the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply...

orientation of S. Thus the stress state of the material must be described by a tensor, called the (Cauchy) stress tensor; which is a linear function...

measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures of stress can be...

constitutive models (for example, the Cauchy Stress tensor is variant to a pure rotation, while the deformation strain tensor is invariant; thus creating problems...

of the Cauchy stress tensor and infinitesimal strain tensor, and C i j k l {\displaystyle C^{ijkl}} are the components of the elasticity tensor. Summation...

of Cauchy stress tensor, σ I , σ I I , σ I I I {\displaystyle {{\sigma }_{I}},{{\sigma }_{II}},{{\sigma }_{III}}}  denote principal values of Cauchy stress...

_{v}^{2}=3J_{2}=3k^{2}} Substituting J 2 {\displaystyle J_{2}} with the Cauchy stress tensor components, we get σ v 2 = 1 2 [ ( σ 11 − σ 22 ) 2 + ( σ 22 − σ 33...

relativity (stress–energy tensor, curvature tensor, ...). In applications, it is common to study situations in which a different tensor can occur at...

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

Use of Cartesian tensors occurs in physics and engineering, such as with the Cauchy stress tensor and the moment of inertia tensor in rigid body dynamics...

Gravitational stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical...

two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical...

}}\nabla \cdot {\boldsymbol {\sigma }}+\mathbf {f} .} By setting the Cauchy stress tensor σ {\textstyle {\boldsymbol {\sigma }}} to be the sum of a viscosity...

Stress tensor may refer to: Cauchy stress tensor, in classical physics Stress deviator tensor, in classical physics Piola–Kirchhoff stress tensor, in...

the Cauchy stress tensor. This part is given by the normal stresses that occur in almost all situations. The anisotropic part of the stress tensor gives...

In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant; at least one of the indices of a mixed...

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...

of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...

principle, that means determining, implicitly or explicitly, the Cauchy stress tensor at every point. The external forces may be body forces (such as gravity...

of the stress increment tensor on the strain increment tensor be correct (work conjugacy requirement). The relation between the Cauchy stress and the...

principal stresses (the eigenvalues of the Cauchy stress tensor) is zero. That is, there is Cartesian coordinate system in which the stress tensor has the...

{\boldsymbol {\sigma }}} is the Cauchy stress tensor, ε {\displaystyle {\boldsymbol {\varepsilon }}} is the infinitesimal strain tensor, u {\displaystyle \mathbf...

gradient to the first or second Piola-Kirchhoff stress tensor. For an isotropic material the Cauchy stress tensor σ {\displaystyle {\boldsymbol {\sigma }}}...

various areas, including: Classical treatment of tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning...

differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature...

refinement of Augustin-Louis Cauchy's relations which were used to derive the equations satisfied by the Cauchy stress tensor. To give a more precise definition...

{\mathbf {q} }} where σ {\displaystyle \mathbf {\sigma } } is the Cauchy stress tensor. v {\displaystyle \mathbf {v} } is the flow velocity. and q {\displaystyle...

\mathbb {T} } is the Cauchy stress tensor, and ∇ ⋅ {\displaystyle \nabla \cdot } is the divergence operator. The Cauchy stress tensor for an incompressible...

theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in general...

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...