Closed-form evaluation of 2D static lattice sums

In the present paper, employing properties of the complete elliptic integrals of the first and second kind, we deduce closed-form formulae for the lattice sums and other new formulae. Applications to the effective properties of regular and random composites are discussed. We also discuss the Eisenstein summation method and the Rayleigh method used in computations

Effective properties of composites with periodic random packing of ellipsoids

The aim of this paper is to evaluate the effective properties of composite materials with periodic random packing of ellipsoids of different volume fractions and aspect ratios. Therefore, we employ computational homogenization. A very efficient MD-based method is applied to generate the periodic random packing of the ellipsoids. The method is applicable even for extremely high volume fractions up to 60%. The influences of the volume fraction and aspect ratio on the effective properties of the composite materials are studied in several numerical examples.NSFC/51474157National Basic Research Program of China/973Shanghai Qimingxing Program/16QA1404000State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology Key/SKLGDUEK152

Structure-property correlations in model composite materials

We investigate the effective properties (conductivity, diffusivity and elastic moduli) of model random composite media derived from Gaussian random fields and overlapping hollow spheres. The morphologies generated in the models exhibit low percolation thresholds and give a realistic representation of the complex microstructure observed in many classes of composites. The statistical correlation functions of the models are derived and used to evaluate rigorous bounds on each property. Simulation of the effective conductivity is used to demonstrate the applicability of the bounds. The key morphological features which effect composite properties are discussed

Three-point bounds and other estimates for strongly nonlinear composites

A variational procedure due to Ponte Castañeda et al. [Phys. Rev. B 46, 4387 (1992)] is used to determine three-point bounds and other types of estimates for the effective response of strongly nonlinear composites with random microstructures. The variational procedure makes use of estimates for the effective properties of linear comparison composites to generate corresponding estimates for nonlinear composites. Several equivalent forms of the variational procedure are derived. In particular, it is shown that the mean-field theory of Wan et al. [Phys. Rev. B 54, 3946 (1996)], which also makes use of a linear comparison composite, together with a certain decoupling approximation, leads to results that are precisely identical to those that can be obtained from the earlier variational procedure. Finally, three-point bounds and other estimates are computed for power-law composites with cell-type microstructures, and the results are compared with random resistor network simulations available from the literature

Elasticity of Random Multiphase Materials: Percolation of the Stiffness Tensor

Topology and percolation effects play an important role in heterogeneous materials, but have rarely been studied for higher-order tensor properties. We explore the effective elastic properties of random multiphase materials using a combination of continuum computational simulations and analytical theories. The effective shear and bulk moduli of a class of symmetric-cell random composites with high phase contrasts are determined, and reveal shortcomings of classical homogenization theories in predicting elastic properties of percolating systems. The effective shear modulus exhibits typical percolation behavior, but with its percolation threshold shifting with the contrast in phase bulk moduli. On the contrary, the effective bulk modulus does not exhibit intrinsic percolation but does show an apparent or extrinsic percolation transition due to cross effects between shear and bulk moduli. We also propose an empirical approach for bridging percolation and homogenization theories and predicting the effective shear and bulk moduli in a manner consistent with the simulations.National Science Foundation (U.S.) (Contract CMMI-1332789)National Science Foundation (U.S.) (Contract DMR-0346848

The causal differential scattering approach to calculating the effective properties of random composite materials with a particle size distribution

An implementation of the Causal Differential Method (CDM) for modelling the effective properties of a random two-phase composite material is presented. Such materials are commonly used as ultrasonic transducer matching layersor backing layers. The method is extended to incorporate a particle size distribution in the inclusion phase. Numerical issues regarding the implementation and convergence of the method are discussed. It is found that, for a given frequency of excitation, the calculated velocity for the composite has a distribution whose variance increases as the volume fraction of inclusions increases. The model predictions would suggest that to reliably and repeatedly manufacture these composites, with a desired mechanical impedance, a low volume fraction of inclusions should be used

Study of the Effective Thermal Conductivity of Polymer Composites with Varying Filler Arrangements

Alternative thermal management solutions for electronic devices are being widely explored due to the increasing heat concentration that results from shrinking sizes and increasing power of modern electronics. Clearly, there is a need to spread the heat effectively in these systems, and polymer composites can potentially provide high thermal conductivity at low filler fraction while maintaining desirable mechanical properties for electronic packaging. The present study aims to investigate the effective thermal conductivity of various copper filler arrangements in a polymer matrix. The polymer composites are fabricated using laser cut acrylic templates to embed aligned copper rods in epoxy and create different configurations, from ordered to random arrangements, while maintaining a constant volume fraction. Heat conduction through the cross-section of the composites is studied using an infrared (IR) camera that enables 2D mapping of temperatures. The effective thermal conductivity of the composites is obtained using a simplified 1-D reference-bar type technique. The experimentally obtained effective thermal conductivity is validated using both simulation software and relationships from the effective medium theory. The resulting effective thermal conductivity of the different configurations are compared to obtain an optimum filler configuration. Furthermore, the experimental and simulation results help provide an understanding of the effect percolation networks have on the effective thermal behavior of composite materials. Such polymer composites, with enhanced conductive properties, can be implemented in electronic packaging as an alternative to conventional heat dissipation methods (i.e. mechanical fans, heat sinks, fins, etc.)

Numerical Evaluation of the Effective Elastic Properties of 2D Overlapping Random Fibre Composites

We present a numerical investigation of the elastic coefficients of random fibre composites with high contrast of properties. Here we consider a numerical study based on the generation of representative volume elements (RVEs) with overlapping random fibre network. Such a concept requires an important Monte-Carlo draw of patterns as well as an accurate determination of RVE size. In this paper, this latter is done by estimating the evolution of the standard deviation according to the number of realizations for given values of RVE size. We consider the use of an appropriate model for an automatic, reliable and fast generation of RVEs : the model with an n-order approximate geometry that allows the construction of complex overlapping fibre network. It is well-established that the morphology of the microstructure greatly affects the mechanical response of such kind material. Some morphological features, namely orientation, aspect ratio and dispersion are investigated by considering them as random variables in the design of RVEs. The results are subsequently linked to the percolation phenomenon that occurs when fibres overlap and form some pathways inside the soft phase. This phenomenon influences effective properties of heterogeneous media, particularly in the case of a high contrast of properties