Stress (mechanics)

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Stress is the force per unit area on a body that tends to cause it to change shape.^[2]

Stress is a measure of the internal forces in a body between its particles.^[2] These internal forces are a reaction to the external forces applied on the body that cause it to separate, compress or slide.^[2] External forces are either surface forces or body forces. Stress is the average force per unit area that a particle of a body exerts on an adjacent particle, across an imaginary surface that separates them.

The formula for uniaxial normal stress is:

${\displaystyle {\sigma }={\frac {F}{A}}}$

where σ is the stress, F is the force and A is the surface area.

In SI units, force is measured in newtons and area in square metres. This means stress is newtons per square meter, or N/m². However, stress has its own SI unit, called the pascal. 1 pascal (symbol Pa) is equal to 1 N/m². In Imperial units, stress is measured in pound-force per square inch, which is often shortened to "psi". The dimension of stress is the same as that of pressure.

In continuum mechanics, the loaded deformable body behaves as a continuum. So, these internal forces are distributed continually within the volume of the material body. (This means that the stress distribution in the body is expressed as a piecewise continuous function of space and time.) The forces cause deformation of the body's shape. The deformation can lead to a permanent shape change or structural failure if the material is not strong enough.

Some models of continuum mechanics treat force as something that can change. Other models look at the deformation of matter and solid bodies, because the characteristics of matter and solids are three dimensional. Each approach can give different results. Classical models of continuum mechanics assume an average force and do not properly include "geometrical factors". (The geometry of the body can be important to how stress is shared out and how energy builds up during the application of the external force.)

1. ↑ Walter D. Pilkey, Orrin H. Pilkey (1974). Mechanics of solids. p. 292.
2. ↑ ^{2.0 2.1 2.2} Daintith, John, ed. (2005). A Dictionary of Physics (Fifth ed.). Oxford University Press. p. 509. ISBN 978-0-19-280628-4.