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

In: Proceedings in Applied Mathematics and Mechanics, Jg. 7 (2007) ; 1, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, S. 4040043-4040044
ISSN: 1617-7061
Zeitschriftenaufsatz / Fach: Bauwissenschaften
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 L2-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.