Stress (mechanics)

Mechanics

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Figure 1.1 Stress in a loaded deformable material body assumed as a continuum.

Figure 1.2 Axial stress in a prismatic bar axially loaded.

Figure 1.3 Normal stress in a prismatic (straight member of uniform cross-sectional area) bar. The stress or force distribution in the cross section of the bar is not necessarily uniform. However, an average normal stress $\sigma_\mathrm{avg}\,\!$ can be used.

Figure 1.4 Shear stress in a prismatic bar. The stress or force distribution in the cross section of the bar is not necessarily uniform. Nevertheless, an average shear stress $\tau_\mathrm{avg}\,\!$ is a reasonable approximation.

In continuum mechanics, stress is the force that an object pushes back with when it is being deformed (its shape is changed by a force acting from outside the object). In other words, it is the internal forces acting within a deformable body.

Stress states the average force per unit of the surface area within the body where the internal forces are acting. Specifically, it shows the intensity of the internal forces acting between the particles in the deformable body across imaginary internal surfaces. These internal forces are a reaction to the external forces applied on the body that cause it to deform. External forces are either surface forces or body forces.

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.)

The dimension of stress is the same as that of pressure, and therefore the SI unit for stress is the pascal (symbol Pa), which is equivalent to one newton per square meter (unit area), or N/m². In Imperial units, stress is measured in pound-force per square inch, which is often shortened to "psi".

Related pages

• Bending
• Kelvin probe force microscope
• Residual stress
• Shot peening
• Strain
• Strain tensor
• Stress–energy tensor
• Stress–strain curve
• Stress concentration
• Transient friction loading
• Virial stress
• Yield stress
• Yield surface
• Virial theorem

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More reading

• Beer, Ferdinand Pierre; Elwood Russell Johnston, John T. DeWolf (1992). Mechanics of Materials. McGraw-Hill Professional. ISBN 0071129391.
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• Chen, Wai-Fah; Baladi, G.Y. (1985). Soil Plasticity, Theory and Implementation. ISBN 0444424555, 0444416625.
• Chou, Pei Chi; Pagano, N.J. (1992). Elasticity: tensor, dyadic, and engineering approaches. Dover books on engineering. Dover Publications. pp. 1–33. ISBN 0486669580. http://books.google.com/books?id=9-pJ7Kg5XmAC&lpg=PP1&pg=PA1#v=onepage&q=&f=false.
• Davis, R. O.; Selvadurai. A. P. S. (1996). Elasticity and geomechanics. Cambridge University Press. pp. 16–26. ISBN 0521498279. http://books.google.ca/books?id=4Z11rZaUn1UC&lpg=PP1&pg=PA16#v=onepage&q=&f=false.
• Dieter, G. E. (3 ed.). (1989). Mechanical Metallurgy. New York: McGraw-Hill. ISBN 0-07-100406-8.
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• Jones, Robert Millard (2008). Deformation Theory of Plasticity. Bull Ridge Corporation. pp. 95–112. ISBN 0978722310. http://books.google.ca/books?id=kiCVc3AJhVwC&lpg=PP1&pg=PA95#v=onepage&q=&f=false.
• Jumikis, Alfreds R. (1969). Theoretical soil mechanics: with practical applications to soil mechanics and foundation engineering. Van Nostrand Reinhold Co.. ISBN 0442041993. http://books.google.ca/books?id=NPZRAAAAMAAJ&source=gbs_navlinks_s.
• Landau, L.D. and E.M.Lifshitz. (1959). Theory of Elasticity.
• Love, A. E. H. (4 ed.). (1944). Treatise on the Mathematical Theory of Elasticity. New York: Dover Publications. ISBN 0-486-60174-9.
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