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Article

Karra, Satish ; Rajagopal, Kumbakonam R.
Development of three dimensional constitutive theories based on lower dimensional experimental data. (English). Applications of Mathematics, vol. 54 (2009), issue 2, pp. 147-176
MSC: 74A15, 74A20, 74D10, 76A02, 76A05, 76A10 | MR 2491852 | Zbl 1200.76005 | DOI: 10.1007/s10492-009-0010-z
Keywords:
constitutive relations; Lagrange multiplier; Helmholtz potential; rate of dissipation; viscoelasticity; Burgers' fluid; maximum entropy production
Summary:
Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate of entropy production, etc. In this paper we show different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that can all describe the same experimental data. All of these three dimensional models, in one dimension, reduce to the model proposed by Burgers to describe the viscoelastic behavior of bodies.
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