Christensen RM

Coussy O

MacMinn CW

Wang HF


            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
            
              
                R
                
                  /
                
                L
                ≲
                100
              
            
            . When
            R
            &lt;3
            L
            /2 (
            R
            =3
            L
            /2) liquid inclusions stiffen (cloak the far-field signature of) the solid.
          </jats:p

Francesco Mancarella

Robert W. Style

John S. Wettlaufer

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Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Surface tension and the Mori–Tanaka theory of non-dilute soft composite solids

Surface tension and the Mori–Tanaka theory of non-dilute soft composite solids

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