  We present a new physics informed neural network (PINN) algorithm for solving
brittle fracture problems. While most of the PINN algorithms available in the
literature minimize the residual of the governing partial differential
equation, the proposed approach takes a different path by minimizing the
variational energy of the system. Additionally, we modify the neural network
output such that the boundary conditions associated with the problem are
exactly satisfied. Compared to conventional residual based PINN, the proposed
approach has two major advantages. First, the imposition of boundary conditions
is relatively simpler and more robust. Second, the order of derivatives present
in the functional form of the variational energy is of lower order than in the
residual form. Hence, training the network is faster. To compute the total
variational energy of the system, an efficient scheme that takes as input a
geometry described by spline based CAD model and employs Gauss quadrature rules
for numerical integration has been proposed. Moreover, we utilize the concept
of transfer learning to obtain the crack path in an efficient manner. The
proposed approach is used to solve four fracture mechanics problems. For all
the examples, results obtained using the proposed approach match closely with
the results available in the literature. For the first two examples, we compare
the results obtained using the proposed approach with the conventional residual
based neural network results. For both the problems, the proposed approach is
found to yield better accuracy compared to conventional residual based PINN
algorithms.
