Optimal Data-Generation Strategy for Machine Learning Yield Functions in Anisotropic Plasticity

Abstract

Trained machine learning (ML) algorithms can serve as numerically efficient surrogate models of sophisticated but numerically expensive constitutive models of material behavior. In the field of plasticity, ML yield functions have been proposed that serve as the basis of a constitutive model for plastic material behavior. If the training data for such ML flow rules is gained by micromechanical models, the training procedure can be considered as a homogenization method that captures essential information of microstructure-property relationships of a given material. However, generating training data with micromechanical methods, as for example, the crystal plasticity finite element method, is a numerically challenging task. Hence, in this work, it is investigated how an optimal data-generation strategy for the training of a ML model can be established that produces reliable and accurate ML yield functions with the least possible effort. It is shown that even for materials with a significant plastic anisotropy, as polycrystals with a pronounced Goss texture, 300 data points representing the yield locus of the material in stress space, are sufficient to train the ML yield function successfully. Furthermore, it is demonstrated how data-oriented flow rules can be used in standard finite element analysis.