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Mixed finite element methods; finite element exterior calculus; nonlinear elasticity; incompressible elasticity; Hilbert complex

Arash_Yavari's picture

Compatible-Strain Mixed Finite Element Methods for Incompressible Nonlinear Elasticity

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity — compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields.

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