Effect of horizon shape in peridynamics

As a new continuum mechanics formulation, peridynamics has a non-local character by having an internal length scale parameter called horizon. Although the effect of the size of the horizon has been studied earlier, the shape of the horizon can also be influential. In this study, the effect of horizon shape is investigated for both ordinary state-based and non-ordinary state-based peridynamics. Three different horizon shapes are considered including circle, irregular and square. Both static and dynamic analyses are studied by considering plate under tension and vibration of a plate problems. For both static and dynamic conditions, square shape could not capture accurate vertical displacements for ordinary-state based peridynamics. On the other hand, results obtained for all three horizon shapes agree very well with finite element analysis results for non-ordinary state-based peridynamics.