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Mixed finite elements; finite element exterior calculus; nonlinear elasticity; geometric mechanics; Hilbert complex

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Compatible-Strain Mixed Finite Element Methods for 2D Compressible Nonlinear Elasticity

In this paper, using the Hilbert complexes of nonlinear elasticity, the approximation theory for Hilbert complexes, and the finite element exterior calculus, we introduce a new class of mixed finite element methods for 2D nonlinear elasticity -- compatible-strain mixed finite element methods (CSFEM). We consider a Hu-Washizu-type mixed formulation and choose the displacement, the displacement gradient, and the first Piola-Kirchhoff stress tensor as independent unknowns. We use the underlying spaces of the Hilbert complexes as the solution and test spaces.

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