Active macro-zone approach for incrementalelastoplastic-contact analysis

The symmetric boundary element method, based on the Galerkin hypotheses, has found an application inthe nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. Inthis paper, we want to treat these complex phenomena together as a linear complementarity problem.A mixed variable multidomain approach is utilized in which the substructures are distinguished intomacroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strainsmay occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted(weak) form on the boundary sides and in the nodes (strong) between contiguous substructures have to beintroduced, in order to attain the solving equation system governing the elastoplastic-contact/detachmentproblem. The elastoplasticity is solved by incremental analysis, called for active macro-zones, and uses thewell-known concept of self-equilibrium stress field here shown in a discrete form through the introductionof the influence matrix (self-stress matrix). The solution of the frictionless contact/detachment problem wasperformed using a strategy based on the consistent formulation of the classical Signorini equations rewrittenin discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contactor detachment.