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On spatial effects of modelling in linear viscoelasticity. (English) Zbl 0899.73137

Summary: The parameters of a linear model of a viscoelastic material are determined by testing the material in homogeneous (i.e. spatially constant) states. Some of the qualitative properties of the behaviour of the material observed in the tests may be unexpectedly lost if the material is confined, so that the behaviour varies in space and is thus not homogeneous. One such property is the (Lyapunov) stability of the deformation. To ensure that the material possesses these properties, it is necessary to impose some additional restrictions on the model parameters. These restrictions are found by analyzing the boundary value problems for viscoelastic bodies of various shapes and subjected to various boundary conditions.

MSC:

74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
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