{"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":[],"views":2425,"_links":{"self":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/5598","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5598"}],"version-history":[{"count":0,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/5598\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/media\/5606"}],"wp:attachment":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5598"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5598"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5598"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}