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Therefore, for cubic materials, we can think of anisotropy, , as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent: = / [(+)] = (+). The latter expression is known as the Zener ratio , a r {\displaystyle a_{r}} , where C i j {\displaystyle C_{ij}} refers to elastic constants in ...
A volume such as a computed tomography is said to have isotropic voxel spacing when the space between any two adjacent voxels is the same along each axis x, y, z. E.g., voxel spacing is isotropic if the center of voxel (i, j, k) is 1.38 mm from that of (i+1, j, k) , 1.38 mm from that of (i, j+1, k) and 1.38 mm from that of (i, j, k+1) for all ...
P-wave anisotropic prestack depth migration (APSDM) can produce a seismic image that is very accurate in depth and space. As a result, unlike isotropic PSDM, it is consistent with well data and provides an ideal input for reservoir characterization studies. However, this accuracy can only be achieved if correct anisotropy parameters are used.
These simple mediums are called isotropic, and the relationships between the fields can be expressed using constants. For more complex materials, such as crystals and many metamaterials, these fields are not necessarily parallel. When one set of the fields are parallel, and one set are not, the material is called anisotropic.
These directional differences in strength can be quantified with Hankinson's equation. They are a subset of anisotropic materials, because their properties change when measured from different directions. A familiar example of an orthotropic material is wood. In wood, one can define three mutually perpendicular directions at each point in which ...
A transversely isotropic material is one with physical properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse plane has infinite planes of symmetry and thus, within this plane, the material properties are the same in all directions. Hence, such materials are also known as "polar anisotropic" materials.
This model has the general form and the isotropic form respectively =: = +. where : is tensor contraction, is the second Piola–Kirchhoff stress, : is a fourth order stiffness tensor and is the Lagrangian Green strain given by = [() + + ()] and are the Lamé constants, and is the second order unit tensor.
where is the volume, the anisotropy constant, and the angle between the easy axis and the particle's magnetization. When shape anisotropy is explicitly considered, the symbol N {\displaystyle {\mathcal {N}}} is often used to indicate the anisotropy constant, instead of K {\displaystyle K} .