{"id":18493,"date":"2018-12-19T18:43:25","date_gmt":"2018-12-19T18:43:25","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=18493"},"modified":"2021-07-28T19:29:18","modified_gmt":"2021-07-28T19:29:18","slug":"hyperelastic-equibiaxial-tension-test","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/hyperelastic-equibiaxial-tension-test\/","title":{"rendered":"Validation Case: Hyperelastic Equibiaxial Tension Test"},"content":{"rendered":"\n\n\n\n<p class=\"wp-block-paragraph\">This validation case belongs to an hyperelastic equibiaxial tension test in solid mechanics. The aim of this test case is to validate the following parameters:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Hyperelasticity under equibiaxial tension<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The simulation results of SimScale were compared to the results derived from [Treloar]\\(^1\\).<\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=8980553149952113438\" class=\"hw-btn    \" rel=\"noopener \" target=\"_blank\"    >\n        View Project    <\/a>\n<\/div>\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"geometry\" >Geometry<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The geometry used for the case is as follows: <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/06\/GEOM.png\"><img loading=\"lazy\" decoding=\"async\" width=\"927\" height=\"815\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/06\/GEOM.png\" alt=\"cube geometrical model\" class=\"wp-image-30372\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/06\/GEOM.png 927w, https:\/\/frontend-assets.simscale.com\/media\/2020\/06\/GEOM-300x264.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/06\/GEOM-768x675.png 768w\" sizes=\"auto, (max-width: 927px) 100vw, 927px\" \/><\/a><figcaption>Figure 1: Geometry model for the cube<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The cube has an edge length of 1 \\(m\\).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"analysis-type-and-mesh\" >Analysis Type and Mesh<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tool Type<\/strong>: Code_Aster<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analysis Type<\/strong>: Static Non-Linear<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mesh and Element Types<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The mesh for the cube geometry was computed using SimScale&#8217;s Standard meshing algorithm.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter is-style-stripes\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Case<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Mesh Type<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Number of <\/strong><br><strong>Nodes<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Element Type<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">All<\/td><td class=\"has-text-align-center\" data-align=\"center\">Standard<\/td><td class=\"has-text-align-center\" data-align=\"center\">1184<\/td><td class=\"has-text-align-center\" data-align=\"center\">1st order tetrahedral<\/td><\/tr><\/tbody><\/table><figcaption>Table 1: Finite element model for each case<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image.png\"><img loading=\"lazy\" decoding=\"async\" width=\"840\" height=\"790\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image.png\" alt=\"tetrahedral mesh for uniaxial validation case simscale\" class=\"wp-image-46786\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image.png 840w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-300x282.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-768x722.png 768w\" sizes=\"auto, (max-width: 840px) 100vw, 840px\" \/><\/a><figcaption>Figure 2: Tetrahedral element mesh for the cube<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"simulation-setup\" >Simulation Setup<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Material<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hyperelasticity material, with the following parameters for each type of law:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Neo Hooke:<ul><li>\\(C_{10} = \\) 2.398 \\(Pa\\)<\/li><li>\\(D_{1} = \\) 1e-6 \\(1\/Pa\\)<\/li><\/ul><\/li><li>Mooney-Rivlin:<ul><li>\\(C_{10} = \\) 1.751 \\(Pa\\)<\/li><li>\\(C_{01} = \\) 4.625e-2 \\(Pa\\)<\/li><li>\\(D_{1} = \\) 1e-6  \\(1\/Pa\\)<\/li><\/ul><\/li><li>Signorini:<ul><li>\\(C_{10} = \\) 5.365 \\(Pa\\)<\/li><li>\\(C_{01} = \\) -2.477 \\(Pa\\)<\/li><li>\\(C_{20} = \\) 6.337e-1 \\(Pa\\)<\/li><li>\\(D_{1} = \\) 1e-6  \\(1\/Pa\\)<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Boundary Conditions<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Constraints:<ul><li>Face ABFE with zero x-displacement<\/li><li>Face AEHD with zero y-displacement<\/li><li>Face ABCD with zero z-displacement<\/li><li>Face DCGH with imposed 4 \\(m\\) x-displacement<\/li><li>Face BFGC with imposed 4 \\(m\\) y-displacement<\/li><\/ul><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"reference-solution\" >Reference Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The reference solution is of the experimental type and was extracted from [Treloar]\\(^1\\). It corresponds with the nominal stress-strain material curve. The values were extracted using <a rel=\"noreferrer noopener\" href=\"https:\/\/apps.automeris.io\/wpd\/\" target=\"_blank\">WebPlotDigitizer<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"result-comparison\" >Result Comparison<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Comparison of the nominal stress-strain curves computed from reaction force on the faces with zero displacement, versus the reference data is shown in Figure 3:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-4.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-4-1024x768.png\" alt=\"nominal stress strain result curves comparison for equibiaxial validation case\" class=\"wp-image-46794\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-4-1024x768.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-4-300x225.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-4-768x576.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-4.png 1200w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption>Figure 3: Nominal stress-strain curves comparison with Treloar \\(^1\\)<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Following are the contours of the final deformed shape and the von Mises stress from the Signorini case results, where the hyperelastic equibiaxial tension load effect can be appreciated:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-2.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"667\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-2-1024x667.png\" alt=\"deformed shape color plot for equibiaxial validation case\" class=\"wp-image-46792\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-2-1024x667.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-2-300x195.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-2-768x500.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2021\/07\/image-2.png 1243w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption>Figure 4: Final deformed shape of the cube, with color representing deformation magnitude for the Signorini case<\/figcaption><\/figure>\n\n\n\n\n<div class='hw-block hw-references hw-references'>\n    <p class='hw-references__title'>References<\/p>\n    <ul class='hw-references__list'>\n\n        <li><cite>L. R. G. Treloar, &#8220;Stress-strain data for vulcanised rubber under various types of deformation&#8221;, Trans. Faraday Soc., 40:59\u201370, 1944.<\/cite><\/li>\n    <\/ul>\n<\/div>\n\n\n\n<div class=\"hw-block hw-note hw-note--info hw-note\">\n    <div class=\"hw-note__title\">\n        <p class=\"hw-note__titleText\"><i class=\"fa fa-exclamation-circle\" aria-hidden=\"true\"><\/i>Note<\/p>\n    <\/div>\n    <div class=\"hw-note__body\">\n        <p>If you still encounter problems validating you simulation, then please post the issue on our <a href=\"https:\/\/www.simscale.com\/forum\/\">forum<\/a> or <a href=\"mailto:support@simscale.com\">contact us<\/a>.<\/p>\n    <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>This validation case belongs to an hyperelastic equibiaxial tension test in solid mechanics. The aim of this test case is...","protected":false},"author":94,"featured_media":0,"parent":17191,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-documentation.php","meta":{"_acf_changed":false,"_crdt_document":"","inline_featured_image":false,"footnotes":""},"class_list":["post-18493","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18493","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/users\/94"}],"replies":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/comments?post=18493"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18493\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/17191"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=18493"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}