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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 72
Application of the Concept of Evolving Structure Tensors to the Modeling of Initial and Induced Anisotropy in Engineering Structures at Large Deformations B. Svendsen+ and S. Reese*
+Department of Mechanical Engineering, University of Dortmund, Germany
Full Bibliographic Reference for this paper
B. Svendsen, S. Reese, "Application of the Concept of Evolving Structure Tensors to the Modeling of Initial and Induced Anisotropy in Engineering Structures at Large Deformations", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 72, 2004. doi:10.4203/ccp.79.72
Keywords: thermodynamic formulation, inelasticity, induced anisotropy, structure tensors.
Summary
In this work, a thermodynamic approach to the modeling and simulation of
induced elastic and inelastic material behaviour in the phenomenological realm as
based on the concept of evolving structure tensors is discussed. From the constitutive
point of view, these quantities determine the material symmetry properties. In addition,
the stress and other dependent constitutive fields are isotropic functions of these by
definition. The evolution of these during loading then results in an evolution of the
anisotropy of the material. From an algorithmic point of view, the current approach
leads to constitutive models which are quite amenable to numerical implementation.
To demonstrate the applicability of the resulting constitutive formulation, we apply
it to the cases of (i), metal plasticity with combined hardening involving both
deformation- and permanently-induced anisotropy relevant to the modeling of
processes such as metal forming, and to (ii), deformation-induced anisotropy in an
initially orthotropic pneumatic membrane consisting of a rubber matrix and nylon fibres.
The approach developed in this work offers a thermodynamically consistent framework to
model materials which behave, in a broad sense, anisotropically. Within this framework,
the approach taken here is based on two basic assumptions. The first is the concept of
elastic isomorphism extended from the classical form of earlier works to now include the
effects of deformation-induced anisotropy on the evolution of the vector- and tensor-valued
internal variables. As shown in earlier work, in the context of this assumption, the local
inelastic deformation in the material becomes associated with the plastic part
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