Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity

0570769 - MÚ 2024 RIV CZ eng J - Článek v odborném periodiku
Kovtunenko, V. A. - Eliaš, J. - Krejčí, P. - Monteiro, Giselle Antunes - Runcziková, J.
Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity.
Archivum mathematicum. Roč. 59, č. 3 (2023), s. 275-286. ISSN 0044-8753
Grant CEP: GA ČR(CZ) GA20-14736S
Institucionální podpora: RVO:67985840
Klíčová slova: hypoplasticity * rate-independent dynamic system * cyclic behavior
Obor OECD: Pure mathematics
Způsob publikování: Open access
http://dx.doi.org/10.5817/AM2023-3-275

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.
Trvalý link: https://hdl.handle.net/11104/0342106