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The normal and shear components of the stress tensor on these planes are called octahedral normal stress and octahedral shear stress, respectively. Octahedral plane passing through the origin is known as the π-plane ( π not to be confused with mean stress denoted by π in above section) .
Therefore, in a coordinate system with axes ,,, the stress tensor is a diagonal matrix, and has only the three normal components ,, the principal stresses. If the three eigenvalues are equal, the stress is an isotropic compression or tension, always perpendicular to any surface, there is no shear stress, and the tensor is a diagonal matrix in ...
In the relativistic formulation of electromagnetism, the nine components of the Maxwell stress tensor appear, negated, as components of the electromagnetic stress–energy tensor, which is the electromagnetic component of the total stress–energy tensor. The latter describes the density and flux of energy and momentum in spacetime.
This tensor, a one-point tensor, is symmetric. If the material rotates without a change in stress state (rigid rotation), the components of the second Piola–Kirchhoff stress tensor remain constant, irrespective of material orientation. The second Piola–Kirchhoff stress tensor is energy conjugate to the Green–Lagrange finite strain tensor.
In continuum mechanics, the most commonly used measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures of stress can be defined: [1] [2] [3] The Kirchhoff stress (). The nominal stress ().
The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some ... The components of dF along each ...
The theory of the Reynolds stress is quite analogous to the kinetic theory of gases, and indeed the stress tensor in a fluid at a point may be seen to be the ensemble average of the stress due to the thermal velocities of molecules at a given point in a fluid. Thus, by analogy, the Reynolds stress is sometimes thought of as consisting of an ...
where is a symmetric but otherwise arbitrary second-rank tensor field that is at least twice differentiable, and is known as the Beltrami stress tensor. [1] Its components are known as Beltrami stress functions.