Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Anisotropic Plasticity and Application to Plane Stress

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_225-1



Plasticity is the ability of a material to deform in an irreversible manner. Unlike elasticity for which deformations are reversible, plasticity leads to permanent shape changes after a sufficient load is applied to a material. Anisotropic plasticity is the dependence of plastic properties on the loading direction. For plane stress states, loading is defined using only three stress components out of six for a general stress tensor. The description of plastic anisotropy for plane stress states is simpler than for general stress states but it has a wide range of practical applications in processes such as sheet forming.


In uniaxial tension, the stress-strain behavior of metals and alloys at low strain is, at first order, reversible and linear. This behavior is well described by Hooke’s law, in which the stress is proportional to the strain through the elastic modulus E. This law can be generalized to all...

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The authors gratefully acknowledge the supports of POSCO and the Global Innovation Research Organization in TUAT for this entry. In addition, the authors are indebted to Dr. Tomoyuki Hakoyama (The RIKEN) for help with the parameter identification analysis in section “Application to Steel”.


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Authors and Affiliations

  1. 1.Graduate Institute of Ferrous TechnologyPohang University of Science and TechnologyPohangRepublic of Korea
  2. 2.Division of Advanced Mechanical Systems Engineering, Institute of Engineering (double as Institute of Global Innovation Research)Tokyo University of Agriculture and TechnologyTokyoJapan
  3. 3.Department of Mechanical EngineeringUniversity of New HampshireDurhamUSA

Section editors and affiliations

  • Sergey Alexandrov
    • 1
  1. 1.Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia