Maugis-Dugdale model

A deep insight into the problem of contact mechanics involved in a conductivity measurement using an SFM tip can be found in the paper by Lantz et al. [441]. In this article the contact area was derived for the case of ohmic contacts using the Maugis-Dugdale model [104] (see Sect. 2.1). However, the uncertainty is still related to the problem of the conductivity of the tip apex. If a sharp tip is not absolutely necessary, a possible solution to this problem is to add electro-chemically a copper layer to the chromium sub-layer (Fig. 33e,f). 

The JKR and DMT theories were found to be limiting cases of the more general Maugis-Dugdale model that can explain the smooth transition between the two models. 

Maugis, D. (1992), Adhesion of spheres JKR-DMT transition using a Dugdale model. Journal of Colloid and Interface Science 150, 243-269. 

Maugis D. Adhesion of spheres The JKR-DMT transition using a dugdale model. J Colloid Interface Sci 1992 150 243-269. 

Fig. 18. Adhesive contact of elastic spheres. pH(r) and pa(r) are the Hertz pressure and adhesive tension distributions, (a) JKR model uses a Griffith crack with a stress singularity at the edge of contact (r = a) (b) Maugis model uses a Dugdale crack with a constant tension aa in a < r < c [1111.

It is somewhat disconcerting that the MYD analysis seems to present a sharp transition between the JKR and DMT regimes. Specifieally, in light of the vastly different response predicted by these two theories, one must ponder if there would be a sharp demarcation around /x = 1. This topic was recently explored by Maugis and Gauthier-Manuel [46-48]. Basing their analysis on the Dugdale fracture mechanics model [49], they concluded that the JKR-DMT transition is smooth and continuous. 

Another remarkable contribution to Tabor s idea is an analytical solution obtained by Maugis [17]. The key assumption in his model was that the traction form was represented in terms of the Dugdale approximation, in which the attraetive... 

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