Improving the initial guess for the Newton-Raphson protocol in time-dependent simulations

TL;DR

This paper introduces a linearisation method for visco-plastic models that improves initial guesses in Newton-Raphson iterations, significantly reducing computational effort in time-dependent simulations.

Contribution

A novel linearisation procedure around a reference state that accounts for time-dependence, enhancing initial guess accuracy in Newton-Raphson methods for visco-plastic simulations.

Findings

Reduces CPU time by about 50%.

Halves the number of Newton-Raphson iterations needed.

Improves accuracy of initial guesses in time-dependent models.

Abstract

A general linearisation procedure for the consistent tangent of a small-strain visco-plastic material model is presented in this note. The procedure is based on multi-variable linearisation around a so-called 'reference state'. In particular, the linerarisation of the time integration scheme is found to yield an extra term compared to classical expressions, which only appears because the material response is time-dependent. It has the effect of yielding a very accurate initial guess for the Newton-Raphson protocol based on the ongoing viscous flow. It is shown, using a modern variational FFT-based solver, that the extra term reduces both the CPU time and the number of Newton-Raphson iterations by around a factor two.