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arXiv · 2412.16027

Integral representation for a relaxed optimal design problem for non-simple grade two materials

Ana Cristina Barroso·Elvira Zappale
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Abstract

A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained. Departing from an energy with a bulk term depending on the deformation gradient and its derivatives, as well as a perimeter term, the functional in question corresponds to the relaxation of this energy with respect to a pair $(\chi,u)$, where $\chi$ is the characteristic function of a set of finite perimeter and $u$ is a function of bounded hessian.

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Ana Cristina Barroso, Elvira Zappale. 2024-12-20. Integral representation for a relaxed optimal design problem for non-simple grade two materials. https://arxiv.org/abs/2412.16027

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