Unified strength theory

The unified strength theory (UST).

[1][2][3][4] 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.

[5][6][7] Mathematically, the formulation of UST is expressed in principal stress state as

is the uniaxial tensile strength and

is tension-compression strength ratio (

The unified yield criterion (UYC) is the simplification of UST when

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.

), the principal stress state (

) may be converted to the twin-shear stress state (

Twin-shear element models proposed by Mao-Hong Yu are used for representing the twin-shear stress state.

[1] 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

and C should be obtained by uniaxial failure state

By substituting Eqs.

(3a), and substituting Eqs.

The development of the unified strength theory can be divided into three stages as follows.

Twin-shear yield criterion (UST with

Twin-shear strength theory (UST with

Unified strength theory[1].

Unified strength theory has been used in Generalized Plasticity,[11] Structural Plasticity,[12] Computational Plasticity[13] and many other fields[14][15]