Orthotropic material

In material science and solid mechanics, orthotropic materials have material properties that differ along three mutually-orthogonal twofold axes of rotational symmetry. 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 the properties are different. These are the axial direction (along the grain), the radial direction, and the circumferential direction. Because the preferred coordinate system is cylindrical-polar, this type of orthotropy is also called polar orthotropy. Mechanical properties, such as strength and stiffness, measured axially (along the grain) are typically better than those measured in the radial and circumferential directions (across the grain). These directional differences in strength can be quantified with Hankinson's equation.

Another example of an orthotropic material is sheet metal formed by squeezing thick sections of metal between heavy rollers. This flattens and stretches its grain structure. As a result, the material becomes anisotropic—its properties differ between the direction it was rolled in and each of the two transverse directions.

If orthotropic properties vary between points inside an object, it possesses both orthotropy and inhomogeneity. This suggests that orthotropy is the property of a point within an object rather than for the object as a whole (unless the object is homogeneous). The associated planes of symmetry are also defined for a small region around a point and do not necessarily have to be identical to the planes of symmetry of the whole object.

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 third one. Isotropic materials have an infinite number of planes of symmetry.

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