Local-solution approach to quasistatic rate-independent mixed-mode delamination

TL;DR

This paper rigorously analyzes the quasistatic, rate-independent delamination process in mixed mode, introducing a stress-driven local solution concept and demonstrating convergence of a semi-implicit discretization in a 2D example.

Contribution

It develops a new stress-driven local solution framework for mixed-mode delamination and proves convergence of a semi-implicit discretization method.

Findings

Convergence of the discretization to stress-driven local solutions.

Relevance of the solution concept demonstrated on a 2D example.

Approximate maximum-dissipation behavior observed.

Abstract

The quasistatic rate-independent evolution of a delamination at small strains in the so-called mixed mode, i.e.~distinguishing opening (Mode I) from shearing (Mode II) is rigorously analyzed in the context of a concept of stress-driven local solutions. The model has separately convex stored energy and is associative, namely the 1-homogeneous potential of dissipative force driving the delamination depends only on rates of internal parameters. An efficient fractional-step-type semi-implicit discretisation in time is shown to converge to specific, stress-driven like) local solutions that may approximately obey the maximum-dissipation principle. Making still a spatial discretisation, this convergence as well as relevancy of such solution concept are demonstrated on a nontrivial 2-dimensional example.