Abstract
We revisit the indentation of a thin solid sheet of size suspended on a circular hole of radius in a smooth rigid substrate, addressing the effects of boundary conditions at the hole's edge. Introducing a basic theoretical model for the van der Waals (vdW) sheet-substrate attraction, we demonstrate the dramatic effect of replacing the clamping condition (Schwerin model) with a sliding condition, whereby the supported part of the sheet is allowed to slide towards the indenter and relax the induced hoop compression through angstrom-scale deflections from the thermodynamic equilibrium (determined by the vdW potential). We highlight the possibility that the indentation force may not exhibit the commonly anticipated cubic dependence on the indentation depth , in which the proportionality constant is governed by the sheet's stretching modulus and the hole's radius , but rather a pseduolinear response , whereby the proportionality constant is governed by the bending modulus, the vdW attraction, and the sheet's size .
1 More- Received 6 August 2020
- Revised 4 March 2021
- Accepted 11 March 2021
DOI:https://doi.org/10.1103/PhysRevE.103.043002
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