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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 interactions forces between a material point and all the other ones with which it can interact, are modeled as a central forces field. This type of forces field can be imagined as a mesh of bonds connecting each point of the body with every other interacting points 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 [2][3] ( for plane stress and for plane strain in two-dimesnional configurations; for three-dimensional ones), "state-base" peridynamics, has been formulated [4]. 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 its interaction zone.
The characteristic feature of peridynamics, which make it differs from classical local mechanics, is the presence of finite-range bond between any two points of the material body: it is a feature that approach such formulations to discrete meso-scale theories of matter.