Coupling regularization and adaptive \(hp\)-BEM for the solution of a delamination problem. (English) Zbl 1393.74246
Summary: 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 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 prove the very first a-posteriori error estimate for the nonsmooth variational problem utilizing a novel mixed regularized formulation, thus enabling \(hp\)-adaptivity. Various numerical experiments illustrate the behavior, strengths and limitations of the proposed high-order approximation scheme.
MSC:
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 74M15 | Contact in solid mechanics |
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