the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply...
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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...
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constitutive models (for example, the Cauchy Stress tensor is variant to a pure rotation, while the deformation strain tensor is invariant; thus creating problems...
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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...
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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...
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relativity (stress–energy tensor, curvature tensor, ...). In applications, it is common to study situations in which a different tensor can occur at...
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Elasticity (physics) (section Cauchy elastic materials)
the material rate of the Cauchy stress tensor, and L {\displaystyle {\boldsymbol {L}}} is the spatial velocity gradient tensor. If only these two original...
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of the stress increment tensor on the strain increment tensor be correct (work conjugacy requirement). The relation between the Cauchy stress and the...
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Von Mises yield criterion (redirect from Von Mises 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...
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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...
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Gravitational stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical...
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Stress tensor may refer to: Cauchy stress tensor, in classical physics Stress deviator tensor, in classical physics Piola–Kirchhoff stress tensor, in...
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two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical...
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of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...
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}}\nabla \cdot {\boldsymbol {\sigma }}+\mathbf {f} .} By setting the Cauchy stress tensor σ {\textstyle {\boldsymbol {\sigma }}} to be the sum of a viscosity...
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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...
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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...
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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...
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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...
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gradient to the first or second Piola-Kirchhoff stress tensor. For an isotropic material the Cauchy stress tensor σ {\displaystyle {\boldsymbol {\sigma }}}...
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Linear elasticity (redirect from Navier-Cauchy equations)
{\boldsymbol {\sigma }}} is the Cauchy stress tensor, ε {\displaystyle {\boldsymbol {\varepsilon }}} is the infinitesimal strain tensor, u {\displaystyle \mathbf...
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Hyperelastic material (section Cauchy stress)
{C}}}}~.} This stress tensor can subsequently be converted into any of the other conventional stress tensors, such as the Cauchy stress tensor which is given...
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Pseudotensor (redirect from Pseudo-tensor)
spacetime Tensor – Algebraic object with geometric applications Tensor density – Generalization of tensor fields Tensor field – Assignment of a tensor continuously...
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principle, that means determining, implicitly or explicitly, the Cauchy stress tensor at every point. The external forces may be body forces (such as gravity...
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Signorini problem (section The form of the stress tensor in the formulation of Signorini and Fichera)
u_{k}}{\partial x_{i}}}\right)\right)} is the infinitesimal strain tensor The Cauchy stress tensor has therefore the following form (5) σ i k = − ∂ W ∂ ε...
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various areas, including: Classical treatment of tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning...
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differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature...
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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...
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electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a...
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Finite strain theory (redirect from Cauchy-Green tensor)
deformation tensor or Green's deformation tensor (the IUPAC recommends that this tensor be called the Cauchy strain tensor), defined as: C = F T F = U 2 or C...
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