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In the present work, the problem of coupling multiple physical phenomenon in a finite element framework with an interface between two or more non-conforming meshes is considered. Recently the research group at the Institute for Computational Mechanics, Technische Universität München has developed a dual mortar method of monolithic coupling for fluid structure interactions (FSI) involving incompressible fluid. The research group at the Center for Aerospace Structures, University of Colorado at Boulder has developed a residual based method of monolithic coupling that includes FSI, as well as fluid thermal coupling including nonlinear surface effects such as ablation. Both methods take advantage of the benefits of solving a monolithic system which is of the same size as the uncoupled system and does not include Lagrange multipliers in the final system. One of the primary benefits of this is the ability to use well developed iterative linear solvers. The goal of this summer research is to combine the capabilities of both research groups so as to extend the dual mortar method to include compressible FSI problems and fluid thermal interactions with nonlinear surface affects.

A two-dimensional, finite deformation frictional contact formulation with Coulomb?s law is presented. The approach considers multibody contact and is based on a mortar formulation. The enforcement of contact constraints is realized with dual Lagrange multipliers. These alternative multiplier spaces are constructed in a way that the multipliers can easily be eliminated from the global system of equations by static condensation such that the system size does not increase. Friction kinematic variables are formulated in an objective way and enter non-smooth complementarity functions for expressing the contact constraints. An active set strategy is derived by applying a semismooth Newton method, which treats contact nonlinearities, material and geometrical nonlinearities in one single iterative scheme. By further carrying out a consistent linearization for both normal and frictional contact forces and constraints, a robust and highly efficient algorithm for linear and higher order (quadratic) interpolation is achieved. Efficiency of the proposed method and quality of results are demonstrated in serveral exemples.