A data-driven yield criterion for porous ductile single crystals containing spherical voids via physics-informed neural networks

Abstract

Yield criteria for porous material have been widely used to model the decrease of yield strength caused by porosity during ductile failure which deserves long-term efforts in modelling to remedy the current drawbacks. To improve their accuracy, a method of building yield criteria for porous single crystals based on physics-informed neural networks (PINNs) has been developed, and the newly well-trained yield functions are capable of predicting the yield stress of porous single crystals with different porosity, stress states and crystal orientations. The reliability of the yield functions is guaranteed by the precise datasets generated by the crystal plasticity finite-element method. In particular, through embedding the associated flow rule into the training process, the PINN-based yield function not only achieves higher accuracy in comparison with the analytical methods (e.g. variational nonlinear homogenization or limit analysis) but also avoids the improper appearance of grooves that happens in feed-forward neural networks. The proposed framework enjoys an excellent portability as the yield functions can be rebuilt in the similar non-trivial procedure when new influencing factors must be introduced, which makes us believe in its potential to be extended.