On the elastodynamic solution of frictional contact problems using variational inequalities

This article is concerned with the development, implementation and application of variational inequalities to treat the general elastodynamic contact problem. The solution strategy is based upon the iterative use of two subproblems. Quadratic programming and Lagrange multipliers are used to solve the respective rst and second subproblems and to identify the candidate contact surface and contact stresses. This approach guarantees the imposition of the active kinematic contact constraints, avoids the use of special contact elements and the interference of the user in dictating the accuracy of the solution. A modi ed Newmark formulation is developed to integrate the resulting time-dependent variational inequality. This newly devised implicit time integration scheme is unconditionally stable, second-order accurate, avoids numerical oscillations present in the traditional Newmark method, and does not cause numerical dissipation. To demonstrate the versatility and accuracy of the newly proposed algorithm, several examples are examined and compared with existing solutions where the penalty method has been employed