Extending a Physics-Based Constitutive Model using Genetic Programming

TL;DR

This paper introduces a genetic programming approach to automatically derive functional relationships for model parameters in physics-based material models, enabling better interpolation across processing conditions.

Contribution

It presents explicit and implicit genetic programming methods to extend constitutive models by deriving interpretable expressions for calibration parameters.

Findings

Implicit method yields more accurate results

Explicit method is computationally less expensive

Approach enables interpolation between processing parameters

Abstract

In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on processing conditions. Currently, these parameters must be optimized to fit measured data since their relations to processing conditions (e.g. deformation temperature, strain rate) are not fully understood. We present a new approach that identifies the functional dependency of calibration parameters from processing conditions based on genetic programming. We propose two (explicit and implicit) methods to identify these dependencies and generate short interpretable expressions. The approach is used to extend a physics-based constitutive model for deformation processes. This constitutive model operates with internal material variables such as a dislocation density and contains a number of parameters, among them three calibration parameters. The derived expressions extend the constitutive model and replace the calibration parameters. Thus, interpolation between various processing parameters is enabled. Our results show that the implicit method is computationally more expensive than the explicit approach but also produces significantly better results.