The unified strength theory (UST).Yu M. H., He L. N. (1991) A new model and theory on yield and failure of materials under the complex stress state. Mechanical Behaviour of Materials-6 (ICM-6). Jono M and Inoue T eds. Pergamon Press, Oxford, (3), pp. 841–846. https://doi.org/10.1016/B978-0-08-037890-9.50389-6Yu M. H. (2004) Unified Strength Theory and Its Applications. Springer: Berlin. Zhao, G.-H.; Ed., (2006) Handbook of Engineering Mechanics, Rock Mechanics, Engineering Structures and Materials (in Chinese), China's Water Conservancy Resources and Hydropower Press, Beijing, pp. 20-21Yu M. H. (2018) Unified Strength Theory and Its Applications (second edition). Springer and Xi'an Jiaotong University Press, Springer and Xi'an. 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. Teodorescu, P.P. (Bucureşti). (2006). Review: Unified Strength Theory and its applications, Zentralblatt MATH Database 1931 – 2009, European Mathematical Society,, FIZ Karlsruhe & Springer-VerlagAltenbach, H., Bolchoun, A., Kolupaev, V.A. (2013). Phenomenological Yield and Failure Criteria, in Altenbach, H., Öchsner, A., eds., Plasticity of Pressure-Sensitive Materials, Serie ASM, Springer, Heidelberg, pp. 49-152.Kolupaev, V. A., Altenbach, H. (2010). Considerations on the Unified Strength Theory due to Mao-Hong Yu (in German: Einige Überlegungen zur Unified Strength Theory von Mao-Hong Yu), Forschung im Ingenieurwesen, 74(3), pp. 135-166.
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 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 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 The development of the unified strength theory can be divided into three stages as follows. 1. Twin-shear yield criterion (UST with and )Yu M. H. (1961) Plastic potential and flow rules associated singular yield criterion. Res. Report of Xi'an Jiaotong University. Xi'an, China (in Chinese)Yu MH (1983) Twin shear stress yield criterion. International Journal of Mechanical Sciences, 25(1), pp. 71-74. https://doi.org/10.1016/0020-7403(83)90088-7
2. Twin-shear strength theory (UST with )Yu M. H., He L. N., Song L. Y. (1985) Twin shear stress theory and its generalization. Scientia Sinica (Sciences in China), English edn. Series A, 28(11), pp. 1174–1183..
3. Unified strength theory. Applications Unified strength theory has been used in Generalized Plasticity,Yu M. H. et al., (2006) Generalized Plasticity. Springer: Berlin. Structural Plasticity,Yu M. H., Ma G. W., Li J. C. (2009) Structural Plasticity: Limit, Shakedown and Dynamic Plastic Analyses of Structures. ZJU Press and Springer: Hangzhou and Berlin. Computational PlasticityYu M. H., Li J. C. (2012) Computational Plasticity, Springer and ZJU Press: Berlin and Hangzhou. and many other fieldsFan, S. C., Qiang, H. F. (2001). Normal high-velocity impaction concrete slabs-a simulation using the meshless SPH procedures. Computational Mechanics-New Frontiers for New Millennium, Valliappan S. and Khalili N. eds. Elsevier Science Ltd, pp. 1457-1462Guowei, M., Iwasaki, S., Miyamoto, Y. and Deto, H., 1998. Plastic limit analyses of circular plates with respect to unified yield criterion. International journal of mechanical sciences, 40(10), pp.963-976. https://doi.org/10.1016/S0020-7403(97)00140-9
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