Development of interpretable, data-driven plasticity models with symbolic regression

In many applications, such as those which drive new material discovery, constitutive models are sought that have three characteristics: (1) the ability to be derived in automatic fashion with (2) high accuracy and (3) an interpretable nature. Traditionally developed models are usually interpretable but sacrifice development time and accuracy. Purely data-driven approaches are usually fast and accurate but lack interpretability. In the current work, a framework for the rapid development of interpretable, data-driven constitutive models is pursued. The approach is characterized by the use of symbolic regression on data generated with micromechanical finite element models. Symbolic regression is the search for equations of arbitrary functional form which match a given dataset. Specifically, an implicit symbolic regression technique is developed to identify a plastic yield potential from homogenized finite element response data. Through three controlled test cases of varying complexity, the approach is shown to successfully produce interpretable plasticity models. The controlled test cases are used to investigate the robustness and scalability of the method and provide reasonable recommendations for more complex applications. Finally, the recommendations are used in the application of the method to produce a porous plasticity model from data corresponding to a representative volume element of voids within a metal matrix. Published by Elsevier Ltd.

Automated summary

This paper presents a framework for the rapid development of interpretable, data-driven constitutive models using symbolic regression technique. The approach successfully produces interpretable plasticity models through controlled test cases, demonstrating the robustness and scalability of the method. Reasonable recommendations are provided for more complex applications based on the controlled test cases.