The unified strength theory (UST). proposed by Yu Mao-Hong is a series of yield criteria (see yield surface) and failure criteria (see Material failure theory). It is a generalized classical strength theory which can be used to describe the yielding or failure of material begins when the combination of principal stresses reaches a critical value.
Mathematically, the formulation of UST is expressed in principal stress state as <br> <br> where are three principal stresses, is the uniaxial tensile strength and is tension-compression strength ratio (). The unified yield criterion (UYC) is the simplification of UST when , i.e. <br/> <br/>
The limit surfaces of the unified strength theory in principal stress space are usually a semi-infinite dodecahedron cone with unequal sides. The shape and size of the limiting dodecahedron cone depends on the parameter b and . The limit surfaces of UST and UYC are shown as follows.
Due to the relation (), the principal stress state () may be converted to the twin-shear stress state () or (). Twin-shear element models proposed by Mao-Hong Yu are used for representing the twin-shear stress state. Considering all the stress components of the twin-shear models and their different effects yields the unified strength theory as <br> <br> The relations among the stresses components and principal stresses read <br> <br> <br> The and C should be obtained by uniaxial failure state<br> <br> <br> By substituting Eqs.(4a), (4b) and (5a) into the Eq.(3a), and substituting Eqs.(4a), (4c) and (5b) into Eq.(3b), the and C are introduced as<br> <br>
The development of the unified strength theory can be divided into three stages as follows.<br> 1. Twin-shear yield criterion (UST with and )<br> <br> <br> 2. Twin-shear strength theory (UST with ).<br> <br> <br> 3. Unified strength theory.<br>
Unified strength theory has been used in Generalized Plasticity, Structural Plasticity, Computational Plasticity and many other fields