Calculus of Variations and Geometric Measure Theory

A. Braides - A. Causin - M. Solci

A homogenization result for interacting elastic and brittle media

created by braidesa on 21 Sep 2018
modified on 02 Jun 2019


Published Paper

Inserted: 21 sep 2018
Last Updated: 2 jun 2019

Journal: Proceedings A. Roy. Soc. London
Volume: 474
Year: 2018
Doi: 10.1098/rspa.2018.0118


We consider energies modelling the interaction of two media parameterized by the same reference set, such as those used to study interactions of a thin film with a stiff substrate, hybrid laminates, or skeletal muscles. Analytically, these energies consist of a (possibly non-convex) functional of hyperelastic type and a second functional of the same type such as those used in variational theories of brittle fracture, paired by an interaction term governing the strength of the interaction depending on a small parameter. The overall behaviour is described by letting this parameter tend to zero and exhibiting a limit effective energy using the terminology of Gamma-convergence. Such energy depends on a single state variable and is of hyperelastic type. The form of its energy function highlights an optimization between microfracture and microscopic oscillations of the strain, mixing homogenization and high-contrast effects.