A bayesian optimisation methodology for the inverse derivation of viscoplasticity model constants in high strain-rate simulations

Abstract

We present an inverse methodology for deriving viscoplasticity constitutive model parameters for use in explicit finite element simulations of dynamic processes using functional experiments, i.e., those which provide value beyond that of constitutive model development. The developed methodology utilises Bayesian optimisation to minimise the error between experimental measurements and numerical simulations performed in LS-DYNA. We demonstrate the optimisation methodology using high hardness armour steels across three types of experiments that induce a wide range of loading conditions: ballistic penetration, rod-on-anvil, and near-field blast deformation. By utilising such a broad range of conditions for the optimisation, the resulting constitutive model parameters are generalised, i.e., applicable across the range of loading conditions encompassed the by those experiments (e.g., stress states, plastic strain magnitudes, strain rates, etc.). Model constants identified using this methodology are demonstrated to provide a generalisable model with superior predictive accuracy than those derived from conventional mechanical characterisation experiments or optimised from a single experimental condition.

Keywords

• Constitutive modelling
• Finite element
• Bayesian optimisation
• Finite element model updating