Bastien, Jérôme; Schatzman, Michelle; Lamarque, Claude-Henri Study of some rheological models with a finite number of degrees of freedom. (English) Zbl 0954.74011 Eur. J. Mech., A, Solids 19, No. 2, 277-307 (2000). 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. Cited in 16 Documents MSC: 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 Keywords:differential inclusion; friction; Saint-Venant element; elastoplasticity; maximal monotone graph; existence; uniqueness; maximal monotone operators; hysteresis cycles; polygonal cycles PDFBibTeX XMLCite \textit{J. Bastien} et al., Eur. J. Mech., A, Solids 19, No. 2, 277--307 (2000; Zbl 0954.74011) Full Text: DOI