Address:
Institute for Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstr. 36, 8010 Graz, Austria and Lavrent’ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
Institute for Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstr. 36, 8010 Graz, Austria
Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Praha 6, Czech Republic
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Praha 6, Czech Republic
E-mail:
Abstract: A long-time dynamic for granular materials arising in the hypoplastic theory of Kolymbas type is investigated. It is assumed that the granular hardness allows exponential degradation, which leads to the densification of material states. The governing system for a rate-independent strain under stress control is described by implicit differential equations. Its analytical solution for arbitrary inhomogeneous coefficients is constructed in closed form. Under cyclic loading by periodic pressure, finite ratcheting for the void ratio is derived in explicit form, which converges to a limiting periodic process (attractor) when the number of cycles tends to infinity.
AMSclassification: primary 34C55; secondary 37N15, 74C15, 74L10.
Keywords: hypoplasticity, rate-independent dynamic system, cyclic behavior, hysteresis, ratcheting, attractor, implicit ODE, closed-form solution, numerical simulation.
DOI: 10.5817/AM2023-3-275