Stress (physics)

In physics, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. Stress is a tensor quantity with nine terms, but can be described fully by six terms due to symmetry. Simplifying assumptions are often used to represent stress as a vector for engineering calculations.

Cauchy's principle

Augustin Louis Cauchy enunciated the principle that, within a body, the forces that an enclosed volume imposes on the remainder of the material must be in equilibrium with the forces upon it from the remainder of the body.

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This intuition provides a route to characterizing and calculating complicated patterns of stress. To be exact, the stress at a point may be determined by considering a small element of the body that has an area ΔA, over which a force ΔF acts. By making the element infinitesimally small, the stress vector σ is defined as the limit:

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:

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sigma = lim_{Delta A o 0} rac {Delta F} {Delta A} = {dF over dA}

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Being a vector, the stress has two components, one in the plane of the area A, the shear stress, and one perpendicular, the normal stress. The shear stress can be further decomposed into two orthogonal components within the plane, thus giving rise to three stress components acting on this plane.

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