Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM

摘要

The quasistatic normal-compliance contact problem of isotropic homogeneouslinear visco-elastic bodies with Coulomb friction at small strains inKelvin-Voigt rheology is considered. The discretization is made by asemi-implicit formula in time and the Symmetric Galerkin Boundary ElementMethod (SGBEM) in space, assuming that the ratio of the viscosity andelasticity moduli is a given relaxation-time coefficient. The obtainedrecursive minimization problem, formulated only on the contact boundary, has anonsmooth cost function. If the normal compliance responds linearly and the 2Dproblems are considered, then the cost function is piecewise-quadratic, whichafter a certain transformation gets the quadratic programming (QP) structure.However, it would lead to second-order cone programming in 3D problems.Finally, several computational tests are presented and analysed, withadditional discussion on numerical stability and convergence of the involvedapproximated Poincar\'e-Steklov operators.