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On uniqueness in linear viscoelasticity: A family of counterexamples. (English) Zbl 0621.73039
Within the framework of linear viscoelasticity a two-parameter family of relaxation functions is exhibited which allows nonuniqueness of the infinitesimal strain, for a given stress, in the space of sinusoidal-in- time strain histories. These relaxation functions are shown to be compatible with thermodynamics and to have a positive equilibrium elastic modulus.

MSC:
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
74A15 Thermodynamics in solid mechanics
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