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

0570769 - MÚ 2024 RIV CZ eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA20-14736S
Institutional support: RVO:67985840
Keywords : hypoplasticity * rate-independent dynamic system * cyclic behavior
OECD category: Pure mathematics
Method of publishing: 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.
Permanent Link: https://hdl.handle.net/11104/0342106