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...

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

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...

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...

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

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...

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

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

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

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

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

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

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...

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

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...

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...

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...

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

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...

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

In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components...

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

mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear...

strain tensor ε i j {\displaystyle \varepsilon _{ij}} , similarly to the Cauchy stress tensor, can be expressed as the sum of two other tensors: a mean...

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

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...

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

In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space...