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

2024/12/20 by Barroso, Ana Cristina, Zappale, Elvira
#26B25 #49J45 #49Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2412.16027

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 (χ,u), where χ is the characteristic function of a set of finite perimeter and u is a function of bounded hessian.

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