Viscoelasticity behavior for finite deformations, using a consistent hypoelastic model based on Rivlin materials - Archive ouverte HAL Access content directly
Journal Articles Continuum Mechanics and Thermodynamics Year : 2016

Viscoelasticity behavior for finite deformations, using a consistent hypoelastic model based on Rivlin materials

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Abstract

When constructing viscoelastic models, rate-form relations appear naturally to relate strain and stress tensors. One has to ensure that these tensors and their rates are indifferent with respect to the change of observers and to the superposition with rigid body motions. Objective transports are commonly accepted to ensure this invariance. However, the large number of transport operators developed makes the choice often difficult for the user and may lead to physically inconsistent formulation of hypoelasticity. In this paper, a methodology based on the use of the Lie derivative is proposed to model consistent hypoelasticity as an equivalent incremental formulation of hyperelasticity. Both models are shown to be reversible and completely equivalent. Extension to viscoelasticity is then proposed from this consistent model by associating consistent hypoelastic models with viscous behavior. As an illustration, Mooney–Rivlin nonlinear elasticity is coupled with Newton viscosity and a Maxwell-like material is investigated. Numerical solutions are then presented to illustrate a viscoelastic material subjected to finite deformations for a large range of strain rates.
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Dates and versions

hal-02283376 , version 1 (10-09-2019)

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Guillaume Altmeyer, Benoît Panicaud, Emmanuelle Rouhaud, Mingchuan Wang, Arjen Roos, et al.. Viscoelasticity behavior for finite deformations, using a consistent hypoelastic model based on Rivlin materials. Continuum Mechanics and Thermodynamics, 2016, 28 (6), pp.1741-1758. ⟨10.1007/s00161-016-0507-0⟩. ⟨hal-02283376⟩
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