Calibration of constitutive models using genetic algorithms

Abstract

Constitutive models, describing material response to load, are an essential part of computational materials engineering. Semi-empirical constitutive laws including the Johnson–Cook and Zerilli–Armstrong models are widely used in finite element simulation for easy computability and rapid run time. The reliability of these models depends on accurate and reproducible fitting of parameters. This work presents a genetic algorithm (GA) based tool to fit parameters in constitutive models. The GA approach is capable of finding the global optimum parameter set in a robust, repeatable, and computationally efficient manner. It has been demonstrated that the obtained fits are better than those using traditional term-wise optimisation. Allowed to fit freely, the GA method will be likely to produce non-physical parameter values. However, by constraining the fit, the GA method can produce parameters that are physically reasonable and minimise the error when extrapolating to unseen data. Finally, the GA method may be used to choose between a variety of possible constitutive models based on a transparent best fit approach. The model has been demonstrated by using datasets from the literature for DH–36 steel and Ti-6Al-4V. This includes data from different studies, in which there are both random and systematic variations. The framework developed here is made freely available and modifiable, and may be extended to include other constitutive models as required.