Abstract
In this work, the stiffness, i.e., the derivative of the load-separation curve, is studied for self-affine fractal surfaces with non-Gaussian height distribution. In particular, the heights of the surfaces are assumed to follow a Weibull distribution. We find that a linear relation between stiffness and load, well established for Gaussian surfaces, is not obtained in this case. Instead, a power law, which can be motivated by dimensionality analysis, is a better descriptor. Also unlike Gaussian surfaces, we find that the stiffness curve is no longer independent of the Hurst exponent in this case. We carefully asses the possible convergence errors to ensure that our conclusions are not affected by them.
Highlights
In this work, the stiffness, i.e., the derivative of the load-separation curve, is studied for self-affine fractal surfaces with non-Gaussian height distribution
Where q = qx2 + qy[2] is the modulus of the wave-number, C0 is a constant that determines the rms height of the surface, q1 and q0 are lower and upper wave-numbers and H is the Hurst exponent, which characterizes the decay of the power spectrum and can be related to the fractal dimension of the surface through Df = 3 − H
One is often constrained in the values one may pick due to computational limitations and must compromise and try to reduce convergence errors as much as possible
Summary
The stiffness, i.e., the derivative of the load-separation curve, is studied for self-affine fractal surfaces with non-Gaussian height distribution. One is often constrained in the values one may pick due to computational limitations and must compromise and try to reduce convergence errors as much as possible Once these values are fixed and the height lateral dimension are appropriately normalized (see Methods), H is the only parameter needed to characterize these surfaces. One is that an efficient method to generate this type of surface with the desired degree of control (i.e., specifying well defined power spectrum and height distribution at the same time) has been u navailable[20] To overcome this difficulty, a recent method presented by the authors can be used[21]. We will not attempt to study non-Gaussian surfaces in general but we will focus only on surfaces with heights following a Weibull probability distribution
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