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

Victor A. Kovtunenko; Ján Eliaš; Pavel Krejčí; Giselle A. Monteiro; Judita Runcziková

Archivum Mathematicum (2023)

  • Issue: 3, page 275-286
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Kovtunenko, Victor A., et al. "Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity." Archivum Mathematicum (2023): 275-286. <http://eudml.org/doc/298994>.

@article{Kovtunenko2023,
abstract = {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.},
author = {Kovtunenko, Victor A., Eliaš, Ján, Krejčí, Pavel, Monteiro, Giselle A., Runcziková, Judita},
journal = {Archivum Mathematicum},
keywords = {hypoplasticity; rate-independent dynamic system; cyclic behavior; hysteresis; ratcheting; attractor; implicit ODE; closed-form solution; numerical simulation},
language = {eng},
number = {3},
pages = {275-286},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity},
url = {http://eudml.org/doc/298994},
year = {2023},
}

TY - JOUR
AU - Kovtunenko, Victor A.
AU - Eliaš, Ján
AU - Krejčí, Pavel
AU - Monteiro, Giselle A.
AU - Runcziková, Judita
TI - Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 3
SP - 275
EP - 286
AB - 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.
LA - eng
KW - hypoplasticity; rate-independent dynamic system; cyclic behavior; hysteresis; ratcheting; attractor; implicit ODE; closed-form solution; numerical simulation
UR - http://eudml.org/doc/298994
ER -

References

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