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Quantitatively, the stress is expressed by the Cauchy traction vector T defined as the traction force F between adjacent parts of the material across an imaginary separating surface S, divided by the area of S. [9]: 41–50 In a fluid at rest the force is perpendicular to the surface, and is the familiar pressure.
Traction can also refer to the maximum tractive force between a body and a surface, as limited by available friction; when this is the case, traction is often expressed as the ratio of the maximum tractive force to the normal force and is termed the coefficient of traction (similar to coefficient of friction).
In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation , from which the stress and strain can be determined (see tensile testing ).
The Euler–Cauchy stress principle states that upon any surface (real or imaginary) that divides the body, the action of one part of the body on the other is equivalent (equipollent) to the system of distributed forces and couples on the surface dividing the body, [2] and it is represented by a field (), called the traction vector, defined on ...
The Hertzian contact stress usually refers to the stress close to the area of contact between two spheres of different radii. It was not until nearly one hundred years later that Kenneth L. Johnson , Kevin Kendall , and Alan D. Roberts found a similar solution for the case of adhesive contact. [ 5 ]
The relation between matter distribution and spacetime curvature is given by the Einstein field equations, which require tensor calculus to express. [ 81 ] : 43 [ 88 ] The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the ...
In solid mechanics, the tangent modulus is the slope of the stress–strain curve at any specified stress or strain. Below the proportional limit (the limit of the linear elastic regime) the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most accurately found from ...
As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain. This relationship is known as Hooke's law. A geometry-dependent version of the idea [a] was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv".