Shakedown in frictional contact of discrete elastic systems: A review

Young Ju Ahn, Anders Klarbring, Andrea Spagnoli, Michele Terzano

Research output: Contribution to journalArticlepeer-review


When exposed to cyclic quasi-static loading, elastic bodies in contact may develop a favourable condition where slip ceases after a few cycles, an occurrence commonly known as frictional shakedown. If the amplitude of the cyclic load is greater than a so-called shakedown limit, shakedown cannot occur. In this review paper, the validity of shakedown theorems in the context of conforming contacts with à la Coulomb friction is first discussed. Then, an optimisation method for determining the shakedown limit of elastic discrete three-dimensional systems is reviewed. Finally, an incremental Gauss–Seidel algorithm, extended to three-dimensional systems, is here illustrated in details for the first time. The algorithm allows us to describe the transient response of normal-tangential coupled systems under a given cyclic loading scenario, and to determine their possible shakedown depending on the initial conditions. An example concerning a discrete conforming contact problem, where either coupling or uncoupling conditions can be imposed, is illustrated.

Original languageEnglish
Article number111470
JournalInternational Journal of Solids and Structures
Publication statusPublished - 1 Apr 2022


  • Contact
  • Friction
  • Incremental analysis
  • Limit analysis
  • Linear programming
  • Shakedown

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics
  • Materials Science(all)
  • Modelling and Simulation


Dive into the research topics of 'Shakedown in frictional contact of discrete elastic systems: A review'. Together they form a unique fingerprint.

Cite this