The localized intensive deformation in the damaged solids requires highly refined discretization for accurate prediction, which significantly increases the computational cost. While adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh-based methods to perform adaptive model refinement in modeling the evolving localizations. In this work, neural network-enhanced reproducing kernel particle method (NN-RKPM) is proposed [1], where the location, orientation, and the shape of the solution transition near localization is automatically captured by the NN approximation via the minimization of total potential energy. The standard RK approximation is then utilized as a background discretization to approximate the smooth part of the solution to permit a much coarser discretization than the high-resolution discretization needed to capture sharp solution transition with the conventional methods. The proposed neural network approximation is regularized by introducing a length scale related to the objective dissipation energy. For modeling fracture, a modified NN-RKPM is proposed, where the neural network enhancement is formulated under the partition of unity framework with reproducing kernel function as the partition of unity function. The effectiveness of the proposed two NN-RKPM formulations is verified by a series of evolving localization and crack propagation examples. REFERENCES [1] Baek, J., Chen, J. S., Susuki, K., Neural network enhanced Reproducing Kernel Particle Method for modeling localizations, International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, 2022.