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Modelled behaviour of granular material during loading and unloading

Krejčí, Pavel;  Siváková, Lenka;  Chleboun, Jan — 2019

Programs and Algorithms of Numerical Mathematics

The main aim of this paper is to analyze numerically the model behaviour of a granular material during loading and unloading. The model was originally proposed by D. Kolymbas and afterward modified by E. Bauer. For our purposes the constitutive equation was transformed into a rate independent form by introducing a dimensionless time parameter. By this transformation we were able to derive explicit formulas for the strain-stress trajectories during loading-unloading cycles and compare the results...

On Lyapunov stability in hypoplasticity

Kovtunenko, Victor A.;  Krejčí, Pavel;  Bauer, Erich;  Siváková, Lenka;  Zubkova, Anna V. — 2017

Proceedings of Equadiff 14

We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function....

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