0587707 - MÚ 2025 RIV US eng J - Journal Article
Kovtunenko, V. A. - Krejčí, Pavel - Monteiro, Giselle Antunes - Runcziková, J.
Hysteresis of implicit equations in hypoplasticity for soil materials with granular hardness degradation.
Journal of Mathematical Sciences. Roč. 280, č. 3 (2024), s. 453-467. ISSN 1072-3374
R&D Projects: GA MŠMT(CZ) 8X23001
Institutional support: RVO:67985840
Keywords : attractor * dynamic system * environmental degradation
OECD category: Pure mathematics
Method of publishing: Open access
https://doi.org/10.1007/s10958-024-07089-x

We study a hypoplastic model for soil and granular materials stemming from geomechanical engineering which further incorporates effects of degradation of the granular hardness, therefore allowing for the description of environmental weathering. The governing system is described by a nonlinear system of transcendental-differential equations for stress and strain rate, which is investigated with respect to its long-time dynamic. Under deviatoric stress control, two different solutions of the underlying, implicit differential equations are constructed analytically. The spherical components of stress and strain rate converge asymptotically to an attractor and lead to the sparsification of material states. Whereas under cyclic loading-unloading carried out in a numerical simulation, finite ratcheting of the deviatoric strain rate is observed in the form of a square spiral.
Permanent Link: https://hdl.handle.net/11104/0354802