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- Cauchy_stress_tensor abstract "In continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor, named after Augustin-Louis Cauchy, is a second order tensor of type (2,0) (that is, a linear map), with nine components that completely define the state of stress at a point inside a material in the deformed placement or configuration. The tensor relates a unit-length direction vector n to the stress vector T(n) across an imaginary surface perpendicular to n:where,The Cauchy stress tensor obeys the tensor transformation law under a change in the system of coordinates. A graphical representation of this transformation law is the Mohr's circle for stress.The Cauchy stress tensor is used for stress analysis of material bodies experiencing small deformations: It is a central concept in the linear theory of elasticity. For large deformations, also called finite deformations, other measures of stress are required, such as the Piola–Kirchhoff stress tensor, the Biot stress tensor, and the Kirchhoff stress tensor.According to the principle of conservation of linear momentum, if the continuum body is in static equilibrium it can be demonstrated that the components of the Cauchy stress tensor in every material point in the body satisfy the equilibrium equations (Cauchy's equations of motion for zero acceleration). At the same time, according to the principle of conservation of angular momentum, equilibrium requires that the summation of moments with respect to an arbitrary point is zero, which leads to the conclusion that the stress tensor is symmetric, thus having only six independent stress components, instead of the original nine.There are certain invariants associated with the stress tensor, whose values do not depend upon the coordinate system chosen, or the area element upon which the stress tensor operates. These are the three eigenvalues of the stress tensor, which are called the principal stresses.".
- Cauchy_stress_tensor thumbnail Components_stress_tensor_cartesian.svg?width=300.
- Cauchy_stress_tensor wikiPageID "3323565".
- Cauchy_stress_tensor wikiPageRevisionID "603581074".
- Cauchy_stress_tensor hasPhotoCollection Cauchy_stress_tensor.
- Cauchy_stress_tensor subject Category:Continuum_mechanics.
- Cauchy_stress_tensor subject Category:Solid_mechanics.
- Cauchy_stress_tensor subject Category:Tensors.
- Cauchy_stress_tensor comment "In continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor, named after Augustin-Louis Cauchy, is a second order tensor of type (2,0) (that is, a linear map), with nine components that completely define the state of stress at a point inside a material in the deformed placement or configuration.".
- Cauchy_stress_tensor label "Cauchy stress tensor".
- Cauchy_stress_tensor label "Tenseur des contraintes".
- Cauchy_stress_tensor label "Tensor tensão de Cauchy".
- Cauchy_stress_tensor label "Тензор напряжений".
- Cauchy_stress_tensor label "موتر الإجهاد لكوشي".
- Cauchy_stress_tensor sameAs Τανυστής_τάσεων_Cauchy.
- Cauchy_stress_tensor sameAs Tenseur_des_contraintes.
- Cauchy_stress_tensor sameAs Tensor_tensão_de_Cauchy.
- Cauchy_stress_tensor sameAs m.0r4qf4v.
- Cauchy_stress_tensor sameAs Q13409892.
- Cauchy_stress_tensor sameAs Q13409892.
- Cauchy_stress_tensor wasDerivedFrom Cauchy_stress_tensor?oldid=603581074.
- Cauchy_stress_tensor depiction Components_stress_tensor_cartesian.svg.
- Cauchy_stress_tensor isPrimaryTopicOf Cauchy_stress_tensor.