This article is cited in 1 paper

Mechanics of Solids

Mathematical model of viscoelastic softening material with exponential creep kernel

S. V. Gorbunov

Samara State Technical University, Samara, Russia

Abstract: 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.

Keywords: viscoelastic material, Lyapunov stability of solutions, exponential creep kernel, stability region of solutions, tertiary creep, stability of numerical iterative calculation.

UDC: 539.376

MSC: Primary 74G55; Secondary 74Cxx

Original article submitted 02/XI/2011
revision submitted – 13/III/2012

DOI: 10.14498/vsgtu1068

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