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The total elastic stiffness of two contacting bodies with a microscopicallyrough interface has an interfacial contribution K that is entirely attributableto surface roughness. A quantitative understanding of K is important because itcan dominate the total mechanical response and because it is proportional tothe interfacial contributions to electrical and thermal conductivity incontinuum theory. Numerical simulations of the dependence of K on the appliedsqueezing pressure p are presented for nominally flat elastic solids with arange of surface roughnesses. Over a wide range of p, K rises linearly with p.Sublinear power-law scaling is observed at small p, but the simulations revealthat this is a finite-size effect. We derive accurate, analytical expressionsfor the exponents and prefactors of this low-pressure scaling of K by extendingthe contact mechanics theory of Persson to systems of finite size. In agreementwith our simulations, these expressions show that the onset of the low-pressurescaling regime moves to lower pressure as the system size increases.

Finite-size scaling in the interfacial stiffness of rough elastic contacts