Numéro |
J. Phys. IV France
Volume 105, March 2003
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Page(s) | 31 - 37 | |
DOI | https://doi.org/10.1051/jp4:20030168 |
J. Phys. IV France 105 (2003) 31
DOI: 10.1051/jp4:20030168
On the use of evolving structure tensors to model initial and induced elastic and inelastic anisotropy at finite deformation
S. Reese1 and B. Svendsen21 Department of Civil Engineering, Ruhr University Bochum, 44780 Bochum, Germany
2 Department of Mechanical Engineering, University of Dortmund, 44227 Dortmund, Germany
Abstract
The purpose of this work is the formulation and application of an approach to the phenomeno-logical modeling of a class of
materials which may in general exhibit anisotropic elastic and inelastic
behaviour at large deformation. This is done in the framework of a thermodynamic, intemal-variable-based formulation for such
behaviour as based on two basic assumptions: (i), the modeling of the local
inelastic deformation in the material as a material isomorphism, and (ii), the modeling of the intemal
variables as structure tensors. The first of these assumptions follows from the idea that the local inelas-
tic deformation does not influence the form of the dependence of the constitutive relations on the other
independent constitutive variables. As shown in earlier work, one consequence of this assurnption is
the multiplicative decomposition of the deformation gradient into elastic and inelastic parts. And frorn
a therrnodynamic point of view, it is consistent with the idea that only a part of the local deformation
results in energy storage in the material. Assumption (ii) leads among other things to concrete forms for
the constitutive relations and the reduction of the flow rule to an evolution relation for the plastic right
Cauchy-Green deformation or its inverse for general anisotropic behaviour. Finally, application of the
general approach to the special cases of (1), non-linear kinematic and isotropic hardening in rnetals, and (2), anisotropic
polymer membranes, is briefly discussed and demonstrated.
© EDP Sciences 2003