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Anisotropic elastic–plastic analysis of shells at large strains. A comparison of multiplicative and additive approaches to enhanced finite element design and constitutive modelling
Author(s) -
Miehe Christian,
Apel Nikolas
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1145
Subject(s) - finite element method , constitutive equation , plasticity , orthotropic material , tangent modulus , shell (structure) , hyperelastic material , mathematics , finite strain theory , tangent , anisotropy , measure (data warehouse) , multiplicative function , mathematical analysis , materials science , structural engineering , computer science , geometry , modulus , physics , engineering , composite material , quantum mechanics , database
The article presents new aspects of large‐strain anisotropic elastoplastic analyses of shells. On the side of computational shell analysis we focus on recently developed brick‐type mixed finite shell elements based on trilinear displacement interpolations equipped with enhanced strain modes and shell‐typical assumed strain modifications. Here, we compare two classes of this shell element design based on a multiplicative and an additive definition of an enhanced strain measure, respectively. Furthermore, for both types of continuum‐based shell elements we outline unified interfaces to strain‐driven constitutive stress update algorithms of anisotropic finite plasticity. On the side of computational plasticity we investigate two classes of constitutive models suitable for the description of anisotropic elastoplastic response at finite strains. The first framework uses a multiplicative definition of an elastic strain measure based on a plastic map, the second an additively defined elastic strain measure based on a plastic metric. Both constitutive frameworks use Hencky‐type logarithmic strain measures and are specified to a model problem of orthotropic elastic–plastic response of a standard material. The algorithmic treatment of the two constitutive models is based on an incremental variational formulation that defines the stresses and consistent tangent moduli in terms of a function evaluation. We compare the performances of the two finite element formulations and the two constitutive models by means of numerical simulations of sheet drawing processes. For the range of metal plasticity at moderate strains it is shown that results obtained with the different approaches are close to each other, while the additive approaches provide simpler and more efficient settings. Copyright © 2004 John Wiley & Sons, Ltd.