By definition, an orthotropic material has at least 2 orthogonal planes of symmetry, where material properties are independent of direction within each plane. Such materials require 9 independent variables (i.e. elastic constants) in their constitutive matrices.

In contrast, a material without any planes of symmetry is fully anisotropic and requires 21 elastic constants, whereas a material with an infinite number of symmetry planes (i.e. every plane is a plane of symmetry) is isotropic, and requires only 2 elastic constants.

The compliance matrix takes the form,

where .

Note that, in orthotropic materials, there is no interaction between the normal stresses s_x, s_y, s_z and the shear strains e_yz, e_zx, e_xy

The factor 2 multiplying the shear modulii in the compliance matrix results from the difference between shear strain and engineering shear strain, where , etc.

where,

The fact that the stiffness matrix is symmetric requires that the following statements hold,

The factor of 2 multiplying the shear modulii in the stiffness matrix results from the difference between shear strain and engineering shear strain, where , etc.