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• Both objects (in our case, sphere and plate) are semi-infinitely large bodies (R1, R2 >> R₁,R₂ >> a, where a is contact radius).

Reference* S. Timoshenko and J.N. Goodier: "Theory of Elasticity" --  Chap. 13: Sect. 125, "Pressure between Two Spherical Bodies in Contact"

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In the above set of equations, it can be shown that σ_that σ_ij = σ__ji due to moment balance!  Furthermore, we begin by making valid assumptions with regards to our problem of interest.  First, we assume that there is no body force (b = 0) anywhere in our model.  In addition, we model our problem as a plane stress problem, which means that all of the out-of-plane stress components involving θ-direction, can be assumed to equal zero (σ__θ = τ__θr = τ__θz = 0).  These assumptions lead to the following simplifications:

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