Frictional contact multi-point constraint in two dimensions

Abstract

Node-to-Segment slideline frictional contact formulation as one of the simplest penalty-based contact algorithms could be further simplified to a general Multi-Point Constraint formulation. This effective MPC formulation is proposed in this paper.Two case specific and a general MPC formulations are proposed which uses the distance vector of the master boundaries with respect to a unique point for the calculation of the contact interaction. Accordingly, the general master surface is reduced to a control node and its MPC distance vector and MPC normal matrix. As a result, the numerous expressions for the contact stiffness matrix will be reduced to its first simple expression, exclusively.Static and dynamic examples are solved to illustrate that the MPC algorithm proposed maintains the same accuracy of Node-to-Segment algorithms while presents the efficiency and user-friendly properties of the multiple-point constraint algorithms used in advanced finite element programs.