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Stress physics - Why is stress a symmetric tensor? | A Wisdom Archive on Stress physics - Why is stress a symmetric tensor? | | Stress physics - Why is stress a symmetric tensor? A selection of articles related to Stress physics - Why is stress a symmetric tensor? | |
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Stress physics, Stress physics - Books, Stress physics - Cauchy's principle, Stress physics - Generalized notation, Stress physics - Mohr's circle, Stress physics - Plane stress, Stress physics - Principal stresses, Stress physics - Residual stress, Stress physics - Stress in one-dimensional bodies, Stress physics - Stress in three dimensions, Stress physics - Stress measurement, Stress physics - Stress tensor, Stress physics - Units, Stress physics - Why is stress a symmetric tensor?, Strain tensor, Stress-energy tensor, Stress concentration
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ARTICLES RELATED TO Stress physics - Why is stress a symmetric tensor? | | | |  Stress physics - Why is stress a symmetric tensor?: Encyclopedia II - Stress physics - Stress in one-dimensional bodiesThe idea of stress originates in two simple, but important, observations of the loading (in tension) of a one-dimensional body, for example, a steel wire.
When a wire is pulled tight, it stretches (undergoes strain). Up to a certain limit, the amount it stretches is proportional to the load divided by the cross-sectional area of the wire, σ = F/A.
Failure occurs when the load exceeds a critical value for the material, the tensile strength multiplied by the cross-sectional area ...
See also:Stress physics, Stress physics - Stress in one-dimensional bodies, Stress physics - Cauchy's principle, Stress physics - Plane stress, Stress physics - Principal stresses, Stress physics - Mohr's circle, Stress physics - Stress in three dimensions, Stress physics - Stress tensor, Stress physics - Generalized notation, Stress physics - Why is stress a symmetric tensor?, Stress physics - Stress measurement, Stress physics - Units, Stress physics - Residual stress, Stress physics - Books Read more here: » Stress physics: Encyclopedia II - Stress physics - Stress in one-dimensional bodies |
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| | | | Stress physics - Why is stress a symmetric tensor?: Encyclopedia II - Stress physics - Residual stress Residual stresses are stresses that remain after the original cause of the stresses has been removed. Residual stresses occur for a variety of reasons, including inelastic deformations and heat treatment. Heat from welding may cause localized expansion. When the finished weldment cools, some areas cool and contract more than others, leaving residual stresses. Castings may also have large residual stresses due to uneven cooling.
While uncontrolled residual stresses are undesirable, many designs rely on them. For example, toughened glas ...
See also:Stress physics, Stress physics - Stress in one-dimensional bodies, Stress physics - Cauchy's principle, Stress physics - Plane stress, Stress physics - Principal stresses, Stress physics - Mohr's circle, Stress physics - Stress in three dimensions, Stress physics - Stress tensor, Stress physics - Generalized notation, Stress physics - Why is stress a symmetric tensor?, Stress physics - Stress measurement, Stress physics - Units, Stress physics - Residual stress, Stress physics - Books Read more here: » Stress physics: Encyclopedia II - Stress physics - Residual stress |
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| | | | Stress physics - Why is stress a symmetric tensor?: Encyclopedia II - Stress physics - Stress tensor Because the behavior of a body does not depend on the coordinates used to measure it, stress can be described by a tensor. The stress tensor is symmetric and can always be resolved into the sum of two symmetric tensors:
a mean or hydrostatic stress tensor, involving only pure tension and compression; and
a shear stress tensor, involving only shear stress.
In the case of a fluid, Pascal's law shows that the hydrostatic stress is the same in all directions, at least to a first approximat ...
See also:Stress physics, Stress physics - Stress in one-dimensional bodies, Stress physics - Cauchy's principle, Stress physics - Plane stress, Stress physics - Principal stresses, Stress physics - Mohr's circle, Stress physics - Stress in three dimensions, Stress physics - Stress tensor, Stress physics - Generalized notation, Stress physics - Why is stress a symmetric tensor?, Stress physics - Stress measurement, Stress physics - Units, Stress physics - Residual stress, Stress physics - Books Read more here: » Stress physics: Encyclopedia II - Stress physics - Stress tensor |
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| | | | Stress physics - Why is stress a symmetric tensor?: Encyclopedia II - Stress physics - Plane stress Plane stress is a two-dimensional state of stress (Figure 2). This 2-D state models well the state of stresses in a flat, thin plate loaded in the plane of the plate. Figure 2 shows the stresses on the x- and y-faces of a differential element. Not shown in the figure are the stresses in the opposite faces and the external forces acting on the material. Since moment equilibrium of the differential element shows that the shear stresses on the perpendicular faces are equal, the 2-D state of stresses is characterized by three independent stress components (σ ...
See also:Stress physics, Stress physics - Stress in one-dimensional bodies, Stress physics - Cauchy's principle, Stress physics - Plane stress, Stress physics - Principal stresses, Stress physics - Mohr's circle, Stress physics - Stress in three dimensions, Stress physics - Stress tensor, Stress physics - Generalized notation, Stress physics - Why is stress a symmetric tensor?, Stress physics - Stress measurement, Stress physics - Units, Stress physics - Residual stress, Stress physics - Books Read more here: » Stress physics: Encyclopedia II - Stress physics - Plane stress |
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| | | | Stress physics - Why is stress a symmetric tensor?: Encyclopedia II - Stress physics - 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.
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 ve ...
See also:Stress physics, Stress physics - Stress in one-dimensional bodies, Stress physics - Cauchy's principle, Stress physics - Plane stress, Stress physics - Principal stresses, Stress physics - Mohr's circle, Stress physics - Stress in three dimensions, Stress physics - Stress tensor, Stress physics - Generalized notation, Stress physics - Why is stress a symmetric tensor?, Stress physics - Stress measurement, Stress physics - Units, Stress physics - Residual stress, Stress physics - Books Read more here: » Stress physics: Encyclopedia II - Stress physics - Cauchy's principle |
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| | | | Stress physics - Why is stress a symmetric tensor?: Encyclopedia II - Stress physics - Stress in three dimensions The considerations above can be generalized to three dimensions. However, this is very complicated, since each shear loading produces shear stresses in one orientation and normal stresses in other orientations, and vice versa. Often, only certain components of stress will be important, depending on the material in question.
The von Mises stress is derived from the distortion energy theory and is a simple way to combine stresses in three dimensions to calculate failure criteria of ductile materials. In this way, the strength of material in a 3-D state of stress can b ...
See also:Stress physics, Stress physics - Stress in one-dimensional bodies, Stress physics - Cauchy's principle, Stress physics - Plane stress, Stress physics - Principal stresses, Stress physics - Mohr's circle, Stress physics - Stress in three dimensions, Stress physics - Stress tensor, Stress physics - Generalized notation, Stress physics - Why is stress a symmetric tensor?, Stress physics - Stress measurement, Stress physics - Units, Stress physics - Residual stress, Stress physics - Books Read more here: » Stress physics: Encyclopedia II - Stress physics - Stress in three dimensions |
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