On Lyapunov stability in hypoplasticity

Kovtunenko, Victor A.; Krejčí, Pavel; Bauer, Erich; Siváková, Lenka; Zubkova, Anna V.

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 107-116

Abstract

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We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function.

How to cite

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Kovtunenko, Victor A., et al. "On Lyapunov stability in hypoplasticity." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 107-116. <http://eudml.org/doc/294918>.

@inProceedings{Kovtunenko2017,
abstract = {We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function.},
author = {Kovtunenko, Victor A., Krejčí, Pavel, Bauer, Erich, Siváková, Lenka, Zubkova, Anna V.},
booktitle = {Proceedings of Equadiff 14},
keywords = {Nonlinear ODE, rate-independent problem, asymptotic behavior, attractor, Lyapunov function, proportional loading, hypoplasticity, granular media},
location = {Bratislava},
pages = {107-116},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {On Lyapunov stability in hypoplasticity},
url = {http://eudml.org/doc/294918},
year = {2017},
}

TY - CLSWK
AU - Kovtunenko, Victor A.
AU - Krejčí, Pavel
AU - Bauer, Erich
AU - Siváková, Lenka
AU - Zubkova, Anna V.
TI - On Lyapunov stability in hypoplasticity
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 107
EP - 116
AB - We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function.
KW - Nonlinear ODE, rate-independent problem, asymptotic behavior, attractor, Lyapunov function, proportional loading, hypoplasticity, granular media
UR - http://eudml.org/doc/294918
ER -

References

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  3. Bauer, E., Wu, W., A hypoplastic model for granular soils under cyclic loading, , Proc. Int. Workshop Modern Approaches to Plasticity, D. Kolymbas, ed., Elsevier, 2010, pp. 247–258. 
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  7. Khludnev, A.M., Kovtunenko, V.A., Analysis of Cracks in Solids, , WIT-Press, Southampton, Boston, 2000. 
  8. Kolymbas, D., An outline of hypoplasticity, , Arch. Appl. Mech., 61 (1991), pp. 143–151. 
  9. Kovtunenko, V.A., Zubkova, A.V., Mathematical modeling of a discontinuous solution of the generalized Poisson–Nernst–Planck problem in a two-phase medium, , Kinet. Relat. Mod., 11 (2018), pp.119–135. MR3708185
  10. Niemunis, A., Extended Hypoplastic Models for Soils, , Habilitation thesis, Ruhr University, Bochum, 2002. 
  11. Niemunis, A., Herle, I., Hypoplastic model for cohesionless soils with elastic strain range, , Mech. Cohes.-Frict. Mat., 2 (1997), pp. 279–299. 
  12. Svendsen, B., Hutter, K., Laloui, L., Constitutive models for granular materials including quasi-static frictional behaviour: toward a thermodynamic theory of plasticity, , Continuum Mech. Therm., 4 (1999), pp. 263–275. MR1710675
  13. Wu, W., Bauer, E., Kolymbas, D., Hypoplastic constitutive model with critical state for granular materials, , Mech. Mater., 23 (1996), pp. 45–69. 

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