On Lyapunov stability in hypoplasticity

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.