{"id":1919,"date":"2021-04-13T11:59:58","date_gmt":"2021-04-13T10:59:58","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/?p=1919"},"modified":"2022-11-11T10:24:52","modified_gmt":"2022-11-11T10:24:52","slug":"cavitation-in-nematic-elastomer-spheres-supervisor-dr-a-mihai","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/cavitation-in-nematic-elastomer-spheres-supervisor-dr-a-mihai\/","title":{"rendered":"Cavitation in nematic elastomer spheres &#8211; Supervisor: Dr A Mihai"},"content":{"rendered":"\n<p><strong>Title:<\/strong> Cavitation in nematic elastomer spheres<\/p>\n\n\n\n<p><strong>Code:<\/strong> AM2122A<\/p>\n\n\n\n<p><strong>Project Description:<\/strong> <\/p>\n\n\n\n<p>Nematic liquid crystal elastomers are advanced multifunctional<br> materials that combine the exibility of polymeric networks with the ne-<br> matic structure of liquid crystals. Due to their complex molecular architec-<br> ture, they are capable of exceptional responses, such as large spontaneous<br> deformations and phase transitions, which are reversible and repeatable<br> under certain external stimuli (e.g., heat, light, solvents, electric or mag-<br> netic elds). Their accurate description requires multiphysics modelling<br> combining elasticity and liquid crystal theories.<br><br> In particular, instabilities in liquid crystalline solids can be of potential<br> interest in a range of applications. This project focuses on the cavitation<br> instability where a void forms at the centre of a nematic sphere under<br> radial symmetric tensile load. Assuming an initially unit sphere described<br> by a simple neoclassical model for ideal nematic elastomers, the aim is<br> to determine the critical load for the onset of cavitation, and to verify<br> if the associated bifurcation from the trivial solution where the sphere<br> remains undeformed is supercritical, i.e., if the cavity radius increases<br> as the applied load increases. A comparison with similar phenomena in<br> purely elastic spheres will also be performed.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Project offered as a&nbsp;<strong>Double<\/strong> module. <\/p>\n\n\n\n<p><strong>Type: <\/strong>20 credits<\/p>\n\n\n\n<p><strong>Supervisor:<\/strong> Dr Angela Mihai<\/p>\n\n\n\n<p><strong>Prerequisite 2nd year modules:<\/strong> Real Analysis, Calculus of Several Vari-<br>ables, Linear Algebra<\/p>\n\n\n\n<p><strong>Prerequisite 3rd year modules for concurrent study:<\/strong> Partial Differential<br>Equations, Methods of Applied Mathematics, Finite Elasticity<\/p>\n\n\n\n<p><strong>Maximum number of students: <\/strong>1<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: Cavitation in nematic elastomer spheres Code: AM2122A Project Description: Nematic liquid crystal elastomers are advanced multifunctional materials that combine the exibility of polymeric networks with the ne- matic structure of liquid crystals. Due to their complex molecular architec- ture, they are capable of exceptional responses, such as large spontaneous deformations and phase transitions, which &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/cavitation-in-nematic-elastomer-spheres-supervisor-dr-a-mihai\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Cavitation in nematic elastomer spheres &#8211; Supervisor: Dr A Mihai<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[2,4,7],"tags":[],"class_list":["post-1919","post","type-post","status-publish","format-standard","hentry","category-2021-2022","category-double","category-yr-3-descriptions-2021-2022"],"aioseo_notices":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1919","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/comments?post=1919"}],"version-history":[{"count":3,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1919\/revisions"}],"predecessor-version":[{"id":2062,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1919\/revisions\/2062"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/media?parent=1919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/categories?post=1919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/tags?post=1919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}