Evolution Behavior Analysis of Normal Contact Stiffness of Fractal Surface under Loading and Unloading

In order to analyze the evolution of normal contact stiffness under loading and unloading, an accurate elastic-plastic contact finite element model between rigid plane and fractal surface is established by introducing the equivalent metal matrix deformation in terms of the modified Weierstrass-Mandelbrot function. The effects of the fractal dimension, scale parameter, material properties on the normal contact stiffness were discussed. A method for evaluating the normal contact stiffness was proposed to analyze the evolution of the normal contact stiffness. Numerical simulation shows that there is a positive power function relationship between the normal contact stiffness and the load of fractal surface. Under the same load, at the fractal dimensions (D) of 2.4-2.7 and scale parameters (G) of 1.36×10-13-1.36×10-10 m, the loading normal contact stiffness increases with the increasing of fractal dimension and tangent modulus, but decreases with the increasing of scale parameter. The unloading normal contact stiffness increases with the material strengthening, and the variation amplitude is positively correlated with the fractal dimension, and negatively correlated with the scale parameters and tangent modulus.