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A closely related quantity is the stress tensor σ, which relates the vector force to the vector area via the linear relation =. This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure ...
As it is a second order tensor, the stress deviator tensor also has a set of invariants, which can be obtained using the same procedure used to calculate the invariants of the stress tensor. It can be shown that the principal directions of the stress deviator tensor s i j {\displaystyle s_{ij}} are the same as the principal directions of the ...
Thus the stress state of the material must be described by a tensor, called the (Cauchy) stress tensor; which is a linear function that relates the normal vector n of a surface S to the traction vector T across S. With respect to any chosen coordinate system, the Cauchy stress tensor can be represented as a symmetric matrix of 3×3
In the particular case of an incompressible fluid, the thermodynamic pressure coincides with the mechanical pressure (i.e. the opposite of the hydrostatic stress): = = () In the general case of a compressible fluid , the thermodynamic pressure p is no more proportional to the isotropic stress term (the mechanical pressure), since there is ...
Stress tensor may refer to: Cauchy stress tensor, in classical physics; Stress deviator tensor, in classical physics; Piola–Kirchhoff stress tensor, in continuum mechanics; Viscous stress tensor, in continuum mechanics; Stress–energy tensor, in relativistic theories; Maxwell stress tensor, in electromagnetism
The constant part ε v of the viscous stress tensor manifests itself as a kind of pressure, or bulk stress, that acts equally and perpendicularly on any surface independent of its orientation. Unlike the ordinary hydrostatic pressure, it may appear only while the strain is changing, acting to oppose the change; and it can be negative.
The pressure acts as a generalized force – pressure differences force a change in volume, and their product is the energy lost by the system due to mechanical work. Pressure is the driving force, volume is the associated displacement, and the two form a pair of conjugate variables. The above holds true only for non-viscous fluids.
The stress–energy tensor of a perfect fluid contains only the diagonal ... is the energy density and is the pressure of the fluid. Perfect fluids admit a ...