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For the first time, the mixed-mode dynamic fracture in anisotropic functionally varying microcellular structures is investigated herein. To this end, a recently developed homogenization MATLAB implementation capable of considering material and geometry-induced anisotropy is used, and a continuous medium with equivalent functionality distributed mechanical properties to the original microcellular domain is obtained. Then, the resulting material domain is subjected to dynamic loads, and the crack propagation is predicted by using a novel Timoshenko-based peridynamic model. This innovative method unprecedentedly accounts for a bond-length dependent shear influence factor and a shear strain-based failure criterion. Finally, numerous cases consisting of compact-tension (CT) and Kalthoff-Winkler specimens with several void sizes, shapes, and distribution patterns are numerically solved. The results demonstrate that the crack path is significantly influenced by the void distribution pattern near the crack tip, providing a foundation for engineering crack propagation to prevent it from reaching critical areas of a structure. 

The original two-dimensional bond-based peridynamic (BBPD) framework, which only considers the pairwise forces (compression and tension) between two material points, is extended by incorporating the effect of shear deformation in the calculations and its influence on the failure of the bonds. To this end, each bond is considered as a short Timoshenko beam, and by doing so, the traditional BBPD is enhanced into a more comprehensive model known as multi-polar peridynamic (MPPD). The proposed novel approach explicitly considers the shear influence factor used in Timoshenko beams and introduces a strain-based shear deformation failure criterion. The model is then validated against two benchmark experimental tests (i.e., a standard pure mode I edge crack, and a Kalthoff-Winkler configuration) reported in the literature under in-plane dynamic loading and plane stress conditions. In most cases, the developed model is shown to be more accurate in predicting the crack paths obtained from the experimental results when compared to other theoretical methods delineated in the literature. Furthermore, a noticeable change in crack branching and crack path is observed in a study on the effects of Poisson’s ratio and the loading rate. This investigation also demonstrated that the proposed MPPD model can accommodate materials with Poisson’s ratios up to 1/3, expanding the range beyond the traditional BBPD limitations. 

ABSTRACT A recently developed Timoshenko‐based peridynamic model with a variable micropolar shear influence factor is extended to study the behavior of dynamic crack propagation in functionally graded materials (FGMs). To this end, first, the proposed model is validated against two experimental three‐point bending benchmark problems with different material functions as well as varying loading rates and durations. Then, numerous additional cases with different boundary conditions and material distribution are studied to predict crack initiation and propagation in such mediums. The examples consist of three‐point bending and Kalthoff–Winkler specimens with various material functions under dynamic loads. Finally, the effects of material anisotropy induced by functionally varying material properties on crack propagation path are addressed. It is shown that this new model is advantageous because of its capability to account for shear deformation effects in the bonds previously ignored by the original bond‐based peridynamic models. Moreover, comparing the proposed modified bond‐based model to more complex methods, such as state‐based peridynamics, reveals that the simplicity of the current approach results in lower computational costs while still achieving comparable results.