{"id":253,"date":"2016-06-17T07:25:08","date_gmt":"2016-06-17T07:25:08","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/?p=253"},"modified":"2016-06-17T07:25:08","modified_gmt":"2016-06-17T07:25:08","slug":"homogenisation-in-finite-elasticity-for-composites-with-a-high-contrast-in-the-vicinity-of-rigid-body-motions","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/homogenisation-in-finite-elasticity-for-composites-with-a-high-contrast-in-the-vicinity-of-rigid-body-motions\/","title":{"rendered":"Homogenisation in finite elasticity for composites with a high contrast in the vicinity of rigid-body motions\u00a0"},"content":{"rendered":"<p><em>Kirill\u00a0Cherednichenko (Bath, UK)<\/em><\/p>\n<p>I will describe a multiscale asymptotic framework for the analysis of the macroscopic behaviour of periodic two-material composites with high contrast in a finite-strain setting. I will start by introducing the nonlinear description of a composite consisting of a stiff material matrix and soft, periodically distributed inclusions. I shall then focus on the loading regimes when the applied load is small or of order one in terms of the period of the composite structure. I will show that this corresponds to the situation when the displacements on the stiff component are situated in the vicinity of a rigid-body motion. This allows to replace, in the homogenisation limit, the nonlinear material law of the stiff component by its linearised version. As a main result, I derive (rigorously in the spirit of \u0393-convergence) a limit functional that allows to establish a precise two-scale expansion for minimising sequences. This is joint work with Mikhail Cherdantsev and Stefan Neukamm.<\/p>\n<p><a href=\"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/programme\/\">Back to Programme<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kirill\u00a0Cherednichenko (Bath, UK) I will describe a multiscale asymptotic framework for the analysis of the macroscopic behaviour of periodic two-material composites with high contrast in a finite-strain setting. I will start by introducing the nonlinear description of a composite consisting of a stiff material matrix and soft, periodically distributed inclusions. I shall then focus on &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/homogenisation-in-finite-elasticity-for-composites-with-a-high-contrast-in-the-vicinity-of-rigid-body-motions\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Homogenisation in finite elasticity for composites with a high contrast in the vicinity of rigid-body motions\u00a0<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-253","post","type-post","status-publish","format-standard","hentry","category-abstracts"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/253","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/comments?post=253"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/253\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/media?parent=253"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/categories?post=253"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/tags?post=253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}