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Shap. Mem. Superelasticity (2023).</a>\n\nNeedle-like microstructures are often observed\nin shape memory alloys near macro-interfaces that separate\nregions with different laminate orientation. We study their\nshape with a two-dimensional model based on nonlinear\nelasticity, that contains an explicit parametrization of the\nneedle profiles. Energy minimization leads to specific\npredictions for the geometry of needle-like domains. Our\nsimulations are based on shape optimization of the needle\ninterfaces, using a polyconvex energy density with cubic\nsymmetry for the elastic problem, and a numerical implementation\nvia finite elements on a dynamically changing\ngrid."}}]},{"typeName":"subject","multiple":true,"typeClass":"controlledVocabulary","value":["Mathematical Sciences","Physics"]},{"typeName":"freeKeyword","multiple":true,"typeClass":"compound","value":[{"freeKeywordValue":{"typeName":"freeKeywordValue","multiple":false,"typeClass":"primitive","value":"Martensite"}},{"freeKeywordValue":{"typeName":"freeKeywordValue","multiple":false,"typeClass":"primitive","value":"Needle microstructures"}},{"freeKeywordValue":{"typeName":"freeKeywordValue","multiple":false,"typeClass":"primitive","value":"Shape optimization"}},{"freeKeywordValue":{"typeName":"freeKeywordValue","multiple":false,"typeClass":"primitive","value":"Finite elasticity"}},{"freeKeywordValue":{"typeName":"freeKeywordValue","multiple":false,"typeClass":"primitive","value":"Cubic anisotropy"}}]},{"typeName":"publication","multiple":true,"typeClass":"compound","value":[{"publicationCitation":{"typeName":"publicationCitation","multiple":false,"typeClass":"primitive","value":"Conti, S., Lenz, M., Rumpf, M., Verhülsdonk, J., Zwicknagl, B., Geometry of Needle-Like Microstructures in Shape-Memory Alloys. 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