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An orthotropic material has three mutually orthogonal twofold axes of rotational symmetry so that its material properties are, in general, different along each axis. An object can be both orthotropic and inhomogeneous; it may have orthotropic properties that vary from point to point inside the volume of the object. 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. 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. In particular, the mechanical properties (such as strength and stiffness) along the grain are typically larger than in the radial and circumferential directions. Hankinson's equation provides a means to quantify the difference in strength in different directions. Another example of an orthotropic material is a metal which has been rolled to form a sheet; the properties in the rolling direction and each of the two transverse directions will be different due to the anisotropic structure that develops during rolling. 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. Transversely isotropic materials are special orthotropic materials that have one axis of symmetry (any other pair of axes that are perpendicular to the main one and orthogonal among themselves are also axes of symmetry). One common example of transversely isotropic material with one axis of symmetry is a polymer reinforced by parallel glass or graphite fibers. The strength and stiffness of such a composite material will usually be greater in a direction parallel to the fibers than in the transverse direction, and the thickness direction usually has properties similar to the transverse direction. Another example would be a biological membrane, in which the properties in the plane of the membrane will be different from those in the perpendicular direction. It is important to keep in mind that a material which is anisotropic on one length scale may be isotropic on another (usually larger) length scale. For instance, most metals are polycrystalline with very small grains. Each of the individual grains may be anisotropic, but if the material as a whole comprises many randomly oriented grains, then its measured mechanical properties will be an average of the properties over all possible orientations of the individual grains. == Orthotropy in physics == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「orthotropic material」の詳細全文を読む スポンサード リンク
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