Stiffening solids with liquid inclusions

From bone and wood to concrete and carbon fibre, composites are ubiquitous natural and synthetic materials. Eshelbyâ €™ s inclusion theory describes how macroscopic stress fields couple to isolated microscopic inclusions, allowing prediction of a compositeâ €™ s bulk mechanical properties from a knowledge of its microstructure. It has been extended to describe a wide variety of phenomena from solid fracture to cell adhesion. Here, we show experimentally and theoretically that Eshelbyâ €™ s theory breaks down for small liquid inclusions in a soft solid. In this limit, an isolated dropletâ €™ s deformation is strongly size-dependent, with the smallest droplets mimicking the behaviour of solid inclusions. Furthermore, in opposition to the predictions of conventional composite theory, we find that finite concentrations of small liquid inclusions enhance the stiffness of soft solids. A straightforward extension of Eshelbyâ €™ s theory, accounting for the surface tension of the solid-liquid interface, explains our experimental observations. The counterintuitive stiffening of solids by fluid inclusions is expected whenever inclusion radii are smaller than an elastocapillary length, given by the ratio of the surface tension to Youngâ €™ s modulus of the solid matrix. These results suggest that surface tension can be a simple and effective mechanism to cloak the far-field elastic signature of inclusions.

Duke Scholars

Author Henry Foote