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A variational formulation of constitutive models and updates in non‐linear finite viscoelasticity
Author(s) -
Fancello Eduardo,
Ponthot JeanPhilippe,
Stainier Laurent
Publication year - 2006
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.1525
Subject(s) - viscoplasticity , constitutive equation , viscoelasticity , mathematics , finite element method , multiplicative function , set (abstract data type) , finite strain theory , mathematical optimization , computer science , mathematical analysis , physics , engineering , structural engineering , thermodynamics , programming language
Abstract The purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a minimum principle within each load increment. The set of internal variables is strain‐based and employs, according to the specific model chosen, a multiplicative decomposition of strain into elastic and viscous components. The present approach shares the same technical procedures used for analogous models of plasticity or viscoplasticity, such as the solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration. However, instead of using the classical decomposition of inelastic strains into amplitude and direction , we take advantage of a spectral decomposition that provides additional facilities to accommodate, into simple analytical expressions, a wide set of specific models. Moreover, appropriate choices of the constitutive potentials allow the reproduction of other formulations in the literature. The final part of the paper presents a set of numerical examples in order to explore the characteristics of the formulation as well as its applicability to usual large‐scale FEM analyses. Copyright © 2005 John Wiley & Sons, Ltd.