222\" \/><\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 6:<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5610\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/06\/Derivation_6.gif\" alt=\"\" width=\"500\" height=\"112\" \/><\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 7:<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5611\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/06\/Derivation_7.gif\" alt=\"\" width=\"500\" height=\"261\" \/><\/p>\n<hr \/>\n<p><center><strong><div  class=\"thumbs-rating-container\" id=\"thumbs-rating-5598\" data-content-id=\"5598\"><button class=\"thumbs-rating-up thumbs-rating-voted\" onclick=\"thumbs_rating_vote(5598, 1);\">Vote Up +16<\/button> <button class=\"thumbs-rating-down\" onclick=\"thumbs_rating_vote(5598, 2);\">Vote Down -0<\/button><span class=\"thumbs-rating-already-voted\">You already voted!<\/span><\/div><\/strong><\/center><\/p>\n<ul style=\"list-style-type: square;\">\n<li style=\"text-align: left;\"><strong>\u5fae\u4fe1\u516c\u4f17\u53f7\u00a0( <span style=\"color: #0000ff;\">Wechat\u00a0Subscription<\/span>)<\/strong><\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3636\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\" alt=\"WeChat_QRCode\" width=\"250\" height=\"255\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>\u6b22\u8fce\u5173\u6ce8\u00a0\u201c<span style=\"color: #ff00ff;\">\u7ed3\u6784\u4e4b\u65c5<\/span>\u201d\u00a0\u5fae\u4fe1\u516c\u4f17\u53f7<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The \u03b5-\u03b4 identity (\u03b5-\u03b4\u7b49\u5f0f), one of the most frequently used identity in solid mechanics. Here is a simple derivation of \u00a0the\u00a0\u03b5-\u03b4 identity. Step 1~2: Step 3: Step 4: Step 5: &#8230;<\/p>\n","protected":false},"author":1,"featured_media":5606,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,447],"tags":[769,772,766,767,768,1211,440,771,770,135,293],"class_list":["post-5598","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-geometry","category-solid-mechanics-","tag-derivation","tag-tensor","tag---identity","tag-767","tag-768","tag-1211","tag-440","tag-771","tag-770","tag-135","tag-293"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"CJD\"\/>\n\t<meta name=\"keywords\" content=\"derivation,tensor,\u03b5-\u03b4 identity,\u03b5-\u03b4\u7b49\u5f0f,\u516c\u5f0f\u63a8\u5bfc,\u529b\u5b66,\u56fa\u4f53\u529b\u5b66,\u5f20\u91cf,\u63a8\u5bfc,\u6570\u5b66,\u6709\u9650\u5143\" \/>\n\t<link rel=\"canonical\" href=\"http:\/\/www.jdcui.com\/?p=5598\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.10\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/www.jdcui.com\\\/?p=5598#article\",\"name\":\"Derivation of the \\u03b5-\\u03b4 identity [\\u03b5-\\u03b4\\u7b49\\u5f0f\\u7684\\u63a8\\u5bfc] | \\u5d14\\u6d4e\\u4e1c\\u7684\\u535a\\u5ba2 - www.jdcui.com\",\"headline\":\"Derivation of the \\u03b5-\\u03b4 identity [\\u03b5-\\u03b4\\u7b49\\u5f0f\\u7684\\u63a8\\u5bfc]\",\"author\":{\"@id\":\"http:\\\/\\\/www.jdcui.com\\\/?author=1#author\"},\"publisher\":{\"@id\":\"http:\\\/\\\/www.jdcui.com\\\/#organization\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"http:\\\/\\\/www.jdcui.com\\\/wp-content\\\/uploads\\\/2017\\\/06\\\/Derivation_2.gif\",\"width\":600,\"height\":458},\"datePublished\":\"2017-06-04T00:08:03+08:00\",\"dateModified\":\"2026-02-16T11:41:26+08:00\",\"inLanguage\":\"en-US\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/www.jdcui.com\\\/?p=5598#webpage\"},\"isPartOf\":{\"@id\":\"http:\\\/\\\/www.jdcui.com\\\/?p=5598#webpage\"},\"articleSection\":\"Math &amp; 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