Reciprocal relations, bounds, and size effects for composites with highly conducting interface

We provide a reciprocal relation linking the effective conductivity of a composite with highly conducting phase interfaces to that of a composite with the same phase geometry but with an electrical contact resistance at phase interfaces. A field relationship linking the electric field inside a composite with highly conducting phase interfaces to the current in a composite with contact resistance between phases is found. New size effects exhibited by isotropic particulate suspensions with highly conducting interface are obtained. The effective properties of periodic composites are shown to be monotonically increasing as the size of the period cell tends to zero. The role of surface energy for energy minimizing polydisperse suspensions of disks is examined; a necessary condition for isotropic polydisperse suspensions with minimal effective conductivity is found. For monodisperse suspensions of spheres, a critical radius is found for which the electric field is uniform throughout the composite

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

A versatile interface model for thermal conduction phenomena and its numerical implementation by XFEM

A general interface model is presented for thermal conduction and characterized by two jump relations. The first one expresses that the temperature jump across an interface is proportional to the interfacial average of the normal heat flux while the second one states that the normal heat flux jump is proportional to the surface Laplacian of the interfacial average of the temperature. By varying the two scalar proportionality parameters, not only the Kapitza resistance and highly conducting interface models can be retrieved but also all the intermediate cases can be covered. The general interface model is numerically implemented by constructing its weak form and by using the level-set method and XFEM. The resulting numerical procedure, whose accuracy and robustness are thoroughly tested and discussed with the help of a benchmark problem, is shown to be efficient for solving the problem of thermal conduction in particulate composites with various imperfect interfaces

A versatile interface model for thermal conduction phenomena and its numerical implementation by XFEM

International audienceA general interface model is presented for thermal conduction and characterized by two jump relations. The first one expresses that the temperature jump across an interface is proportional to the interfacial average of the normal heat flux while the second one states that the normal heat flux jump is proportional to the surface Laplacian of the interfacial average of the temperature. By varying the two scalar proportionality parameters, not only the Kapitza resistance and highly conducting interface models can be retrieved but also all the intermediate cases can be covered. The general interface model is numerically implemented by constructing its weak form and by using the level-set method and XFEM. The resulting numerical procedure, whose accuracy and robustness are thoroughly tested and discussed with the help of a benchmark problem, is shown to be efficient for solving the problem of thermal conduction in particulate composites with various imperfect interfaces

Dynamic Response of Tunable Phononic Crystals and New Homogenization Approaches in Magnetoactive Composites

This research investigates dynamic response of tunable periodic structures and homogenization methods in magnetoelastic composites (MECs). The research on tunable periodic structures is focused on the design, modeling and understanding of wave propagation phenomena and the dynamic response of smart phononic crystals. High amplitude wrinkle formation is employed to study a one-dimensional phononic crystal slab consists of a thin film bonded to a thick compliant substrate. Buckling induced surface instability generates a wrinkly structure triggered by a compressive strain. It is demonstrated that surface periodic pattern and the corresponding large deformation can control elastic wave propagation in the low thickness composite slab. Simulation results show that the periodic wrinkly structure can be used as a smart phononic crystal which can switch band diagrams of the structure in a transformative manner. A magnetoactive phononic crystal is proposed which its dynamic properties are controlled by combined effects of large deformations and an applied magnetic field. Finite deformations and magnetic induction influence phononic characteristics of the periodic structure through geometrical pattern transformation and material properties. A magnetoelastic energy function is proposed to develop constitutive laws considering large deformations and magnetic induction in the periodic structure. Analytical and finite element methods are utilized to compute dispersion relation and band structure of the phononic crystal for different cases of deformation and magnetic loadings. It is demonstrated that magnetic induction not only controls the band diagram of the structure but also has a strong effect on preferential directions of wave propagation. Moreover, a thermally controlled phononic crystal is designed using ligaments of bi-materials in the structure.Comment: PhD mechanical engineering, University of Nevada, Reno (2015