On some non-local approximation of nonisotropic Griffith-type functionals

TL;DR

This paper investigates the $ ext{Gamma}$-convergence approximation of nonisotropic Griffith-type functionals with $p$-growth using non-local convolution functionals on Sobolev spaces, advancing understanding of nonlocal modeling in fracture mechanics.

Contribution

It introduces a novel non-local convolution approximation scheme for nonisotropic Griffith functionals with $p$-growth, establishing $ ext{Gamma}$-convergence results.

Findings

Established $ ext{Gamma}$-convergence of non-local functionals to Griffith-type functionals.

Extended approximation techniques to nonisotropic, $p$-growth settings.

Provided mathematical framework for nonlocal fracture models.

Abstract

The approximation in the sense of $\Gamma$-convergence of nonisotropic Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, by means of a suitable sequence of non-local convolution type functionals defined on Sobolev spaces, is analysed.