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Rate‐type Model for electro‐rheological Material Behaviour consistent with Extended Thermodynamics: Application to a steady viscometric flow
Author(s) -
Sadiki A.,
Balan C.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310072
Subject(s) - rheology , constitutive equation , nonlinear system , viscoelasticity , mechanics , thermodynamics , equations of motion , shear rate , electric field , physics , materials science , statistical physics , classical mechanics , finite element method , quantum mechanics
Based on extended thermodynamics, a class of rate‐type constitutive equations for electrorheological materials is presented. It is shown unlike many recent works using standard methods of continuum mechanics, that this approach, which consists in postulating expressions which relate the time derivative of the Cauchy stress to the motion, takes well account of the viscoelastic‐plastic effects as well as the coupling between the motion and the electric field. By considering special cases it turns out that the derived nonlinear algebraic model embeds a variety of existing differential models in the literature. The accuracy of the model is illustrated by considering a steady shear flow in which the electric field is applied perpendicularly to the flow direction. Analytical solutions with various parameter variations are obtained and discussed. The model predicts well the behaviour associated with material instabilities observed in viscometric flows for which the existence of the yield stress is required as confirmed by many experiments.