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Isotropic materials are useful since they are easier to shape, and their behavior is easier to predict. Anisotropic materials can be tailored to the forces an object is expected to experience. For example, the fibers in carbon fiber materials and rebars in reinforced concrete are oriented to withstand tension.
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 ...
Additionally, all crystal structures, including the cubic crystal system, are anisotropic with respect to certain properties, and isotropic to others (such as density). [4] The anisotropy of a crystal’s properties depends on the rank of the tensor used to describe the property, as well as the symmetries present within the crystal.
While the constituents can often be modeled as having isotropic behaviour, the microstructure characteristics (shape, orientation, varying volume fraction, ..) of heterogeneous materials often leads to an anisotropic behaviour. Anisotropic material models are available for linear elasticity.
A basic distinction is between isotropic materials, which exhibit the same properties regardless of the direction of the light, and anisotropic ones, which exhibit different properties when light passes through them in different directions. The optical properties of matter can lead to a variety of interesting optical phenomena.
In contrast, materials with positional order but no orientational order are known as plastic crystals. [19] Most thermotropic LCs will have an isotropic phase at high temperature: heating will eventually drive them into a conventional liquid phase characterized by random and isotropic molecular ordering and fluid-like flow behavior
In single-crystal materials (e.g. silicon wafers), this effect can allow very high anisotropy, as shown in the figure. The term "crystallographic etching" is synonymous with "anisotropic etching along crystal planes". However, for some non-crystal materials like glass, there are unconventional ways to etch in an anisotropic manner. [2]
In materials where susceptibility is anisotropic (different depending on direction), susceptibility is represented as a tensor known as the susceptibility tensor. Many linear dielectrics are isotropic, but it is possible nevertheless for a material to display behavior that is both linear and anisotropic, or for a material to be non-linear but ...