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

• Published in: Computers & structures Vol. 252; no. C; p. 106557
• Main Authors: Bomarito, G.F., Townsend, T.S., Stewart, K.M., Esham, K.V., Emery, J.M., Hochhalter, J.D.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.08.2021; Elsevier BV; Elsevier
• Subjects: Accuracy; Complexity; Constitutive models; Finite element method; Genetic programming; Homogenization; Mathematical models; Plastic properties; Plasticity; Regression; Symbolic regression; Homogenization; Symbolic regression; Genetic programming; Plasticity
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2021.106557

•Symbolic regression is used to produce data-driven plasticity models in the form of yield equations.•Tests are performed to verify a known plasticity model can be reproduced from response data with 95% robustness.•A new, interpretable porous plasticity model is produced from response data of a representative volume element. 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.