Analysis of a Cattaneo-Mindlin problem using the boundary element method

In this paper, the Boundary Element Method is employed for the analysis of a Cattaneo-Mindlin problem. In order to obtain the stress over the contact surface, a quadratic continuous formulation for plane elasticity is proposed. In this method, the contact area is the initial unknown. Therefore, an algorithm is developed to compute the area and to discern between slip and stick regions. The Newton method is implemented to solve the resulting unconstrained non-linear system. The results are compared with the analytical solution showing a good agreement. To the authors knowledge this successful combination of the Newton's method with second order boundary elements for the solution of fretting problems with loading and unloading phases is an important and original contribution to the field.