We introduce new bounds and variational principles for the effective elasticity of anisotropic two-phase composites with imperfect bonding conditions between phases. The monotonicity of the bounds in the geometric parameters is used to predict new size effect phenomena for monodisperse and polydisperse suspensions of spheres. For isotropic elastic spheres in a more compliant isotropic matrix we exhibit critical radii for which the stress state, external to the spheres, is unaffected by their presence. Physically all size effects presented here are due to the increase in surface to volume ratio, as the sizes of the inclusions decrease. The scale at which these effects occur is determined by the parameters [Formula: see text] and [Formula: see text]. These parameters measure the relative importance of interfacial compliance and phase compliance mismatch.
In this paper, we derive the Navier slip boundary condition for flows over a rough surface, by combining homogenization methods and boundary layer techniques. The Navier slip condition is derived as the effective boundary condition, in the limit as the roughness becomes small; it is the first order corrector to the no-slip condition on the limiting smooth surface. Using this method, we are simultaneously able to provide a formula for computing the slip length for various geometries. The paper provides a theoretical justification for the observed slip in micro- or nanofluidics, as well as a computational tool. Computations done using FreeFem++ agree with experimental data.
If a neutral inclusion is inserted in a matrix containing a uniform applied electric field, it does not disturb the field outside the inclusion. The well known Hashin coated sphere is an example of a neutral coated inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated spheres and the two-dimensional analogous problem of assemblages of coated disks.
We provide new bounds on the interfacial barrier conductivity for isotropic particulate composites based on measured values of effective properties, known values of component volume fractions, and the formation factor for the matrix phase. These bounds are found to be sharp. Our tool is a new set of variational principles and bounds on the effective properties of composites with imperfect interface obtained by us ͓see R. Lipton and B. Vernescu, Proc. R. Soc. London Ser. A 452, 329 ͑1996͔͒. We apply the bounds to solve inverse problems. For isotropic polydisperse suspensions of spheres we are able to characterize the size distribution of the spherical inclusions based on measured values of the effective conductivity.
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