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.
Mathematical Formulation
Mathematically, the formulation of UST is expressed in principal stress state as
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.
Limit surfaces of Unified Strength Theory
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.
Derivation of Unified Strength Theory
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
The relations among the stresses components and principal stresses read
The and C should be obtained by uniaxial failure state
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
History of Unified Strength Theory
The development of the unified strength theory can be divided into three stages as follows. 1. Twin-shear yield criterion (UST with and )
2. Twin-shear strength theory (UST with ).
3. Unified strength theory.
Applications of the Unified Strength theory
Unified strength theory has been used in Generalized Plasticity, Structural Plasticity, Computational Plasticity and many other fields