Comparison of different least‐squares mixed finite element formulations for hyperelasticity

Abstract

The main goal of this contribution is the solution of geometrically nonlinear problems using the mixed least-squares finite element method (LSFEM). An investigation of a hyperelastic material law based on logarithmic deformation measures is performed. The basis for the proposed LSFEM is a div-grad first-order system consisting of the equilibrium condition and the constitutive equation, see e.g. Cai and Starke [1]. For the interpolation of the solution variables vector-valued Raviart-Thomas functions for the approximation of the stresses and standard Lagrange polynomials for the displacements are used. In order to show the performance of the presented formulations a numerical example is investigated, where we compare the different interpolation combinations used.