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Issue 4, 2015
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Surface tension and the mechanics of liquid inclusions in compliant solids

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Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which has recently been shown to control many processes in soft materials such as gels, elastomers and biological tissue. To extend Eshelby's theory of inclusions to soft materials, we consider liquid inclusions within an isotropic, compressible, linear-elastic solid. We solve for the displacement and stress fields around individual stretched inclusions, accounting for the bulk elasticity of the solid and the surface tension (i.e. isotropic strain-independent surface stress) of the solid–liquid interface. Surface tension significantly alters the inclusion's shape and stiffness as well as its near- and far-field stress fields. These phenomena depend strongly on the ratio of the inclusion radius, R, to an elastocapillary length, L. Surface tension is significant whenever inclusions are smaller than 100L. While Eshelby theory predicts that liquid inclusions generically reduce the stiffness of an elastic solid, our results show that liquid inclusions can actually stiffen a solid when R < 3L/2. Intriguingly, surface tension cloaks the far-field signature of liquid inclusions when R = 3L/2. These results are have far-reaching applications from measuring local stresses in biological tissue, to determining the failure strength of soft composites.

Graphical abstract: Surface tension and the mechanics of liquid inclusions in compliant solids

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Publication details

The article was received on 31 Oct 2014, accepted on 01 Dec 2014 and first published on 01 Dec 2014

Article type: Paper
DOI: 10.1039/C4SM02413C
Author version available: Download Author version (PDF)
Citation: Soft Matter, 2015,11, 672-679
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    Surface tension and the mechanics of liquid inclusions in compliant solids

    R. W. Style, J. S. Wettlaufer and E. R. Dufresne, Soft Matter, 2015, 11, 672
    DOI: 10.1039/C4SM02413C

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