Elastic Contact Between a Geometrically-Anisotropic Bi-Sinusoidal Surface and a Rigid Base
Amir Rostami (Auburn University), Yang Xu (Auburn University), Robert L. Jackson (Auburn University)
Contact Mechanics
Tue 2:40 - 4:00
Barus-Holley 161
In the current study, a semi-analytical model for contact between a homogeneous, isotropic, linear elastic half-space with a geometrically-anisotropic bi-sinusoidal surface (wavelengths are different in the two principle directions) and a rigid base is developed. Two asymptotic load-to-area relations for early and nearly complete contact are derived. The Hertzian elliptic contact theory is applied to approximate the load-to-area relation in the early contact range. The non-contact areas that occur in the nearly complete contact area are treated as mode-I “cracks”. Since this mode-I “crack” is in compression, an approximate relation between load and non-contact (contact) area can be obtained by setting the corresponding stress intensity factor (SIF) to zero. These two asymptotic solutions are validated by two different numerical solutions, namely, a numerical superposition-based model and a finite element model. A piece-wise equation is fit to the numerical solutions to bridge these two asymptotic solutions. Only two independent dimensionless variables are in this curve-fit equation: the dimensionless pressure and the wavelength ratio (ratio of the shorter wavelength to the longer wavelength). According to the numerical solutions, the load to area relation for the geometrically-anisotropic contact is independent of the aspect ratio, i.e., the ratio of the amplitude to the longer wavelength.