Predicting Calibration Parameter Values for Constitutive Models using Genetic Programming

In material science, models are derived to describe emergent properties (e.g. elasticity, strength, conductivity, ...) and their relations to the material and processing conditions. Constitutive models are models that describe the behaviour of materials for instance deformation processes through applied forces. We describe a general method for the extension of constitutive white-box models using genetic programming (GP). The method is demonstrated for a constitutive model which is used in computational mechanics to describe the material response to various thermo-mechanical loading conditions. This model operates with internal material variables such a dislocation density and contains a number of parameters. Among them there are three calibration parameters, which are usually fit to measured data since the relations to the processing conditions (e.g. deformation temperature, strain rate) are not fully understood. Our proposed GP-based method identifies these relations and generates short expressions which can be plugged into the constitutive model instead of the calibration parameters. This would enable interpolation as well as extrapolation which is crucial for constitutive modelling. Our results show that evolving extensions for the constitutive model implicitly with GP leads to better predictive accuracy than explicitly learning independent formulas for predicting calibration parameters with symbolic regression.