Robust explicit computational developments and solution strategies for impact problems involving friction

New explicit dynamic computational developments in conjunction with finite element formulations for impact problems are described in this paper. The proposed methodology is based on employing a variational inequality for dynamic problems involving Coulomb friction with the so-called forward incremental displacement–central difference method specially formulated in this paper for this class of problems. To enforce the constraints on the contact boundary, a linear complementary equation is established by means of a minimization problem subjected to constraints, which is equivalent to discretization of the variational inequality of the dynamic problem. In conjunction with these developments, a new conjugate gradient based explicit solution strategy is described for effectively solving the linear complementary equations. With the motivation for providing effective computational procedures suitable for vectorization and parallel computations, the proposed developments not only provide a fundamentally sound and robust theoretical basis but also serve to be ideally suited for impact problems involving frictional contact on high speed computing environments.