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. 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. 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. Numerical examples presented in this book demonstrate the superior performance of mortar finite element methods for contact simulations.

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