Talk:Peridynamics

Not a weak formulation

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)

Observations and suggestions for improvements

The following observations and suggestions for improvements were collected, following an expert review of the article within the Science, Technology, Society and Wikipedia course at the Politecnico di Milano, in July 2023.

I suggest mentioning that peridynamic formulations can be associated with pair-potentials (bond-based type models) or with multi-body potentials. State-based peridynamic models are models funded on the concept of multi-body potential. However, other PD formulations based on pair-potentials do not suffer from the limitation regarding the Poisson’s ratio (see micropolar formulations etc)). On the other hand, there are PD formulations based on multi-body potentials that are not state-based (see for instance conjugated PD models etc). Moreover, the discussion focuses on isotropic elasticity but PD formulations for anisotropic materials have been also proposed.

--Aandurro (talk) 13:08, 18 July 2023 (UTC)

Hi, thank you for the reply and sorry for the late response.

I agree with you that other formulation different from state based do not suffer from Poisson ratio limitations. It has been my fault to not mention them. I would be glad if you can send me some references. Otherwise I will search for it.

Best regards.

Nunzio NunzioDimola (talk) 14:32, 24 July 2023 (UTC)