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I am a novice getting my toes wet in continuum mechanics and nonlinear elasticity. I have seen papers that use both approaches in developing constitutive connections to compliment balance equations of various sorts. My question is the energy inequality more general than the virtual work approach? I am tackling a visco-elastic problem where I will need to account for the time dependent relaxation of the material. Can this not be handled by virtual work since energy will be lost rather than conserved?

I ask because virtual work seems a bit more straight forward but I wonder if it is at the expense of applicability. I am looking for the pros and cons of both approaches.

Thanks in advance!

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  • $\begingroup$ This does not sound like a computational science problem, more like physics $\endgroup$
    – Maxim Umansky
    Mar 2, 2021 at 17:41
  • $\begingroup$ @Maxim Umansky Sort of sits neatly in between spaces because the driver for one's choice could be the computational ease. $\endgroup$
    – TheCodeNovice
    Mar 2, 2021 at 18:12
  • $\begingroup$ This does not belong to computational science. Virtual work is the restatement of conservation of momentum (closer to 1st law of thermo). Clausius-Duhem is the 2nd law of thermo. Constitutive equations can be rejected if they don't satisfy the 2nd law - you can't decide such laws based on momentum conservation only. $\endgroup$
    – Biswajit Banerjee
    Mar 3, 2021 at 19:43

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