A peridynamic-informed deep learning model for brittle damage prediction
Roozbeh Eghbalpoor Azadeh Sheidaei
In this study, a novel approach that combines the principles of peridynamic
(PD) theory with PINN is presented to predict quasi-static damage and crack
propagation in brittle materials. To achieve high prediction accuracy and
convergence rate, the linearized PD governing equation is enforced in the
PINN's residual-based loss function. The proposed PD-INN is able to learn and
capture intricate displacement patterns associated with different geometrical
parameters, such as pre-crack position and length. Several enhancements like
cyclical annealing schedule and deformation gradient aware optimization
technique are proposed to ensure the model would not get stuck in its trivial
solution. The model's performance assessment is conducted by monitoring the
behavior of loss function throughout the training process. The PD-INN
predictions are also validated through several benchmark cases with the results
obtained from high-fidelity techniques such as PD direct numerical method and
Extended-Finite Element Method. Our results show the ability of the nonlocal
PD-INN to predict damage and crack propagation accurately and efficiently.