ABSTRACT
The early research in peridynamics focused on the theory’s attractiveness for modeling fracture, while utilizing simple constitutive models. It is a common misconception that the peridynamic theory as introduced in [53] was presented solely as a Navier one-parameter isotropic elasticity model [34]. A careful rereading of Section 15 of the original paper shows an outline of a generalization that was further developed and presented in full detail in [58]. This chapter presented models for peridynamic fluids and isotropic elastic solids that recover their classical analog as limiting cases. It also introduced some new terminology and notation for handling the mathematics of peridynamic states, which are essentially generalizations of tensors. This terminology has led many researchers to use the adjectives bond-based and state-based when referring to peridynamics, where “bond-based” refers to elasticity models of the one-parameter type, as they derive from a central force-potential between material points similar to a simple molecular bond, and “state-based” refers to the generalized theory †. While detailing the peridynamic theory in [58] the authors introduced additional terminology related to constitutive modeling such as ordinary and non-ordinary materials.
