  Physics-Informed Neural Networks (PINNs) have aroused great attention for its
ability to address forward and inverse problems of partial differential
equations. However, approximating discontinuous functions by neural networks
poses a considerable challenge, which results in high computational demands and
low accuracy to solve fracture mechanics problems within standard PINNs
framework. In this paper, we present a novel method called Discontinuity
Embedded Deep Energy Method (DEDEM) for modeling fracture mechanics problems.
In this method, interfaces and internal boundaries with weak/strong
discontinuities are represented by discontinuous functions constructed by
signed distance functions, then the representations are embedded to the input
of the neural network so that specific discontinuous features can be imposed to
the neural network solution. Results demonstrate that DEDEM can accurately
model the mechanical behaviors of cracks on a large variety of fracture
problems. Besides, it is also found that DEDEM achieves significantly higher
computational efficiency and accuracy than the existing methods based on domain
decomposition techniques.
