Geng, YN, Cai, ZX and Fu, YB (2017) On the near-critical behavior of cavitation in elastic plane membranes. International Journal of Non-Linear Mechanics. ISSN 0020-7462

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Abstract Material cavitation under tensile loading is often studied by assuming the pre-existence of a small void. In this case the void would initially grow but without significant change in its size, and cavitation is said to take place if this slow growth is followed by rapid growth at higher load values. In the limit when the original void radius δ tends to zero, there will be no growth until a load or stretch measure, λ say, reaches a well-defined critical value λ cr at which a cavity appears suddenly. In this paper we study the near-critical asymptotic behavior of cavitation in plane membranes when δ is not zero but small, and show that the near-critical behavior is governed by a scaling law in the form λ − λ cr = C ( δ / L ) m , where L is the undeformed outer radius of the plane membrane, and C and m are non-dimensional constants. The positive power m in general depends on the material model used, but for the three classes of material models considered, it happens to be equal to 2 ( 1 + ν ) / ( 3 + ν ) in each case, where ν is Poisson’s ratio for infinitesimal deformations. If a pre-existing void is viewed as an imperfection, then this scaling law describes the imperfection sensitivity of cavitation: it states that in the presence of imperfections significant void growth would occur when λ were increased to within an order ( δ / L ) m interval around λ cr .

Item Type: Article
Additional Information: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Elsevier at - please refer to the terms of use of the publisher.
Uncontrolled Keywords: Cavitation, Imperfection sensitivity, Void growth, Membrane
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 20 Apr 2017 15:30
Last Modified: 07 Apr 2021 09:09

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