Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites—i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori–Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R, to an elastocapillary lengthscale, L. Interfacial tension substantially impacts the effective elastic moduli of the composite when . When R<3L/2 (R=3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.
- Received December 18, 2015.
- Accepted April 8, 2016.
- © 2016 The Author(s)
Published by the Royal Society. All rights reserved.