A penalty-based cell vertex finite volume method for two-dimensional contact problems

In this paper, a penalty-based cell vertex finite volume method (P-CV-FVM) is proposed for the computation of two-dimensional contact problems. The deformation of objects during contact is described using the Total Lagrangian momentum equation. The governing equations are discretized using the cell vertex finite volume method. The control volume is constructed around each grid node to facilitate the efficient and accurate calculation of contact stress using penalty functions. By analyzing a classic contact example, the appropriate range of scaling factors in the penalty function method is obtained. Multiple contact problems are calculated and the results are compared with those from the finite element method (FEM). The results indicate that a stable and accurate solution can only be obtained with a scaling factor range of 10³–10¹² under this method. In addition, the mesh convergence of this method is better than that of FEM, and it meets the computational accuracy of Hertz contact and frictional contact problems.