Damage-driven fracture with low-order potentials: asymptotic behavior, existence and applications

TL;DR

This paper investigates the asymptotic behavior and existence of damage-driven fracture models with low-order nonlinear potentials, enabling the modeling of complex physical phenomena like fluid-driven fracturing and plastic slip.

Contribution

It introduces a novel analysis of $ ext{Gamma}$-convergence for damage to fracture energies incorporating low-order potentials, addressing existence and broadening modeling capabilities.

Findings

Established $ ext{Gamma}$-convergence results for the models.

Proved existence of minimizers under the new framework.

Applied the theory to physical phenomena such as fluid-driven fracturing.

Abstract

We study the $\Gamma$-convergence of damage to fracture energy functionals in the presence of low-order nonlinear potentials that allows us to model physical phenomena such as fluid-driven fracturing, plastic slip, and the satisfaction of kinematical constraints such as crack non-interpenetration. Existence results are also addressed