Calculus of Variations and Geometric Measure Theory

J. Matias - M. Morandotti - E. Zappale

Optimal design of fractured media with prescribed macroscopic strain

created by morandott on 29 Jul 2016
modified on 12 May 2017


Published Paper

Inserted: 29 jul 2016
Last Updated: 12 may 2017

Journal: J. Math. Anal. Appl.
Volume: 449
Pages: 1094-1132
Year: 2017
Doi: 10.1016/j.jmaa.2016.12.043

Preprint SISSA 42$/$2016$/$MATE


In this work we consider an optimal design problem for two-component fractured media for which a macroscopic strain is prescribed. Within the framework of structured deformations, we derive an integral representation for the relaxed energy functional. We start from an energy functional accounting for bulk and surface contributions coming from both constituents of the material; the relaxed energy densities, obtained via a blow-up method, are determined by a delicate interplay between the optimization of sharp interfaces and the diffusion of microcracks. This model has the far-reaching perspective to incorporate elements of plasticity in optimal design of composite media.

Keywords: relaxation, optimal design, Structured deformations, Disarrangements, interfacial energy density, bulk energy density