Peridynamics
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Peridynamics is a non-local formulation of continuum mechanics that is oriented toward deformations with discontinuities, especially fractures. Originally, bond-based peridynamic has been introduced,[1] wherein, internal interaction forces between a material point and all the other ones with which it can interact, are modeled as a central forces field.[2] This type of force fields can be imagined as a mesh of bonds connecting each point of the body with every other interacting point within a certain distance which depends on material property, called peridynamic horizon. Later, to overcome bond-based framework limitations for the material Poisson’s ratio[3][4] ( for plane stress and for plane strain in two-dimesional configurations; for three-dimensional ones), state-base peridynamics, has been formulated.[5] Its characteristic feature is that the force exchanged between a point and another one is influenced by the deformation state of all other bonds relative to its interaction zone.[1]
The characteristic feature of peridynamics, which makes it different from classical local mechanics, is the presence of finite-range bond between any two points of the material body: it is a feature that approaches such formulations to discrete meso-scale theories of matter.[1]