Elasto-plastic contact problem for nonsmooth nonlinear equations method

In the Nonsmooth Nonlinear Equations Method, the contact constraints are formulated as a set of nonsmooth nonlinear equations and satisfied accurately. The Nonsmooth Damped Newton method (NDN) is used to solve these equations with high computational efficiency. In this paper, the Nonsmooth Nonlinear Equations Method (NNEQM) is extended to the elasto-plastic case in which small strain, Von Mises yield criteria, isotropic hardening law and associated flow rule are considered. For three-dimensional static elastoplastic frictional contact problem (3D-SEPFCP), two kinds of subproblems are needed to be solved: one is the elastoplastic problem and the other is the contact problem. A method combining NNEQM with Newton-Raphson method is presented as NNEQM1. Moreover, the elastoplastic problem can be formulated as linear complementary problem or nonsmooth equations which are solved by the methods in Mathematical Programming. Therefore, all the contact constraints and yield criteria at the Gauss Points in elements are expressed as a unified set of nonlinear nonsmooth equations which can be solved by NDN. The method is also considered as another way to solve 3D-SEPFCP and denoted as NNEQM2. Numerical example is given to show that the validity of these two approaches and a comparison between them has been made. It is concluded that the two approaches are easily convergent, the first one is more efficient than the second one, and the results derived by NNEQM1 is more accurate.