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In the dilute limit Eshelby's inclusion theory captures the behavior of awide range of systems and properties. However, because Eshelby's approachneglects interfacial stress, it breaks down in soft materials as the inclusionsize approaches the elastocapillarity length $L$. Here, we use a three-phasegeneralized self-consistent method to calculate the elastic moduli ofcomposites comprised of an isotropic, linear-elastic compliant solid hosting aspatially random monodisperse distribution of spherical liquid droplets. Asopposed to similar approaches, we explicitly capture the liquid-solidinterfacial stress when it is treated as an isotropic, strain-independentsurface tension. Within this framework, the composite stiffness depends solelyon the ratio of the elastocapillarity length $L$ to the inclusion radius $R$.Independent of inclusion volume fraction, we find that the composite isstiffened by the inclusions whenever $R < 3L/2$. Over the same range ofparameters, we compare our results with alternative approaches (dilute andMori-Tanaka theories that include surface tension). Our framework can be easilyextended to calculate the composite properties of more general soft materialswhere surface tension plays a role.

Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids