Stabilized method for contact mechanics and dissipative interfacial kinematic processes

This paper presents an interface stabilized method for contact mechanics and interfacial frictional processes between two elastic bodies. The unique aspect of the method is its variational coupling of the interacting surfaces, eliminating the need for master-slave type algorithms. Method is developed and implemented in the context of finite deformation kinematics by employing Variational Multiscale ideas at the contact surfaces. Invoking an overlapping decomposition of the displacement field into coarse- and fine-scales along the interfaces, a two-level coupled system of equations is obtained. This consists of a set of coarse-scale variational equations governing the deformation of the two bodies, and a set of fine-scale variational equations that are confined to a narrow band along the contacting surfaces. The local solution of the fine-scale equations provides analytical expressions for the Lagrange multipliers that optimally enforce the displacement and traction boundary conditions on the contacting surfaces. Additionally, an analytical expression for the interfacial stabilization tensor is derived, which depends on the material constitutive models from both sides. The stabilization tensor incorporates concepts of stress averaging and area averaging, adjusting itself as the elements undergo geometric deformation. A unique aspect of the formulation is that it is free of any tunable parameters, and it can accommodate interfacial friction and interfacial damage. Convergence studies confirm the variational consistency of the method under finite strain. 2D and 3D test cases are presented to validate the method and highlight the range of application of the method.