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Glass and metals are examples of isotropic materials. [3] Common anisotropic materials include wood (because its material properties are different parallel to and perpendicular to the grain) and layered rocks such as slate. Isotropic materials are useful since they are easier to shape, and their behavior is easier to predict.
The Young's modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material, stiffness (or compliance) tensors are used instead. In metals, anisotropic elasticity behavior is present in all single crystals with three independent coefficients for cubic crystals, for example.
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.
Orthotropic materials are a subset of anisotropic materials; their properties depend on the direction in which they are measured. Orthotropic materials have three planes/axes of symmetry. An isotropic material, in contrast, has the same properties in every direction. It can be proved that a material having two planes of symmetry must have a ...
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 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.
The hyperelastic material is a special case of a Cauchy elastic material. For many materials, linear elastic models do not accurately describe the observed material behaviour. The most common example of this kind of material is rubber, whose stress-strain relationship can be defined as non-linearly elastic, isotropic and incompressible.
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.