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Surface tension and the mechanics of liquid inclusions in compliant solids
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, United States; University of Oxford, United Kingdom .
2015 (English)In: Soft Matter, ISSN 1744-683X, Vol. 11, no 4, 672-679 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 11, no 4, 672-679 p.
Keyword [en]
Elastic waves, Phase interfaces, Stiffness, Stresses, Surface properties, Surface tension, Tissue, Biological tissues, Bulk elasticity, Displacement and stress fields, Failure strength, Far-field stress, Liquid inclusion, Mechanics of materials and structures, Solid-liquid interfaces
National Category
Materials Engineering
URN: urn:nbn:se:kth:diva-159367DOI: 10.1039/c4sm02413cISI: 000346911900005ScopusID: 2-s2.0-84919933475OAI: diva2:784722
Swedish Research Council

QC 20150130

Available from: 2015-01-30 Created: 2015-01-29 Last updated: 2015-01-30Bibliographically approved

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Wettlaufer, John S.
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