Stability and error analysis for time integrators applied to strain-softening materials Original Research Article

The behavior of explicit time integrators is examined for the field equations of dynamic viscoplasticity in one dimension. The analysis proceeds by linearizing the field equations about the current state and freezing coefficients so that the solution to the system of ordinary differential equations can be computed explicitly. Amplification matrices for the central difference method (with rate tangent constitutive update) and fourth-order Runge-Kutta schemes are obtained by applying these schemes to the resulting linear, constant coefficient equations. These amplification matrices lead to local truncation error estimates for the temporal integrators as well as to estimates of the resulting growth rate.