There are 31 types of crystals. Bodies and things made up of these crystals can be grouped into classes, based on the independent material constants in the linear stress-strain relationship. The most general anisotropic material group, which requires twenty-one independent constants, is also called triclinic material.
Three other important nonisotropic material groups are monoclinic, orthotropic, and transversely isotropic materials.
- Monoclinic materials require thirteen independent material constants. Here the Z plane is the plane of symmetry. This implies that the stress-strain relationships are the same in the positive and negative Z directions.
- Orthotropic materials require nine independent constants. Orthotropic materials have two orthogonal planes of symmetry. In other words, if we rotate the material by 90° about the X-axis or the Y-axis, we obtain the same stress-strain relationships.
- Transversely isotropic materials require five independent material constants. Transversely isotropic materials are isotropic in a plane. In other words, rotation by an arbitrary angle about the Z-axis does not change the stress-strain relationship, and the material is isotropic in the XY plane.
- Isotropic materials require only two independent material constants. Rotation about the X, Y, or Z-axis by any arbitrary angle results in the same stress-strain relationship.