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Using the Clausius-Duhem inequality to obtain restrictions on constitutive relations is frequently used in the literature. Although exstensively used, I understand that these restrictions may prohibit some thermodynamic process (or motion). In what way? Is there any relevent literature on this problem and specifically to viscoelastic modeling?
That is an interesting question. As you said, most people apply the Clausis-Duhem inequality to help derive relations between constitutive quantities. The Clausius-Duhem inequality is equivalent to the second law of thermodynamics. There are theories of non-equilibrium thermodynamics (do literature search on that term) that might also have value for constitutive modeling, but I am not aware of many people pursuing that topic at this time.
The procedure described in the paper of Coleman and Noll 1963 is a turning crank in continuum constitutive modeling. Correct me if I am wrong. Exploiting the Clausius-Duhem inequality to obtain relations between constitutive quantities both in equilibrium and in non-equilibrium thermodynamics constrains the exisiting thermodynamic processes thus leading to a loss of generality. These constraints depends on the choice of the set of thermodynamic variables, on the explicit form of the constitutive relations and on the material parameter restrictions, namely grouped under the term of constitutive assumptions. A paper discussing this issue: Leigh,D.C., 1969 (http://www.springerlink.com/content/p061p44591t54131/). What are the limitations of the Coleman and Noll procedure? Is it only the result of a particular choice of the constitutive assumptions? Are some physcial processes automatically excluded and this independently on the choice of the thermodynamic variables?
You are asking some very sticky questions that are difficult to answer. May I ask what is driving your interest in this area :cool:
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