Conduction in jammed systems of tetrahedra

Control of transport processes in composite microstructures is critical to the development of high performance functional materials for a variety of energy storage applications. The fundamental process of conduction and its control through the manipulation of granular composite attributes (e.g., grain shape) are the subject of this work. We show that athermally jammed packings of tetrahedra with ultra-short range order exhibit fundamentally different pathways for conduction than those in dense sphere packings. Highly resistive granular constrictions and few face-face contacts between grains result in short-range distortions from the mean temperature field. As a consequence, 'granular' or differential effective medium theory predicts the conductivity of this media within 10% at the jamming point; in contrast, strong enhancement of transport near interparticle contacts in packed-sphere composites results in conductivity divergence at the jamming onset. The results are expected to be particularly relevant to the development of nanomaterials, where nanoparticle building blocks can exhibit a variety of faceted shapes.Comment: 9 pages, 10 figure

Singular Behavior of Electric Field of High Contrast Concentrated Composites

A heterogeneous medium of constituents with vastly different mechanical properties, whose inhomogeneities are in close proximity to each other, is considered. The gradient of the solution to the corresponding problem exhibits singular behavior (blow up) with respect to the distance between inhomogeneities. This paper introduces a concise procedure for capturing the leading term of gradient's asymptotics precisely. This procedure is based on a thorough study of the system's energy. The developed methodology allows for straightforward generalization to heterogeneous media with a nonlinear constitutive description

Role of the synthesis route on the properties of hybrid LDH-graphene as basic catalysts

Layered double hydroxides (LDH or HT) or their derived mixed oxides present marked acid-base properties useful in catalysis, but they lead to agglomerate inducing a weak accessibility to the active sites. In this study we report the preparation and characterization of HT/Graphene (HT/rGO) nanocomposites as active and selective basic catalysts for the acetone condensation reaction. The graphene high specific surface area and structural compatibility with the HT allowed increasing the number and accessibility of the active sites and activity of this later. Two series of HT/rGO nanocomposites with 0.5 = HT/rGO = 10 mass ratio were prepared by: i) direct HT coprecipitation in the presence of GO; ii) self-assembly of preformed HT with GO. The prepared HT/rGO nanocomposites were dried either in air at 80 °C or freeze-dried. A series of characterizations showed the great influence of the preparation method and HT/rGO mass ratio on both the nanocomposite structure and catalytic activity. An optimum activity was observed for a HT/rGO = 10 catalyst. Particularly, the highest catalytic activity was found in those nanocomposites obtained by coprecipitation and freeze dried (3 times more active than bulk HT) which can be connected to their structure with a better accessibility to the basic sites.Postprint (author's final draft

Asymptotic expansions for high-contrast elliptic equations

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in \cite{ge09_1} where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high and low conductivity inclusions

The role of aggregates in the thermal stability of Mg-PSZ refractories for vacuum induction melting

Mg-PSZ refractories used as vacuum induction melting crucibles are particle-reinforced composites with aggregate and matrix phases comprising fused zirconia. Three commercial varieties were cycled eight times to service temperatures and their microstructural and thermomechanical evolution investigated, with focus placed on the aggregate populations. Two refractories, with large aggregates of similar size, were found to retain stiffness after cycling but in the refractory containing aggregates with high stabiliser levels, reaction between the stabiliser and Al and Si impurities produced secondary phases. Volume changes accompanying formation of these phases, and subsequent thermal expansion mismatches, led to aggregate break-up with consequent reductions in refractory toughness and strength. Secondary phases developed only rarely in the aggregates (with lower levels of stabiliser) of the second refractory. These aggregates remained intact and the refractory retained its toughness and strength. A third refractory contained small, unstabilised aggregates in a stabilised matrix and the strain mismatches that ensued during polymorphic transformation damaged microstructural interfaces. Refractory stiffness halved within eight cycles and toughness and strength were lost. All three refractories displayed R-curve behaviour and quasi-stable fracture curves were observed during bend tests. The study shows that when using fused zirconia aggregates to design refractories, engineers need to i) limit stabiliser concentrations - a difference of just ±1 wt% Mg (in the presence of impurity elements) may determine whether secondary phase formation occurs and ii) eliminate alumina and silica impurities when possible through substitution of zircon sand with baddeleyite as the source for fused zirconia.Open Acces

Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on a reduced basis approximation of the deformation gradient on the microscale. The setup phase is based upon a snapshot POD on deformation gradient fluctuations, in contrast to the widespread displacement-based approach. In order to reduce the computational offline costs, the space of relevant macroscopic stretch tensors is sampled efficiently by employing the Hencky strain. Numerical results show speed-up factors in the order of 5-100 and significantly improved robustness while retaining good accuracy. An open-source demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method.Comment: 28 page