# A peridynamic-informed deep learning model for brittle damage prediction

arXiv: https://arxiv.org/abs/2310.01350 · HTML: https://mlsanity.com/paper/2310.01350/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 78 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions](https://mlsanity.com/paper/2302.14227/) (2023)
- [A nonlocal physics-informed deep learning framework using the peridynamic differential operator](https://mlsanity.com/paper/2006.00446/) (2020)
- [A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture](https://mlsanity.com/paper/2105.06055/) (2021)
- [Linking Properties to Microstructure in Liquid Metal Embedded Elastomers via Machine Learning](https://mlsanity.com/paper/2208.04146/) (2022)

## Abstract (arXiv)

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.