Finite element analysis for large deformation frictional contact problems with finite sliding

In the analysis of frictional contact problems with large deformation, the use of a convected coordinate system is a natural approach, by which the frame indifference of friction law can be maintained. However, in the case of the finite element method, a problem arises due to the discontinuity of the local coordinates between elements when sliding extends over the element boundary. In this work, a method is proposed to solve this problem, i.e., although the formulation is essentially based on a convected coordinate system, the sliding term is redefined as a spatial vector and is calculated using the reference configuration. Thus, finite sliding due to large deformation can be treated, regardless of the limitations of element coordinate systems. Also, the corresponding consistent tangent stiffness is derived to obtain quadratic convergence. The effectiveness of the proposed method is verified in this study by two numerical examples, including an elastoplastic frictional contact problem with large deformation.