An Interface Problem in Solid Mechanics with a Linear Elastic and a Hyperelastic Material

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The three dimensional interface problem is considered with the homogeneous Lame system in an unbounded exterior domain and some quasistatic nonlinear elastic material behavior in a bounded interior Lipschitz domain. The nonlinear material is of the Mooney-Rivlin type of polyconvex materials. We give a weak formulation of the interface problem based on minimizing the energy, and rewrite it in terms of boundary integral operators. Then, we prove existence of solutions.