Reprint of: Shakedown in frictional contact of discrete elastic systems: A review. (15th October 2022)

• Record Type: Journal Article
• Authors: Ahn, Young Ju; Klarbring, Anders; Spagnoli, Andrea; Terzano, Michele
• Is Part Of: International journal of solids and structures. Volume 253(2022)
• Publication Date: 2022-10-15
• Subjects: Shakedown -- Friction -- Contact -- Limit analysis -- Linear programming -- Incremental analysis; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2022.111831
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: 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.