Extending a Physics-Based Constitutive Model using Genetic Programming

In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. In deformation processes, constitutive equations are used to describe the materials response to applied forces. One of the major shortcomings is fitting of model parameters due to unknown relations to processing conditions. We apply genetic programming to extend a physics-based constitutive model, which operates with internal material variables such as a dislocation density. The model contains a number of parameters, among them three calibration parameters. Currently, these must be fit to measured data since the relations to the processing conditions (e.g. deformation temperature, strain rate) are not fully understood. We propose two (explicit and implicit) GP-based methods to identify these relations and generate short but accurate expressions. The derived expressions can be plugged into the constitutive model instead of the calibration parameters and allow the interpolation between the processing parameters. Thus, the number of experiments required normally for parameter fitting can be potentially reduced. The proposed approach is of a general purpose and can be applied in materials modelling, when the dependence of model parameters on impact factors is not well understood.