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Abstract. Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the stress field along the contact boundary. This leads to a hemivariational inequality, which after discretization by finite elements we solve by a nonconvex bundle method, where upper-C 1 criteria have to be minimized. As this is in contrast with other classes of mechanical problems with non-monotone friction laws and in other applied fields, where criteria are typically lower-C 1 , we propose a bundle method suited for both types of nonsmoothness. We prove its global convergence in the sense of subsequences and test it on a typical delamination problem of material sciences.

In this paper, we couple regularization techniques of nondifferentiable optimization with the h-version of the boundary element method (h-BEM) to solve nonsmooth variational problems arising in contact mechanics. As a model example we consider the delamination problem. The variational formulation of this problem leads to a hemivariational inequality (HVI) with a nonsmooth functional defined on the contact boundary. This problem is first regularized and then discretized by a h-BEM. We prove convergence of the h-BEM Galerkin solution of the regularized problem in the energy norm, provide an a-priori error estimate and give a numerical example.

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.