Imperfect Bonding with Nonpenetration Condition

In this contribution three topics are considered. Common to them is a question how to efficiently solve a mechanical problem for a composite material with imperfect bonding between individual material phases. A special attention is paid to the kinematics of the debonding. Namely, to prevent the overlapping of the material phases across the interface where the displacement field is discontinuous. This requirement is expressed as the nonpenetration condition which is a unilateral constraint on the displacements. As a result we have a boundary value problem with unilateral boundary conditions. It is recognized that the simplest way to solve it is to formulate the problem as a variational problem. How can be this done for a time dependent problem is a subject of the first section. To simplify discussion consideration is restricted to a model one dimensional problem. After establishing a stable and consistent numerical method importance of the nonpenetration condition is shown by comparison between solutions with and without imposition of the nonpenetration condition. It is shown that an important step to solve the constrained problem is elimination of the unconstrained degrees of freedom and thus reduction of the problem to the problem with a considerable smaller set of the degrees of freedom. The idea of the reduction of the problem to a smaller set is worth to be pursued on its own.