Yield properties of plastic material

In terms of yield surfaces, the 2D yield surface of an isotropic material will be mirrored over the line sigma_1 = sigma_2. In 3D, an isotropic yield surface will have rotational symmetry about the line sigma_1 = sigma_2 = sigma_3 (the hydrostatic axis). These symmetry constraints imply that the yield surface will intersect each principal stress axis at the same value. Additionally, if the material is isotropically hardened, the yield surface will expand outward concentrically to the original yield surface.

In contrast, a the yield surface for an anisotropic yield surface does not have these symmetry requirements, and can intersect the different principal stress axes at different values. For a 2D yield surface, the degree of anisotropy, R, is given by R = sigma_2 / sigma_1, where R=1 corresponds to an isotropic material.