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The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields.

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The Cauchy stress tensor can be split into: The spherical stress tensor: Also named. mean hydrostatic stress tensor. or . volumetric stress tensor. or. mean normal stress tensor. Is an isotropic tensor and defines a hydrostatic state of stress. Tends to change the volume of the stressed body The stress deviatoric tensor:

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deformation ) for the Cauchy stress tensor is, where . (16) Hence, the exact solution for the unrotated Cauchy stress is where . (17) Substituting Eq. (17) into Eq. (9) shows that the exact solution for the PK2 stress is. (18) These exact solutions demonstrate that the stress is a nonlinear function of

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In principle, the stress tensor has nine independent components. BUT only six of these are independent. That is because the o↵-diagonal elements (those representing tangent or shear...

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The Cauchy stress tensor obeys the tensor transformation law under a change in the system of coordinates. A graphical representation of this transformation law is the Mohr's circle for stress.

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contributed to the concept of shear stresses. Augustin-Louis Cauchy (1789-1857) presented the general concept and mathematical theory of the stress tensor in 1823 and 1827. Cauchy’s childhood fell in the bloodiest period of the French Revolution. Schools were closed and men of science were left to starve or carted off to the guillotine. To escape