Approaches To The Description Of Anisotropic Material Behaviour At Finite Elastic And Plastic Deformations. Theory And Numerics

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The present work deals with purely macroscopic descriptions of anisotropic material behaviour. Key aspects are new developments in the theory and numerics of anisotropicplasticity. After a short discussion of the classification of solids by symmetry transformations a survey about representation theory of isotropic tensor functions and tensor polynomials is given. Next alternative macroscopic approaches to finite plasticity are discussed. When considering a multiplicative decomposition of the deformation gradient into an elastic part and a plastic part, a nine dimensional °ow rule is obtained that allows the modeling of plastic rotation. An alternative approach bases on the introduction of a metric-like internal variable, the so-called plastic metric, that accounts for the plastic deformation of the material. In this context, a new class of constitutive models is obtained for the choice of logarithmic strains and an additive decomposition of the total strain measure into elastic and plastic parts. The attractiveness of this class of models is due to their modular structure as well as the a+nity of the constitutive model and the algorithms inside the logarithmic strain space to models from geometric linear theory. On the numerical side, implicit and explicit integration algorithms and stress update algorithms for anisotropic plasticity are developed. Their numerical e+ciency crucially bases on their careful construction. Special focus is put on algorithms that are suitable for variational formulations. Due to their (incremental) potential property, the corresponding algorithms can be formulated in terms of symmetric quantities. A reduced storage eRort and less required solver capacity are key advantages compared to their standard counterparts.

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