The interaction stresses (pressure and shear stress) for (001) surface between a half-space consisting of a uniform material and a half-space with a spatially periodic material distribution have been derived based on the Lennard-Jones potential. The periodically distributed material property function is expanded as a complex Fourier series. The interaction pressures consist of non-fluctuation terms and fluctuation terms, while the shear stresses have only fluctuation terms. The interaction stresses for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The basic characteristics of the interaction stresses are clarified.

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