Unified strength theory
The unified strength theory. proposed by Yu Mao-Hong is a series of yield criteria and failure criteria. 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 aswhere are three principal stresses, is the uniaxial tensile strength and is tension-compression strength ratio.
The unified yield criterion is the simplification of UST when, i.e.
Limit surfaces
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
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 asThe relations among the stresses components and principal stresses read
The and C should be obtained by uniaxial failure state
By substituting Eqs., and into the Eq., and substituting Eqs., and into Eq., the and C are introduced as
History
The development of the unified strength theory can be divided into three stages as follows.1. Twin-shear yield criterion
2. Twin-shear strength theory.
3. Unified strength theory.