Least‐squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity

The objective of this work is to discuss a least‐squares finite element method with applications to physically nonlinear and anisotropic constitutive equations at small strains. The L 2 ‐norm minimization of the residuals of the given first order system of differential equations leads to a functional, which is a two field formulation in the displacements and the stresses, see e.g. Cai & Starke [1]. These functionals provide the foundation for the formulations of the related least‐squares mixed finite elements. A main focus of the presentation lies on the extension of plane elasticity to anisotropic or nonlinear material behavior. In this context transversely isotropic elasticity and viscoplasticity is considered. Finally a numerical example is presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)