Numerical approximation of a frictional contact problem in elasto‐plasticity based on the penalty approach

Abstract

AbstractA numerical model based on the penalty method for the unilateral contact problem with friction between an elasto‐plastic body and a rigid foundation is presented in this paper. The process is supposed to be static, the material's behavior is described by the nonlinear elastic constitutive Hencky's law, the contact and friction are modeled, respectively, with Signorini's condition and a version of Coulomb's law in which the coefficient of friction depends on the slip. Next, the existence of a unique weak solution to the penalized problem is proved, and its convergence towards that of the variational problem is confirmed. Then, the finite element method is a numerical method that can be successfully used to generate an approximate solution for a problem of this kind. Afterward, a successive iteration technique to solve the problem numerically is proposed, and a convergence result is established. Finally, to prove the reliability and the performance of this approach, numerical experiments of two‐dimensional test problems are carried out.