Theoretical analyses of surface interaction stresses considering two-dimensional periodic material distributions

The interaction stresses (pressure and shear stress) for the (001) surface between a half-space consisting of a homogeneous material and a half-space with a spatially periodic material distribution in two-dimensions (i.e., x- and y-directions) were derived using the Lennard-Jones potential. The periodically distributed material property function was expanded as a complex Fourier series. Because the pressure is the same as that already presented by the authors even though the calculation process is different, only the shear stress in the x-direction is presented here. The shear stress in the y-direction is easily obtained by exchanging variables. The interaction shear stresses for a distribution of two materials as a typical example of a periodic material distribution were calculated. The basic characteristics of the shear stress for parallel planes and inclined planes were quantitatively clarified. Specifically, the distributions of the shear stress, the effects of the surface distance, the duty ratio, the refractive index ratio, and vector diagrams of the shear stresses were presented.