Machine-learning convex and texture-dependent macroscopic yield from crystal plasticity simulations

The influence of the microstructure of a polycrystalline material on its macroscopic deformation response is still one of the major problems in materials engineering. For materials characterized by elastic-plastic deformation responses, predictive computational models to characterize crystal-plasticity (CP) have been developed. However, due to their large demand of computational resources, CP simulations cannot be straightforwardly implemented in hierarchical computational models such as FE2. This bottleneck intensifies the need for the development of macroscopic simulation tools that can be directly informed by microstructural quantities. Using a 3D finite element solver for CP, we generate a macroscopic yield function database based on general loading conditions and crystallographic texture. Leveraging the advancement in statistical modeling we describe and apply a machine learning framework for predicting plane stress macroscopic yield as a function of crystallographic texture. The convexity of the data-driven yield function is guaranteed by using partially input convex neural networks as the predictive tool. Furthermore, in order to allow for the predicted yield function to be directly incorporated in time-integration schemes, as needed for the finite element method, the yield surfaces are interpreted as the boundaries of signed distance function level sets. Results generated for an example cube texture are discussed.