Stress-controlled ratchetting in hypoplasticity: A study of periodically proportional loading cycles

0574182 - MÚ 2024 RIV AT eng J - Journal Article
Bauer, E. - Kovtunenko, V. A. - Krejčí, P. - Monteiro, Giselle Antunes - Runcziková, J.
Stress-controlled ratchetting in hypoplasticity: A study of periodically proportional loading cycles.
Acta Mechanica. Roč. 234, č. 9 (2023), s. 4077-4093. ISSN 0001-5970. E-ISSN 1619-6937
R&D Projects: GA ČR(CZ) GA20-14736S
Institutional support: RVO:67985840
Keywords : granular materials * hypoplasticity * differential equations
OECD category: Pure mathematics
Impact factor: 2.7, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00707-023-03596-1

We investigate rate-independent strain paths in a granular material generated by periodically oscillating stress cycles using a particular constitutive model within the hypoplasticity theory of Kolymbas type. It is assumed that the irreversible hypoplastic effects decay to zero when the void ratio reaches its theoretical minimum, while the void ratio is in turn related to the evolution of the volumetric strain through the mass conservation principle. We show that under natural assumptions on material parameters, both isotropic and anisotropic stress cycles are described by a differential equation whose solution converges asymptotically to a limiting periodic process taking place in the shakedown state when the number of loading cycles tends to infinity. Furthermore, an estimation of how fast, in terms of the number of cycles, the system approaches the limit state is derived in explicit form. It is shown how it depends on the parameters of the model, on the initial void ratio, and on the prescribed stress interval.
Permanent Link: https://hdl.handle.net/11104/0344530