Viscous stress tensor - Wikipedia
The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed to the strain rate, the rate at which it is deforming around that point.
The Stress Tensor for a Fluid and the Navier Stokes Equations 3.1 Putting the stress tensor in diagonal form A key step in formulating the equations of motion for a fluid requires specifying the stress tensor in terms of the properties of the flow, in particular the velocity field, so that
Viscosity: a measure of a fluid’s resistance to deformation by shear stress. For liquids, viscosity corresponds to the informal concept of ”thickness”. A fluid with zero viscosity is called inviscid.
The importance of the stress tensor concept in continuum theory is this: It allows us to describe the state of stress in a continuum in terms of quantities that depend on position and time, but not on the orientation of the surface on which the stress acts.
Because our antisymmetric tensor r describes the solid body rotational uid motion, it can cause no viscous stress. 1.2. Viscous stress tensor. It has been found experimentally that the magnitude of the shear stress in viscous ows is often proportional to the symmetric components of the velocity gradient. This is an analogy to Hooke’s law. In ...
The Newtonian viscous fluid is one where the stress tensor is linear in the components of the velocity derivative matrix, with a stress tensor whose specific form will depend on other physical conditions. To see why a linear relation of this might capture the dominant rheology
The stress tensor and the Navier-Stokes equation - University …
We can further generalize and define the xy component of the viscous stress tensor as The notation is made clearer in Fig. 3.2 . This definition ensures that for a uniform rotation of the fluid there are no viscous stresses.
Viscous stress tensor - WikiMili, The Best Wikipedia Reader
2022年11月13日 · The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed to the strain rate, the rate at which it is deforming around that point.
This stress-strain relationship can be derived by the following two assumptions: 1. The shear stress is independent of a rotation of the coordinate system 2. The shear stress is at most a linear function of the strain rate tensor. So, for example, τxy: τxy =a11εxx +a12εxy +a13εxz +a22εyy +a23εyz +a33εzz
An ideal fluid has a stress tensor that is independent of the rate of deformation, i.e., it has an isotropic component, which is identified as the pressure and has zero viscosity. The forces acting on an element of a continuous medium may be of two kinds.
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