An augmented mixed finite element method for nonlinear elasticity problems

Abstract:

This paper introduces and analyses a full augmented mixed finite element method for the nonlinear elasticity problems with strongly imposed symmetry stress tensor. The mixed method includes the strain tensor as an auxiliary variable, which combines with the usual stress-displacement approach adopted in linear elasticity. By introducing different stability terms, we obtain an argmented mixed finite element variation formulation and a full argmented mixed finite element variation formulation. In order to obtain the well-posedness of the two schemes, we adopt different finite element spaces to approximate the variables and derive the optimal error estimate. Finally, a numerical example is presented to confirm the theoretical analysis.