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MSC: 34D20, 37B25, 74C15
Nonlinear ODE, rate-independent problem, asymptotic behavior, attractor, Lyapunov function, proportional loading, hypoplasticity, granular media
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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