Search results
Results from the WOW.Com Content Network
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 ...
The stress tensor can be expressed as the sum of two other stress tensors: a mean hydrostatic stress tensor or volumetric stress tensor or mean normal stress tensor, , which tends to change the volume of the stressed body; and
In inhomogeneous systems the pressure depends on the position and orientation of the surface on which the pressure acts. Therefore, in inhomogeneous systems a definition of a local pressure is needed. [5] As a general example for a system with inhomogeneous pressure you can think of the pressure in the atmosphere of the earth which varies with ...
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 ...
A metric tensor is a (symmetric) (0, 2)-tensor; it is thus possible to contract an upper index of a tensor with one of the lower indices of the metric tensor in the product. This produces a new tensor with the same index structure as the previous tensor, but with lower index generally shown in the same position of the contracted upper index.
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 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 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.