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In other words, the endpoints of all stress vectors at a given point in the continuum body lie on the stress ellipsoid surface, i.e., the radius-vector from the center of the ellipsoid, located at the material point in consideration, to a point on the surface of the ellipsoid is equal to the stress vector on some plane passing through the point.
The octahedral plane is sometimes referred to as the 'pi plane' [10] or 'deviatoric plane'. [ 11 ] The octahedral profile is not necessarily constant for different values of pressure with the notable exceptions of the von Mises yield criterion and the Tresca yield criterion which are constant for all values of pressure.
Visualisation of a Cauchy stress tensor σ in the Haight-Westergaard stress space. In continuum mechanics, Haigh–Westergaard stress space, or simply stress space is a 3-dimensional space in which the three spatial axes represent the three principal stresses of a body subject to stress.
Figure 7.1 Plane stress state in a continuum. In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 ...
A superlattice is a periodic structure of layers of two (or more) materials. Typically, the thickness of one layer is several nanometers . It can also refer to a lower-dimensional structure such as an array of quantum dots or quantum wells .
This way, the shear stress acting on plane B is negative and the shear stress acting on plane A is positive. The diameter of the circle is the line joining point A and B. The centre of the circle is the intersection of this line with the -axis. Knowing both the location of the centre and length of the diameter, we are able to plot the Mohr ...
Antiplane shear or antiplane strain [1] is a special state of strain in a body. This state of strain is achieved when the displacements in the body are zero in the plane of interest but nonzero in the direction perpendicular to the plane.
The tetrahedron is formed by slicing the infinitesimal element along an arbitrary plane with unit normal n. The stress vector on this plane is denoted by T (n). The stress vectors acting on the faces of the tetrahedron are denoted as T (e 1), T (e 2), and T (e 3), and are by definition the components σ ij of the stress tensor σ.