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Effect of large deformation and surface stiffening on the transmission of a line load on a neo-Hookean half space

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Abstract

A line force acting on a soft elastic solid, say due to the surface tension of a liquid drop, can cause significant deformation and the formation of a kink close to the point of force application. Analysis based on linearized elasticity theory shows that sufficiently close to its point of application, the force is borne entirely by the surface stress, not by the elasticity of the substrate; this local balance of three forces is called Neumann's triangle. However, it is not difficult to imagine realistic properties for which this force balance cannot be satisfied. For example, if the line force corresponds to surface tension of water, the numerical values of (unstretched) solid–vapor and solid–liquid surface stresses can easily be such that their sum is insufficient to balance the applied force. In such cases conventional (or naïve) Neumann's triangle of surface forces must break down. Here we study how force balance is rescued from the breakdown of naïve Neumann's triangle by a combination of (a) large hyperelastic deformations of the underlying bulk solid, and (b) increase in surface stress due to surface elasticity (surface stiffening). For a surface with constant surface stress (no surface stiffening), we show that the linearized theory remains accurate if the applied force is less than about 1.3 times the solid surface stress. For a surface in which the surface stress increases linearly with the surface stretch, we find that the Neumann's triangle construction works well as long as we replace the constant surface stress in the naïve Neumann triangle by the actual surface stress underneath the line load.

Graphical abstract: Effect of large deformation and surface stiffening on the transmission of a line load on a neo-Hookean half space

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Publication details

The article was received on 05 Dec 2017, accepted on 10 Feb 2018 and first published on 12 Feb 2018


Article type: Paper
DOI: 10.1039/C7SM02394D
Citation: Soft Matter, 2018, Advance Article
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    Effect of large deformation and surface stiffening on the transmission of a line load on a neo-Hookean half space

    H. Wu, Z. Liu, A. Jagota and C. Hui, Soft Matter, 2018, Advance Article , DOI: 10.1039/C7SM02394D

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