Mixed-Mode Timoshenko-Based Peridynamics for Dynamic Crack Propagation in Functionally Graded Materials

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.