Stress analysis
Hertz Contact Theory. Point or Line Contacts

The surface pressure distribution generates cohesive forces in both solids, which are evaluated from the stress tensor. This tensor is proportional to the Hertzian pressure p ₀ , the maximum pressure at the center of the contact, and therefore to the cube root of the applied force (square root in the case of line contact). Moreover, this tensor is a function only of the dimensions of the contact ellipse and the Poisson coefficients ν _i of the materials considered. The stress distribution is highly non-linear: the principal stresses are not proportional to each other, and the associated principal directions are oriented according to the position (X, Y, z) of the point under consideration.

To study the stress tensor, we define :

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