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The amount of stretch or compression along material line elements or fibers is the normal strain, and the amount of distortion associated with the sliding of plane layers over each other is the shear strain, within a deforming body. [2] This could be applied by elongation, shortening, or volume changes, or angular distortion. [3]
We now consider an incompressible material under uniaxial tension, with the stretch ratio given as =, where is the stretched length and is the original unstretched length. The pressure p {\displaystyle p} is determined from incompressibility and boundary condition σ 2 = σ 3 = 0 {\displaystyle \sigma _{2}=\sigma _{3}=0} , yielding:
The external body forces appear as the independent ("right-hand side") term in the differential equations, while the concentrated forces appear as boundary conditions. The basic stress analysis problem is therefore a boundary-value problem. Stress analysis for elastic structures is based on the theory of elasticity and infinitesimal strain theory.
[1]: 58 For example, low-carbon steel generally exhibits a very linear stress–strain relationship up to a well-defined yield point. The linear portion of the curve is the elastic region, and the slope of this region is the modulus of elasticity or Young's modulus. Plastic flow initiates at the upper yield point and continues at the lower ...
In physics and continuum mechanics, deformation is the change in the shape or size of an object. It has dimension of length with SI unit of metre (m). It is quantified as the residual displacement of particles in a non-rigid body, from an initial configuration to a final configuration, excluding the body's average translation and rotation (its rigid transformation). [1]
Liquids and gases cannot bear steady uniaxial or biaxial compression, they will deform promptly and permanently and will not offer any permanent reaction force. However they can bear isotropic compression, and may be compressed in other ways momentarily, for instance in a sound wave. Tightening a corset applies biaxial compression to the waist.
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