From Adhesive to Brittle Delamination in Visco-Elastodynamics

TL;DR

This paper develops a mathematical model for dynamic fracture in visco-elastic bodies, incorporating inertia and delamination, and proves the existence of solutions using advanced variational techniques.

Contribution

It introduces a new weak solvability concept for a mixed rate-dependent/rate-independent delamination model with inertia, and establishes existence results through variational convergence.

Findings

Existence of solutions for the dynamic delamination model.

Development of a generalized solution concept for mixed rate-dependent systems.

Application of variational convergence techniques to handle nonsmooth constraints.

Abstract

In this paper we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent flow rule for the delamination parameter is coupled with the momentum balance for the displacement, including inertia. This model features a nonsmooth constraint ensuring the continuity of the displacements outside the crack set, which is marked by the support of the delamination parameter. A weak solvability concept, generalizing the notion of energetic solution for rate-independent systems to the present mixed rate-dependent/rate-independent frame, is proposed. Via refined variational convergence techniques, existence of solutions is proved by passing to the limit in approximating systems which regularize the nonsmooth constraint by conditions for adhesive contact. The presence of the inertial term requires the design of suitable recovery spaces small enough to provide compactness but large enough to recover the information on the crack set in the limit.