Study of some rheological models with a finite number of degrees of freedom. (English) Zbl 0954.74011

Summary: We show that a large number of rheological models can be covered by the existence and uniqueness theory for maximal monotone operators. Numerical simulations display hysteresis cycles when the forcing is periodic. We demonstrate that a given shape of hysteresis cycle in an appropriate class of polygonal cycles can be always realized by adjusting the physical parameters of rheological model.


74C99 Plastic materials, materials of stress-rate and internal-variable type
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
37N15 Dynamical systems in solid mechanics
Full Text: DOI