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By Mao-hong Yu

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Mech. , 31͑7͒, 511–519. Hill R ͑1993͒, A user-friendly theory of orthotropic plasticity in sheet metals, Int. J. Mech. , 35, 19. Barlat F, Becker C, Hayashida Y et al ͑1997͒, Yielding description for solution strengthened aluminum alloys, Int. J. , 13͑4͒, 385– 401. Yu: Advances in strength theories ͓270͔ ͓271͔ ͓272͔ ͓273͔ ͓274͔ ͓275͔ ͓276͔ ͓277͔ ͓278͔ ͓279͔ ͓280͔ ͓281͔ ͓282͔ ͓283͔ ͓284͔ ͓285͔ ͓286͔ ͓287͔ ͓288͔ ͓289͔ ͓290͔ ͓291͔ ͓292͔ ͓293͔ ͓294͔ ͓295͔ 203 Barlat F, Meada Y, Chung K et al ͑1997͒, Yield function development for aluminum alloys sheets, J.

A partial exploitation of the plastic properties of materials was allowed by the standards of many countries for the design of structures. Strength theories are also widely used in the slip line field of plane plastic strain, characteristic line field of plane stress and axial symmetric plasticity problems, linear and non-linear analysis of structures by FEM, BEM, Discontinuous Deformation Analysis ͑DDA͒, Numerical Manifold Method ͑NMM͒, and others. Strength theory is now generalized not only to perfect elasto-plastic and hardening problems, but also strain softening, elasto-brittle-plastic behavior, discontinuities, localization and bifurcation, microcrack propagation, viscoplasticity, post-critical response, fatigue, fracture, damage, mesomechanics, soil-water characteristics of unsaturated soils, strain Appl Mech Rev vol 55, no 3, May 2002 gradient plasticity ͑Fleck and Hutchinson et al ͓710,1036,1046͔͒, and other areas.

Willam KJ and Warnke EP ͑1975͒, Constitutive model for the triaxial behavior of concrete, Int. Assoc. Bridge. Struct. Eng. , 19 1–31. Matsuoka H and Nakai T ͑1974͒, Stress-deformation and strength characteristics of soil under three different principal stresses, Proc. of Japan Society of Civil Engineers, 232, 59–70. Lade PV and Duncan JM ͑1975͒, Elastoplastic stress-strain theory for cohesionless soil, J. Geotech. , 101͑10͒, 1037–1053. Ottosen NS ͑1977͒, A failure citerion for concrete, J. Eng.

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