# Material Groups

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.

1. 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.
2. 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.
3. 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.
4. 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.