Mathematical model of viscoelastic softening material with exponential creep kernel

The variant of mathematical model of uniaxial strain for viscoelastic material with exponential creep kernel is proposed. Lyapunov stability of the solution of the model in case of permanent stress is investigated. The stability region of solutions of mathematical model's differential equations, сorresponding to asymptotically restricted creep of material, is established. Instability region of solutions is in accord with appearance of tertiary creep. Relation between stability of solutions by Lyapunov and stability of iterative calculation for numerical solving the system of equations is established. As an illustration the investigation of model problem is quoted.