On Lyapunov stability in hypoplasticity

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


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.

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Kovtunenko, V., Krejčí, P., Bauer, E., Siváková, L., & Zubkova, A. (2017). On Lyapunov stability in hypoplasticity. Proceedings Of Equadiff 2017 Conference, , 107-116. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/equadiff/article/view/708/553