A direct approach to the evaluation of structural shakedown limit considering limited kinematic hardening and non-isothermal effect

Zhiyuan Ma, Haofeng Chen, Yinghua Liu, Fu-Zhen Xuan

Research output: Contribution to journalArticle


This paper presents a novel direct method for the structural shakedown analysis considering limited kinematic hardening and non-isothermal effect. The Melan’s static shakedown theorem is extended to consider limited kinematic hardening material and implemented into the Linear Matching Method (LMM) shakedown module. Instead of using a specific kinematic hardening rule and an explicit back stress field, the general nonlinear hardening laws are considered by using a two-surface hardening model. A two-stage procedure is developed in the extended LMM algorithm, which can generate the limited hardening shakedown envelope and the unlimited hardening curve efficiently and accurately. Also, the material non-isothermal effect is considered during the computation process of the shakedown limit by proposing a temperature-dependent hardening factor, in place of a constant and fictitious one. To validate the extended LMM method, a numerical test on a thin cylinder pipe with temperature-independent material properties is performed, and the results match well with ones from literature. Then, a numerical study on a typical aero-engine turbine disk is conducted to investigate the influence of temperature-dependent material properties and operating conditions. Several shakedown curves considering kinematic hardening effect are derived and adequately discussed. As a result, the extended LMM shakedown module is proven to be a robust, efficient and versatile tool for practical industrial problems.
Original languageEnglish
Article number103877
Number of pages23
JournalEuropean Journal of Mechanics - A/Solids
Early online date16 Oct 2019
Publication statusPublished - 29 Feb 2020



  • direct method
  • shakedown analysis
  • limited kinematic hardening
  • temperature dependence
  • linear matching method

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