Abstract: Based on fractal theory, a three-dimensional fractal model of normal contact stiffness of joint interfaces is developed. A modified two-variable Weierstrass-Mandelbrot function is adopted to simulate the three-dimensional joints surface. The conditions of existence of elastic deformation, elastoplastic deformation and fully plastic deformation of the single asperity are derived. The relations between size distribution function for all level asperities and size distribution function for each level asperity are given. Then the relations between the joint normal contact stiffness and normal contact load have been obtained. The results show that for the joint interface including only these asperities whose level is less than the elastic critical level, the relations between normal contact stiffness and normal contact load are nonlinear. For these asperities whose level is greater than the elastic critical level, the relations between elastic normal contact stiffness and elastic normal contact load are linear, and the relations between inelastic normal contact stiffness and inelastic normal contact load are nonlinear. For a given contact load, the normal contact stiffness of joint interface is proportional to asperity level, namely the topography of joint interface is smoother, the normal contact stiffness is higher.

Key words: asperity, elastoplastic deformation, joints interface, level, normal contact stiffness