弹塑性三维各向异性分形表面的接触分析

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Weierstrass-Mandelbrot函数能模拟加权、随机重叠的隆起部状表面,该函数是更起作用通用的单变量标量.给出三维各向异性分形表面高度函数的推导过程,分析三维各向异性分形表面特征.将分形维数推广到三维的一般情况,给出弹性、完全塑性接触时单峰的实际接触面积与单峰的横截面积之间的不同关系.理论分析易适用于解释各向异性分形表面与不同材料行为. A more useful generalization of the univariate scalar Weierstrass-Mandelbrot function is a weighted,random superposition of such ridge-like surfaces.The height function of a three-dimensional anisotropic fractal surface is deduced.The three-dimensional anisotropic fractal surface characterization is analyzed.Fractal dimension is extended to the three-dimensional universality.There are different relations between the microcontact real area in elastic and fully plastic contact state and the truncated area of the microcontact.The theoretical analysis can be easily applied to account for anisotropic fractal surfaces and different material behaviors.