Geodesic
Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity
Archivum mathematicum, Tome 59 (2023) no. 3, pp. 275-286.

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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.
DOI : 10.5817/AM2023-3-275
Classification : 34C55, 37N15, 74C15, 74L10
Keywords: hypoplasticity; rate-independent dynamic system; cyclic behavior; hysteresis; ratcheting; attractor; implicit ODE; closed-form solution; numerical simulation 
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     author = {Kovtunenko, Victor A. and Elia\v{s}, J\'an and Krej\v{c}{\'\i}, Pavel and Monteiro, Giselle A. and Runczikov\'a, Judita},
     title = {Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity},
     journal = {Archivum mathematicum},
     pages = {275--286},
     publisher = {mathdoc},
     volume = {59},
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     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-3-275/}
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Kovtunenko, Victor A.; Eliaš, Ján; Krejčí, Pavel; Monteiro, Giselle A.; Runcziková, Judita. Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity. Archivum mathematicum, Tome 59 (2023) no. 3, pp. 275-286. doi : 10.5817/AM2023-3-275. http://geodesic.mathdoc.fr/articles/10.5817/AM2023-3-275/

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