(A) study on elastoplastic contact analysis using smoothed finite element methods

Abstract

In order to overcome limitations of the conventional computational schemes for contact mechanics, a new type of node-to-node contact method has been developed by introducing the smoothed finite element method and the matching mesh algorithm. The key point of the proposed contact method is not to satisfy the contact constraint by constructing the contact elements of the integral type between dissimilar meshes but to attain the node-to-node contact after generating matching meshes. The matching mesh algorithm, which is the core of the proposed contact method, is designed to limit the modified range of the elements to the contact area by using the three dimensional boundary conforming Delaney triangulation and the polyhedral elements. Since the nodal connectivity and inter-element compatibility are directly satisfied in the matching contact interface, the accuracy of the solution is guaranteed compared with the conventional surface-to-surface contact method. The conventional surface-to-surface contact method does not pass the contact patch test accurately when the mesh configuration of the two contacting surfaces is substantially different, but the proposed contact method pass the contact patch test regardless of the mesh configuration on the contact surface. The proposed contact method extends the analysis range of the node to node contact from infinitesimal contact deformations to finite sliding and large deformations through the continuous matching mesh generation. In the finite sliding contact, the proposed method yields a more stable and accurate solution than the conventional contact scheme. By introducing the edge-based smoothed finite element method, the accuracy of the tetrahedral element was improved and effectively constructed were the shape function fields of the polyhedral elements generated by the matching mesh algorithm. The edge-based smoothed finite element method has the best performance among the smoothed finite element methods but has the problem that it cannot be applied to the elasto-plastic constitutive equations due to the volumetric locking phenomenon. In this study, to resolve this problem, the B-bar method was introduced in the edge-based smoothed finite element method. Finally, performed is the elasto-plastic contact analysis involving large deformations and finite sliding using the proposed node-to-node contact method and the proposed B-bar aided edge-based smoothed finite element method. The efficiency and the accuracy of the proposed method are demonstrated through various numerical examples wherein the solutions from the present approach are compared with those from the commercial package code, Abaqus.