Peridynamics with a Cube‐Shaped Neighborhood

Source abstract

ABSTRACT This paper investigates the effects of cube‐shaped neighborhoods in peridynamic theory as an alternative to the traditional spherical neighborhoods. We examine how different neighborhood geometries influence the behavior of various peridynamic formulations, including bond‐based models, state‐based formulations, and correspondence methods. The study reveals that cube‐shaped neighborhoods introduce significant anisotropic effects in standard peridynamic formulations due to directional bias in force calculations. A generalized bond constant is derived for the bond‐based model to maintain consistency with classical continuum mechanics when using cubic neighborhoods. Through numerical examples, including wave propagation and crack growth scenarios, we demonstrate that while cube‐shaped neighborhoods cause undesirable anisotropic behavior in traditional peridynamic models, correspondence‐based formulations remain unaffected due to their averaged deformation gradient approach. The results provide important insights for the selection of neighborhood shapes in peridynamic simulations and highlight the robustness of correspondence formulations against geometric variations in discretization choices.