On the coupling of regularization techniques and the boundary element method for a hemivariational inequality modelling a delamination problem

TL;DR

This paper integrates regularization techniques with adaptive hp-boundary element methods to efficiently solve hemivariational inequalities modeling delamination in composite structures, providing theoretical analysis and numerical validation.

Contribution

It introduces a novel approach combining regularization with hp-BEM for hemivariational inequalities, including error estimates and adaptivity strategies.

Findings

Successful numerical experiments demonstrating high-order accuracy

Effective regularization and adaptivity for complex boundary conditions

Theoretical guarantees for solution uniqueness and error bounds

Abstract

In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a model example we treat the delamination of composite structures with a contaminated interface layer. This problem has a weak formulation in terms of a nonsmooth variational inequality. The resulting hemivariational inequality (HVI) is first regularized and then, discretized by an adaptive $hp$-BEM. We give conditions for the uniqueness of the solution and provide an a-priori error estimate. Furthermore, we derive an a-posteriori error estimate for the nonsmooth variational problem based on a novel regularized mixed formulation, thus enabling $hp$-adaptivity. Various numerical experiments illustrate the behavior, strengths and weaknesses of the proposed high-order approximation scheme.