Classical and Unilateral Contact Analysis in Statics and Dynamics

Abstract

Classical and unilateral contact analysis problems in statics and dynamics are considered. Emphasis is posed on the combination of effective tools from the general theory of nonsmooth mechanics with more classical boundary and finite element methods in statics and dynamics. Unilateral contact interaction belongs to the class of unknown, load-dependent nonlinearity. The main difficulty is the either contact -or separation nature of this nonliner joint. It is shown that elements of nonsmooth analysis, which in the most simple case leads to complementarity relations, can be used for the modelling and the subsequent numerical solution of the mechanical problem. Similar nonlinearities arise in frictional contact problems (in this case, the either-or decision modells the stick-slip effects) or in adhesive contact problems (with applications on delamination modelling, ductile crack modelling etc). Boundary or interface nonlinearities are suitable for boundary element methods. This explains the choice of this method in this chapter. Discussion of further models and extensions, as well as references to appropriate literature, are included.