Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids.
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 [Formula: see text]. WhenR<3L/2 (R=3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.
Nordic Institute for Theoretical Physics (NORDITA) , 10691 Stockholm, Sweden.
Francesco
F
Mancarella
Mathematical Institute, University of Oxford , Oxford OX2 6GG, UK.
Robert W
RW
Style
Nordic Institute for Theoretical Physics (NORDITA), 10691 Stockholm, Sweden; Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK; Yale University, New Haven, CT 06520, USA.
John S
0000-0002-1676-9645
JS
Wettlaufer
elastic moduli; soft composites; surface tension