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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.

74A15 Thermodynamics in solid mechanics
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