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Not a weak formulation[edit]

Peridynamics is different from, and it is not a weak formulation of some differrential equation. Also, the peridynamic horizon is not "an artificial length parameter" as stated in a "criticism of peridynamics". To give an example, at the atomistic scale, where f would be obtained from an atomistic potential, the horizon is determined by the interaction between the atoms, by the range of the potential function. At macroscopic scales, the horizon is a representation, or manifestation, of the microstructure effects etc (see, e.g. Bazant and Jirasek, Journal of Engineering Mechanics, Vol. 128, No. 11, November 1, 2002). We invite the interested parties to consult the references listed in the main article page. Fbobaru (talk) 10:47, 21 November 2008 (UTC)

The text that follows (in italics) has been posted by "cj67" on the main page. It has been moved here for the reasons mentioned in the history page. Beginning of text by "cj67" Integral equations are already used in weak formulations of differential equations, and so are not new. Fracture mechanics has been studied with these methods already, without introducing an artificial length parameter, as is done in peridynamics. Variational methods have been used in these weak settings, and have been shown to be suitable for showing existence, convergence, etc., in static and quasi-static settings. Mathematical models for dynamic fracture also exist, using these weak settings, based on the space BV of functions with bounded variation. End of the text by "cj67" Fbobaru (talk) 11:31, 21 November 2008 (UTC)