The effective shear modulus of a random isotropic suspension of monodisperse liquid -spheres: from the dilute limit to the percolation threshold.

A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid -spherical inclusions ( = 2, 3), each having identical initial radius , in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension . For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus in terms of the shear modulus of the elastomer, the initial elasto-capillary number eCa = /2, the volume fraction of inclusions, and the space dimension .

Critical curvature localization in graphene. II. Non-local flexoelectricity-dielectricity coupling.

As a sequel of part I (Kothari 2018 , 20180054), we present a general thermodynamic framework of flexoelectric constitutive laws for multi-layered graphene (MLG), and apply these laws to explain the role of crinkles in peculiar molecular adsorption characteristics of highly oriented pyrolytic graphite (HOPG) surfaces. The thermodynamically consistent constitutive laws lead to a non-local interaction model of polarization induced by electromechanical deformation with flexoelectricity-dielectricity coupling. The non-local model predicts curvature and polarization localization along crinkle valleys and ridges very close to those calculated by density functional theory (DFT).