A Novel Hybrid Approach for Employing the Fast Convolution-Based Method in Peridynamics with Standard Peridynamic Damage Criterion

The peridynamic mathematical formulation is based on integral equations which allow modeling an autonomous damage evolution. The most used approach to solve peridynamics equations is the meshfree method with one-point Gaussian quadrature, which is not computationally efficient. The reformulation of peridynamic integrals into convolutional form, as shown in the Fast Convolution Based Method, significantly reduces the computational cost. However, its application on crack propagation problems relies on a damage criterion which introduces an undesired mass loss in the region close to the crack surface. To face this problem, a new hybrid method combining the fast convolution-based approach with the meshfree peridynamic formulation is presented. By using the meshfree method only in regions where cracks propagate, the proposed method leverages the computational efficiency of the convolution-based technique and predicts crack paths that are consistent with peridynamic models discretized with the meshfree method. The hybrid model has been developed for both the linearized bond-based and linearized ordinary state-based peridynamic formulations. The capabilities of the proposed method have been studied in 1D and 2D wave propagation problems, as well as in 2D and 3D crack propagation test cases.