# Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials

## TL;DR

This paper demonstrates that nonlinear Griffith models for nonsimple brittle materials converge to linear models under small strain limits, extending previous results to arbitrary space dimensions.

## Contribution

It establishes a linearization result for nonlinear Griffith energies with second gradient dependence in any space dimension via b3-convergence.

## Key findings

- Existence of minimizers for boundary value problems.
- Identification of nonlinear energies with linear Griffith models in the small strain limit.
- Extension of previous linearization results to arbitrary space dimensions.

## Abstract

We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity problems, we prove existence of minimizers for boundary value problems. We then pass to a small strain limit in terms of suitably rescaled displacement fields and show that the nonlinear energies can be identified with a linear Griffith model in the sense of $\Gamma$-convergence. This complements the study in [Arch. Ration. Mech. Anal. 225 (2017), 425-467] by providing a linearization result in arbitrary space dimensions.