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Integral representation for a relaxed optimal design problem for non-simple grade two materials (2412.16027v2)
Published 20 Dec 2024 in math.AP and math.OC
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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