Development of a method for integrating time‐dependent constitutive equations with large, small or negative strain rate sensitivity

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Abstract
A unified numerical method to integrate stiff time‐dependent constitutive equations has been developed. This method is a stable, non‐iterative and self‐correcting solution procedure which works successfully over a wide range in strain rate sensitivity. Time steps are automatically controlled during integration to achieve a user‐specified accuracy. This method is implemented in the program package NONSS whose dual purpose is examination of the behaviour of unified constitutive models by themselves (‘one‐element behaviour’) as well as providing a computationally efficient subroutine for utilizing such models with existing finite element programs for non‐linear structural and metal forming analyses.This paper first reviews the relation between the numerical characteristic of constitutive equations and the choice of integration methods. Then the paper presents the derivation of the governing basic equations in the new method, and also derives a special algorithm which permits large integration steps within the negative strain rate sensitivity (‘serrated yielding’) regime. Examples of the program's performance are given, including plasticity at high and low temperatures, cyclic deformation and multiaxial straining.

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