The Electrical Contact feature node has correlations to evaluate the joint conductance at two contacting surfaces.

The current densities at the upside and downside boundaries depend on the potential difference according to the relations:

At a microscopic level, contact is made at a finite number of spots as in Figure 4-10.

The microscopic surface asperities are characterized by the average height σu, asp and σd, asp and the average slope mu, asp and md, asp. The RMS values σasp and masp are (4.16 in Ref. 1):

The Cooper-Mikic-Yovanovich (CMY) correlation is valid for isotropic rough surfaces and has been formulated using a model assuming plastic deformation of the surface asperities. However, this model does not compute nor store the plastic deformations of the asperities. It means that, despite that a plastic deformation of the asperities is assumed, this contact model has no memory. For example, if a load is applied twice the electrical contact is identical in both cases. The Cooper-Mikic-Yovanovich (CMY) correlation relates hc to the asperities and pressure load at the contact interface:

Here, Hc is the microhardness of the softer material, p is the contact pressure, and σcontact is the harmonic mean of the contacting surface conductivities:

The relative pressure p ⁄ Hc can be evaluated by specifying Hc directly or using the following relation (4.16.1 in Ref. 1) for the relative pressure using c1 and c2, the Vickers correlation coefficient and size index:

The coefficients c1 and c2 are the Vickers correlation coefficient and size index, respectively, and σ0 is equal to 1 µm. For materials with Brinell hardness between 1.30 and 7.60 GPa, c1 and c2 are given by the correlation below (4.16.1 in Ref. 1):

The Brinell hardness is denoted by HB, and H0 is equal to 3.178 GPa.

The Mikic correlation is valid for isotropic rough surfaces and assumes elastic deformations of surface asperities. It gives hc by the following relation:

Here, Econtact is an effective Young’s modulus for the contact interface, satisfying (4.16.3 in Ref. 1):

where Eu and Ed are the Young’s moduli of the two contacting surfaces and νu and νd are the Poisson’s ratios.