Mathematic equation of isotropic hardening and its geometrical representation in principal stress space

A specific isotropic hardening quadric equation for stabilizing materials is proposed and derived in principal stress space, and the corresponding locus and subsequent yield surface are drawn up in proportional loading. After the initial yielding the subsequent yield surface is no longer a circular truncated cone but a ellipsoid when triaxial hardening exponents are diversity and diminution. However, if triaxial hardening exponents are equal, namely hardening radius are the same, the subsequent yield surface is a sphere, or is an ellipse with unequal hardening exponents at biaxial space. If there is no Bauschinger effect, the hardening quadric is symmetrical about equally inclined geometric axis oH with equal negative mean normal stress. The conclusion is suitable only to the stabilizing materials according to Drucker postulation.