Stability of the Numerical Integral of a Viscoplastic Constitutive Equation Using the Nonlinear Hardening Rule

Abstract

A mathematical mechanism of the stability of the numerical integral by one-step Euler method is discussed in applying to a viscoplastic constitutive equation. The algorithm of one-step Euler method is represented by a nonlinear dynamic system and it is shown that its stability can be examined through an analysis of eigen values of the Jacobian at the fixed point of the dynamic system.
Numerical experiments of the viscoplastic deformation give the validity of the theory.