Novel connections and physical implications of thermal metamaterials with imperfect interfaces

Thermal metamaterials are of great importance in advanced energy control and management. Previous studies mainly focused on interfaces with perfect bonding conditions. In principle, imperfectness always exists across interface and the effect is intriguingly important with small-length scales. This work reports the imperfect interface effect in thermal metamaterials thoroughly. Low conductivity- and high conductivity-type interfaces are considered. We show that an object can always be made thermally invisible, with the effect of imperfect interface, as that of a homogeneous background material. This unprecedented condition is derived in an exact and analytic form, systematically structured, with much versatile and physical implications. Conditions for thermal shielding and enhancements are analytically found and numerically exemplified, highlighting the specific role of material and geometric parameters. We find that both types of interfaces are complementing with each other which, all together, will constitute a full spectrum to achieve the thermal invisibility. The analytic finding offers a general perception that adds to the understanding of heat transport mechanism across interfaces in thermal metamaterials, in ways that drastically distinct from that of ideal interfaces. This finding opens up new possibilities for the control and management of thermal metamaterials with imperfect bonding interfaces.

Interface Models in Coupled Thermoelasticity

This work proposes new interface conditions between the layers of a three-dimensional composite structure in the framework of coupled thermoelasticity. More precisely, the mechanical behavior of two linear isotropic thermoelastic solids, bonded together by a thin layer, constituted of a linear isotropic thermoelastic material, is studied by means of an asymptotic analysis. After defining a small parameter ε, which tends to zero, associated with the thickness and constitutive coefficients of the intermediate layer, two different limit models and their associated limit problems, the so-called soft and hard thermoelastic interface models, are characterized. The asymptotic expansion method is reviewed by taking into account the effect of higher-order terms and defining a generalized thermoelastic interface law which comprises the above aforementioned models, as presented previously. A numerical example is presented to show the efficiency of the proposed methodology, based on a finite element approach developed previously.

Maxwell's methodology of estimating effective properties: Alive and well

This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective one; this yields closed-form formula for the effective conductivity. Our review focuses on subsequent developments of Maxwell's idea in various applications and on its range of applicability. The conclusion is that, 145 years later, the methodology is still alive and well.

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

Importance of interfaces in governing thermal transport in composite materials: modeling and experimental perspectives

Thermal management in polymeric composite materials has become increasingly critical in the air-vehicle industry because of the increasing thermal load in small-scale composite devices extensively used in electronics and aerospace systems. The thermal transport phenomenon in these small-scale heterogeneous systems is essentially controlled by the interface thermal resistance because of the large surface-to-volume ratio. In this review article, several modeling strategies are discussed for different length scales, complemented by our experimental efforts to tailor the thermal transport properties of polymeric composite materials. Progress in the molecular modeling of thermal transport in thermosets is reviewed along with a discussion on the interface thermal resistance between functionalized carbon nanotube and epoxy resin systems. For the thermal transport in fiber-reinforced composites, various micromechanics-based analytical and numerical modeling schemes are reviewed in predicting the transverse thermal conductivity. Numerical schemes used to realize and scale the interface thermal resistance and the finite mean free path of the energy carrier in the mesoscale are discussed in the frame of the lattice Boltzmann-Peierls-Callaway equation. Finally, guided by modeling, complementary experimental efforts are discussed for exfoliated graphite and vertically aligned nanotubes based composites toward improving their effective thermal conductivity by tailoring interface thermal resistance.

An O ( h N ) interface model of a three-dimensional curved interphase in conduction phenomena

A thin isotropic three-dimensional curved interphase of thickness h between two isotropic media is considered in the setting of thermal conduction. This interphase is modelled by a surface between the two neighbouring media, and appropriate interface conditions on it are derived for the temperature and normal heat flux fields. The derivation makes use of Taylor expansions for the fields and is correct to O ( h N ), where h denotes the thickness of the interphase. The jumps for the temperature and normal heat flux in the interface model are given in terms of a hierarchy of surface differential forms, which depend on the conductivities of the interphase and surrounding media, and involve surface derivatives of the temperature and normal heat flux along the interface. The analysis is directly transferable to the analogous physical phenomena of electrical conduction, dielectrics, magnetism, diffusion, flow in porous media and anti-plane elasticity.