We study thin films with residual strain by analyzing the limit of non-Euclidean elastic energy functionals as the material’s thickness tends to 0. We begin by extending prior results (Bhattacharya et al. in Arch Ration Mech Anal 228: 143–181, 2016); (Agostiniani et al. in ESAIM Control Opt Calculus Var 25: 24, 2019); (Lewicka and Lucic in Commun Pure Appl Math 73: 1880–1932, 2018); (Schmidt in J de Mathématiques Pures et Appliquées 88: 107–122, 2007) , to a wider class of films, whose prestrain depends on both the midplate and the transversal variables. The ansatz for our convergence result uses a specific type of wrinkling, which is built on exotic solutions to the Monge-Ampere equation, constructed via convex integration (Lewicka and Pakzad in Anal PDE 10: 695–727, 2017). We show that the expression for our limit has a natural interpretation in terms of the orthogonal projection of the residual strain onto a suitable subspace. We also show that some type of wrinkling phenomenon is necessary to match the lower bound of the limit in certain circumstances. These results all assume a prestrain of the same order as the thickness; we also discuss why it is natural to focus on that regime by considering what can happen when the prestrain is larger.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:91620 |
| Date | 04 June 2024 |
| Creators | Padilla-Garza, David |
| Publisher | Springer |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 1432-0835, 187, 10.1007/s00526-022-02262-z |
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