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Least‐squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity
Author(s) -
Schwarz Alexander,
Schröder Jörg
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700803
Subject(s) - viscoplasticity , transverse isotropy , finite element method , elasticity (physics) , mathematical analysis , mathematics , anisotropy , isotropy , nonlinear system , constitutive equation , linear elasticity , norm (philosophy) , physics , thermodynamics , law , optics , quantum mechanics , political science
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)