Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Shakedown and Plastic Collapse in Plane Stress Problems

  • D. C. Pham
  • C. V. Le
  • T. D. Tran
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_271-1



A structure made of elastic plastic material under loading, after an initial stage of possible limited plastic deformation (of finite total plastic dissipation), may eventually shake down to some residual stress state, from which it subsequently responds elastically (hence safely) to the external agencies. Otherwise, the structure is considered as having failed, because of the instantaneous plastic collapse (corresponding to the maximal static load bearing capacity of the structure), or the plastic deformation would accumulate unrestrictively over loading cycles (the mode is called the ratchetting or incremental collapse one), or the plastic deformation should be bounded but vary cyclically and unceasingly (fatigue, cyclic, rotating plasticity, or alternating plasticity collapse).

In principle shakedown incremental checking for a structure can be performed for any sophisticated elastic plastic material model in small or large deformations,...

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Pham DC is supported by VAST Project NCVCC03.01/18-18.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.VAST – Institute of MechanicsBa dinh, HanoiVietnam
  2. 2.Department of Civil EngineeringInternational University – VNU HCMCHo Chi Minh CityVietnam
  3. 3.Faculty of Construction & ElectricityHo Chi Minh City Open UniversityHo Chi Minh CityVietnam

Section editors and affiliations

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