Quasistatic normal compliance contact problem of visco elastic bodies with Coulomb friction implemented by QP and SGBEM
The quasistatic normal compliance contact problem of isotropic homogeneous linear visco elastic bodies with Coulomb friction at small strains in Kelvin Voigt rheology is considered. The discretization is made by a semi implicit formula in time and the Symmetric Galerkin Boundary Element Method (SGBEM) in space, assuming that the ratio of the viscosity and elasticity moduli is a given relaxation time coefficient. The obtained recursive minimization problem, formulated only on the contact boundary, has a nonsmooth cost function. If the normal compliance responds linearly and the 2D problems are considered, then the cost function is piecewise quadratic, which after 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, with additional discussion on numerical stability and convergence of the involved approximated Poincare Steklov operators.