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For calculating large deformations in finite elasticity, we have proposed amethod of successive linear approximation, by considering the relativedescriptional formulation. In this article we briefly describe this method andwe prove the existence and uniqueness of weak solutions for boundary valueproblems for nearly incompressible Mooney-Rivlin materials, that arise in eachstep of the method.

Mathematical analysis of successive linear approximation for Mooney-Rivlin material model in finite elasticity