Mortar finite element methods for large deformation contact mechanics

Large deformation contact problems are found in many important applications in engineering and the sciences. Examples include vehicle crash testing, metal forming applications, and post buckling response. Numerical solution of these problems is quite challenging, with robustness issues in particular arising from extreme nonlinearity and nonsmoothness of the contact operators. These complexities must be handled in the presence of large deformation and significant relative sliding of the contacting bodies. Recently, there have been significant advances in this field, with many formulations becoming available. However, the robustness of these formulations is still a limitation in many problems of interest.; In this work, a mortar finite element formulation is developed for solving large deformation frictional contact problems in a robust and accurate manner. The technique employs an integral projection of contact variables on the contact surface to provide a consistent representation of all contact variables over a single discretization. To assure frame indifference of the frictional constitutive relation, an objective definition of the tangential relative velocity is introduced. A consistent linearization of the discrete global equation is presented in detail to facilitate the Newton-Raphson solution strategy.; A new global searching algorithm based on bounding volume hierarchies, with the distinct advantage of output sensitivity, significantly improves the performance of the mortar formulation. The algorithm is extended to self-contact problems by applying a curvature criterion with a new algorithm to detect subsurface adjacencies. To define the mortar traction fields on contiguous surface patches, a facet sorting algorithm is proposed, based on element connectivity of self-contact element pairs as identified by the searching algorithm.; Finally, a lubricated contact formulation based on the mortar element method is developed. The fluid film thickness is computed with a least squares projection based on dual basis functions. The challenge associated with the Reynolds boundary is circumvented by a penalty regularization of the equivalent complementary problem. Based on the weak form of the solid and the fluid phase equations, the unknown variables related to both phases are solved in a fully coupled system.; Several numerical examples, demonstrating the superior performance of the proposed approaches, are also presented.