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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 ...
The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure. [ 13 ] According to the theory of general relativity , pressure increases the strength of a gravitational field (see stress–energy tensor ) and so adds to the mass-energy cause of gravity .
The stress tensor is a linear function of the strain rate tensor or equivalently the velocity gradient. The fluid is isotropic. For a fluid at rest, ∇ ⋅ τ must be zero (so that hydrostatic pressure results).
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
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.
A scalar field is a tensor field of order zero, [3] and the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form. The scalar field of ((+)) oscillating as increases. Red represents positive values, purple represents negative values, and sky blue represents ...
The distribution function ... where is the pressure tensor. The material derivative is = +. The pressure tensor is defined as the particle mass times the ...