| Summary: | In this work, we propose a novel higher-order nonlocal operator method (NOM) based anisotropic phase-field approach to brittle fractures in rock-like materials and polycrystalline materials. The integral forms of the nonlocal phase-field and its corresponding mechanical model are obtained through the application of a variational principle. The implementation of the higher-order NOM is straightforward as it does not require the use of shape functions and their associated derivatives. Furthermore, the proposed method overcomes the limitation of the original nonlocal operator method, which exhibited first-order interpolation accuracy in the convergence test. The utilization of the reproducing kernel particle method is applied to obtain a nonlocal operator, enhancing both computational stability and accuracy. Moreover, the present method allows for the simulation of crack propagation patterns, both intergranular and transgranular, in polycrystalline materials. The present method is demonstrated through the use of several numerical examples, which provide a detailed understanding of the intricate mechanisms of crack initiation, propagation, and coalescence in both rock-like and polycrystalline materials.
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