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On multiscale significance of Rice’s normality structure. (English) Zbl 1192.74009
Summary: The normality structure proposed by J. R. Rice [J. Mech. Phys. Solids 19, 433-455 (1971; Zbl 0235.73002)] provides a minimal framework of multiscale thermodynamics. As shown in this paper, Rice’s multiscale thermodynamic formalism is exactly consistent with H. Ziegler’s essential notion [An introduction to thermomechanics. North-Holland Publishing Company. XIII (1983; Zbl 0531.73080)] that the entire constitutive response is determined by the knowledge of two scalar potential functions: an energy function and a dissipation function. In Rice’s multiscale thermodynamic formulation, the variational equation relating macroscale and microscale thermodynamic fluxes and forces plays a central role and ensures the equality between microscale and macroscale dissipation rate. The variational equation can be further reformulated into a principle of maximum equivalent dissipation. Based on the variation equation, the transformation from microscale to macroscale is characterized by two linear transformations with the same corresponding matrix.

MSC:
74A15 Thermodynamics in solid mechanics
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