A generalization of B-differentiable equations method for elastoplastic contact problems with dual mortar discretization

In this study, a novel method based on the B-differentiable equations (BDEs) is proposed to solve the three-dimensional (3D) static and dynamic elastoplastic contact problems with friction. The contact conditions are formulated as the BDEs system, which can precisely satisfy Coulomb’s law of friction. Based on the mortar segment-to-segment contact model, the contact constraints are enforced by dual Lagrange multipliers for nonconforming meshes of the contact boundary. The non-smooth and nonlinear system equations composed of equilibrium and contact equations are simultaneously solved by the B-differentiable damping Newton method (BDNM), which has global convergence property. In each iteration, firstly, some contact displacements and contact forces, called substituted contact variables, are expressed by others according to the different contact states and contact conditions. The equilibrium equation is then solved, where the stiffness matrix is updated by substituting the contact variables. At last, the substituted contact variables will be restored. In the proposed method, the contact flexibility matrix is no longer needed, which saves the time for calculating the contact flexibility matrix due to changes in the stiffness matrix resulting from the update of stresses in the iteration step. By comparing with the results obtained by finite element commercial software ANSYS, the accuracy of the proposed algorithm is verified, and the property of convergence and efficiency are demonstrated for the elastoplastic contact problems by several numerical examples.