- It immediately follows that the stress tensor only has six independent components (i.e., , , , , , and ). It is always possible to choose the orientation of a set of Cartesian axes in such a manner that the non-diagonal components of a given symmetric second-order tensor field are all set to zero at a given point in space.
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- The Navier-Stokes equations are the basic governing equations for a viscous, heat conducting fluid. It is a vector equation obtained by applying Newton's Law of Motion to a fluid element and is also called the momentum equation.
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- Models of elastic materials Cauchy type . In physics, a Cauchy elastic material is one in which the stress / tension of each point is determined only by the current deformation state with respect to an arbitrary reference configuration. This type of materials is also called simple elastic material.
- In continuum mechanics, the Cauchy stress tensor, true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components σ i j {\displaystyle \sigma _{ij}} that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration.

T = T0 +L(F0)[H], (2) (T-cauchy) where L(F0)[H] = ∇FF(F0)[HF0] (3) (L-elast) deﬁnes the elasticity tensor relative to the reference conﬁguration κt0. Since the reference stress T0 and the deformation gradient F0 are given in the updated reference state κt0, the elasticity tensor L(F0) is a constant fourth order tensor. 2 ij forms a tensor - a generalization of a vector • known as the Cauchy stress tensor or simply as the stress tensor • other notations are σ ij and T ij • the tensor is second rank: it has two subscripts, i.e., each component has two directions associated with it (normal and stress vector)

May 15, 2014 · The Cauchy stress tensor relate a unit-length direction vector n to a stress vector T across an imagine surface. Planar # Surface Cauchy postulate: The stress vector T is only a function of n (unit-length direction vector n) In following context, bold symbols represent matrices. T=n*σ, where σ is a second-order tensor filed and is independent… A Cauchy’s formula B Principal stresses (eigenvectors and eigenvalues) II Cauchy's formula A Relates traction vector components to stress tensor components (see Figures 5.1, 5.2, 5.3 for derivation) B Ti = σji nj (5.1) 1 Meaning of terms a k Ti=traction vector component: T = T1 i + 2 j +T3 b σij = stress component c n =unit normal vector.

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