A Bayesian-based approach for constitutive model selection and calibration using diverse material responses

Abstract

Constitutive models are essential for analyzing the structural performance of materials under complex loading conditions. However, multiple models with different sets of values of the parameters can describe a particular mechanical response of a material. Thus, treating model selection and parameter calibration separately and relying on a single mechanical response may lead to inaccuracies. Herein, we present a Bayesian-based approach that integrates model selection and calibration into a single-step process while concurrently evaluating multiple mechanical responses. We focus on constitutive models that include both strain and strain-rate hardening and evaluate both indentation and uniaxial tensile responses. Finite element simulations, combined with Gaussian process regressors, are employed to efficiently explore the multidimensional parameter space of all models and their resultant responses. To demonstrate the effectiveness of the proposed approach, we first use computationally generated responses of a known model-parameter combination as reference and compare it with the predicted model-parameter combination. We then apply the approach to experimental data, for which the model-parameter combination is unknown, and validate predictions by assessing a mechanical response not used for model selection and calibration. This validation highlights the robustness and predictive capability of our approach.