Implementation of the Leonov model into FEM

Abstract eng:
The Leonov model, where the Eyring flow model is used to represent the plastic shear rate of the deformation of a material, appears to be a proper choice for the description of non-linear viscoelastic behavior of polymers. This paper outlines formulations of the generalized Leonov model and presents possible approaches to numerical implementation of this constitutive law. A fully explicit method based on forward Euler integration is known to suffer from numerical instabilities, which can be only prevented by taking very short time steps. To eliminate this restriction, a fully implicit method (backward Euler integration), where the solution is established by employing the Newton-Raphson iteration method, is developed. This procedure requires keeping track of the total deformation increment during the iteration as the method is path dependent. Therefore, implementation of this method into the FEM source code requires a special treatment as is shown in this paper.

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