si-PiNet: A novel stress integration method for elastoplastic models

Elastoplastic theory is ubiquitous in engineering for modelling the mechanical behaviours of various materials such as metals and granular matter. Elastoplasticity allows computation of plastic strains and updated stresses with hardening parameters using explicit and/or implicit integration algorithms, requiring strong mathematical and domain knowledge. This study proposes a novel stress integration prior information based neural network (si-PiNet) to achieve step-change improvements in the solution of elastoplastic stress-strain responses. si-PiNet leverages a strong non-linear mapping ability in high-dimensional space to search for the correct stress under a given strain increment. The associated stress prediction is constrained by encoded prior information in the form of elastoplastic theory. To verify feasibility and generalization, si-PiNet is applied to solve three canonical elastoplastic constitutive models, namely von Mises, Mohr-Coulomb and Modified Cam-clay. The results indicate si-PiNet can accurately capture the evolution of stress and hardening of various complex constitutive models, whilst also achieving a lower sensitivity to the magnitude of strain increment compared with conventional stress integration algorithms. si-PiNet provides engineering researchers with a new generic paradigm for the computation of plastic strain and updating of stresses with potential for application to any constitutive model of interest.