Surface tension and the mechanics of liquid inclusions in compliant solids.
Surface tension and the mechanics of liquid inclusions in compliant solids.
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DOI：
10.1039/c4sm02413c
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发表时间：
2014-09
期刊：
影响因子：
3.4
通讯作者：
Robert W. Style;J. Wettlaufer;E. Dufresne
中科院分区：
文献类型：
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作者：
Robert W. Style;J. Wettlaufer;E. Dufresne
埃谢尔比的夹杂物理论对材料和结构力学（包括复合材料、断裂和塑性理论）具有广泛影响。然而，它不包括表面应力的影响，最近已证明表面应力可以控制凝胶、弹性体和生物组织等软材料中的许多过程。为了将埃谢尔比的夹杂物理论扩展到软材料，我们考虑各向同性、可压缩、线弹性固体中的液体夹杂物。我们求解单个拉伸夹杂物周围的位移和应力场，考虑固体的体积弹性和固液界面的表面张力（即与应变无关的各向同性表面应力）。表面张力显着改变夹杂物的形状和刚度及其近场和远场应力场。这些现象很大程度上取决于夹杂物半径 R 与弹性毛细管长度 L 的比率。只要夹杂物小于 100L，表面张力就很重要。虽然 Eshelby 理论预测液体夹杂物通常会降低弹性固体的刚度，但我们的结果表明，当 R<3L/2 时，液体夹杂物实际上可以使固体变硬。有趣的是，当 R=3L/2 时，表面张力掩盖了液体包裹体的远场特征。这些结果具有深远的应用，从测量生物组织中的局部应力到确定软复合材料的失效强度。
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.