Long range elastic deformation model

It is important to note that Slitcher and Drickamer s model does not provide any information on the mechanism leading to the cooperativity term yfnns)- In order to give microscopic physical meaning to the interaction term, several approaches have been proposed [27-32]. The so-called lattice expansion and elastic interaction model appears as the most successful to interpret the available data [27-29]. In this approach the difference in volume between HS and LS molecules is assumed to cause long-range elastic deformations, leading to the cooperative spin-transition mechanism. 

The function f contains all the constitutive (material-dependent) properties and describes how the internal forces depend on the deformation. A standard assumption is that for a given material, f = 0 for all u when jr -rj > S for some > 0 called the horizon. This characteristic distance represents a length scale for the nonlocality of force. Nonlocal models allow to incorporate directly the description of atomistic effects and long-range interactions into a continuum theory. In contrast, classical elasticity theory does not have a length scale - the horizon consists of a point because of the assumption of a contact force. 

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