On the role of the influence function in the peridynamic theory

The influence function in the peridynamic theory is used to weight the contribution of all the bonds participating in the computation of volume-dependent properties. In this work, we use influence functions to establish relationships between bond-based and state-based peridynamic models. We also demonstrate how influence functions can be used to modulate nonlocal effects within a peridynamic model independently of the peridynamic horizon. We numerically explore the effects of influence functions by studying wave propagation in simple one-dimensional models and brittle fracture in three-dimensional models.