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...

fluid, these stresses can be described by a viscous stress tensor that is, almost always, completely determined by the strain rate tensor and by certain...

Newtonian. Fluid mechanics Non-Newtonian fluid Strain rate tensor Viscosity Viscous stress tensor Panton, Ronald L. (2013). Incompressible Flow (Fourth ed...

continuum mechanics Viscous stress tensor, in continuum mechanics Stress–energy tensor, in relativistic theories Maxwell stress tensor, in electromagnetism...

non-Newtonian manner.: 145  The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation...

viscosity tensor that maps the velocity gradient tensor ∂ v k / ∂ r ℓ {\displaystyle \partial v_{k}/\partial r_{\ell }} onto the viscous stress tensor τ i j...

Lamé's stress ellipsoid Reinforced solid Residual stress Shear strength Shot peening Strain Strain tensor Strain rate tensor Stress–energy tensor Stress–strain...

the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow...

ρ is the local fluid density, p is the local pressure, τ is the viscous stress tensor and B represents the sum of the external body forces. The first...

simplifies the viscous stress tensor to a single scalar value μ {\displaystyle \mu } , the dynamic viscosity, which is determined by tensor invariants of...

the tensor s, called the compliance tensor, represents the inverse of said linear map. In a Cartesian coordinate system, the stress and strain tensors can...

of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within...

} (t)} is the Cauchy stress tensor as function of time t, p is the pressure I {\displaystyle \mathbf {I} } is the unity tensor M is the memory function...

} . 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...

fluctuation-dissipation theorem of statistical mechanics is added to the viscous stress tensor and heat flux. The concept of pressure is central to the study of...

pressure and σ {\displaystyle \sigma } is the viscous stress tensor, with the components of the viscous stress tensor given by: σ i j = μ ( ∂ v i ∂ x j + ∂ v...

relationships/equations: (a) constitutive relationships for the viscous stress tensor; (b) constitutive relationships for the diffusive heat flux; (c)...

system of partial differential equations that relate the stress tensor field to the strain tensor field as unknown functions to be determined. Solving for...

\|} generates the Stokeslet. The following formula describes the viscous stress tensor for the special case of Stokes flow. It is needed in the calculation...

{\boldsymbol {\tau }}} is the viscous stress tensor. Note that v v {\displaystyle \mathbf {v} \mathbf {v} } is a tensor (see also tensor product). Differentiating...

Σ as summation symbol). The osmotic pressure in chemistry. The viscous stress tensor in continuum mechanics and fluid dynamics. The lowercase letter...

the diagonal elements of the tensor. The compressional contribution to viscous stress is added as a separate diagonal tensor. Applying these assumptions...

In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes...

or yield stress, and are the result of slip, or dislocation mechanisms at the atomic level. Another type of irreversible deformation is viscous deformation...

individual components of the Reynolds stress tensor are directly computed. These models use the exact Reynolds stress transport equation for their formulation...

={\boldsymbol {0}}} where σ {\displaystyle \sigma } is the stress (sum of viscous and pressure stresses), and f {\displaystyle \mathbf {f} } an applied body...

of the Ladyzenskaya-type model with a non-linear velocity dependent stress tensor was performed unfortunately no analytical solutions could be derived...

suddenly subjected to a stress σ 0 {\displaystyle \sigma _{0}} , then the elastic element would suddenly deform and the viscous element would deform with...

material rate of the Cauchy stress tensor, and L {\displaystyle {\boldsymbol {L}}} is the spatial velocity gradient tensor. If only these two original...

In an incompressible flow, the viscous stress tensor is given as a viscosity, multiplied by the rate-of-strain tensor τ i j = 2 μ eff ( | γ ˙ | ) E i...