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Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity. (English) Zbl 0770.73031
Summary: The integral constitutive equations of a multipolar viscoelastic material are analyzed from the thermodynamic point of view. They are shown to be approximated by those of the differential-type viscous materials when the processes are slow. As a consequence of the thermodynamic compatibility of the viscoelastic model, the coefficients of viscosity of the approximate viscous model are shown to have an Onsager-type symmetry. This symmetry was employed earlier in the proof of the existence of solutions for the corresponding equations.
MSC:
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74A20 Theory of constitutive functions in solid mechanics
74A15 Thermodynamics in solid mechanics
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