On the shape of effective inclusion in the Maxwell homogenization scheme for anisotropic elastic composites

The paper focuses on the main uncertainty involved in classical Maxwell’s (1873) homogenization method for elastic composites. Maxwell’s scheme that equates the far fields produced by a set of inhomogeneities and by a fictitious domain with unknown effective properties (“effective inclusion”) is re-written in terms of the compliance and stiffness contribution tensors. It is shown that the shape of the effective inclusion substantially affects the overall elastic properties. The choice of this shape in the case of anisotropic composite is a non-trivial problem that has never been discussed in literature. In this paper, we show that the problem appears due to incompleteness of the Maxwell scheme and show that the problem can be realized when the effective inclusion is of ellipsoidal shape. We discuss how the aspect ratios of the ellipsoid have to be chosen and illustrates the approach by two examples – material with cracks having orientation scatter and a three-phase transversely-isotropic composite. It is also shown that tensor of the effective elastic constants calculated in the framework of Maxwell’s scheme is always symmetric with respect to couples of indices.     

Effect of soy protein subunit composition and processing conditions on stability and particle size distribution of soymilk

The influence of soy protein subunit composition on the particle size distribution and solid content of soymilk and various supernatant fractions was investigated. A well-established seed variety (Harovinton), containing all protein subunits, and eleven null soybean genotypes lacking specific glycinin and β-conglycinin subunits were investigated, to determine the effect of protein composition on the physico-chemical characteristic of soymilk. Soymilk made from Harovinton and soybean lines null in glycinin showed significantly higher total solid yields than the other genotypes evaluated. Soymilks prepared from soybeans null for glycinin or lacking glycinin's group I (A₁, A₂) showed a smaller particle size distribution compared to soybean lines containing glycinin. In general, unheated soymilk made from lines having glycinin showed a bimodal size distribution with large particles, with a decrease in the particle size distribution after heating and heating with homogenization. The results of this work will help in the evaluation of breeding lines with a specific protein composition tailored to a specific processing functionality.     

An application of a homogenization method to the estimation of effective thermal conductivity of a hydrogen storage alloy bed considering variation of contact conditions between alloy particles

A homogenization method is applied to the estimation of effective thermal conductivity of a hydrogen storage alloy bed. By including the contact conditions between the alloy particles, the effect of contact conditions on the thermal conductivity is investigated.     

Effect of homogenization treatment on the fracture behaviour of silicon nitride/graphene nanoplatelets composites

Si₃N₄ based composites with 7 wt.% of graphene nanoplatelets (GNPs) were prepared using different homogenization methods. Si₃N₄/GNPs powder mixtures were dispersed in isopropanol and homogenized by attritor milling, ball milling or planetary ball milling. The ball milling technique was also used for the homogenization of Si₃N₄/GNPs mixture in dry state. Fractography analysis was carried out in order to assess the individual homogenization treatment. Depending on the homogenization methods, the size of the processing flaws varied from 20 μm up to 400 μm. The agglomeration of the GNPs and the residual porosity were found as the most frequently observed types of the critical flaws. The planetary ball milling with previous ultrasonication of GNPs in isopropanol was found to be the most promising homogenization technique, resulting in the composites with the highest bending strength (average value is 740 MPa) and the lowest average size of the processing flaws (around 20 μm).     

高速匀浆法提取辣蓼茎中总黄酮

以辣蓼茎为原料,对匀浆法提取辣蓼茎中总黄酮工艺进行了研究,确定了最优工艺参数:提取1次,提取时间2 min,60%的乙醇溶剂,转速为20 000 r/min,料液比为1∶25 g/m L。在最佳条件下,提取并测定了辣蓼茎中总黄酮含量,结果表明,黄酮提取率为4.75%。     

Methodology for nanoindentation-assisted prediction of macroscale elastic properties of high performance cementitious composites

This paper describes a methodology applied for determination of macroscale elastic properties of high performance cementitious composites (HPCC) based on nanoindentation measurements. For that, the elastic properties of HPCC mixtures with quartz filler and fly ash were evaluated at different length scales by nanoindentation (microscale) and the static and dynamic elastic moduli and compressive strength tests (macroscale). The nanoindentation results, obtained from a representative microlevel area by grid indentation with subsequent phase deconvolution, were complemented by an independent porosimetry test and inserted into a two-step analytical homogenization scheme to predict the overall macroscale properties. The final results indicate that the presented methodology allows a reliable advanced prediction of HPCC elastic properties, which is promising for the concrete industry since it would allow for reducing the number of large scale experiments and producing of a more predictable composite in an easier and experimentally less expensive way.     

Microstructural design of connective base cells for functionally graded materials

Control of compositions and microstructures plays a significant role on developing functionally graded material (FGM). The existing fabrication technologies allow placing multiple compositions in such a way that a desirable gradient of effective physical properties can be achieved. It is interesting to explore how to design microstructure for the same purpose. This paper introduces an inverse homogenization procedure to FGM design. A quasi-periodic base cell (PBC) is optimized for attaining a specific gradient of Young's modulus. To ensure proper connectivity between adjacent PBCs, heat sinks originally used in thermal conduction problem are employed as connection constraints. The capability of this technique is demonstrated by the examples of FGM microstructural design.     

Stability Problems in Soil‐Structure Interfaces: Experimental Observations and Numerical Study

This article presents experimental results of tests on soil‐structure interfaces carried out on a new “ring simple shear” apparatus specially developed at Ecole Nationale des Ponts and Chaussées, Paris, for such studies. In this apparatus strain localization takes place at or near the surface of the rotating steel drum that forms the soil‐structure interface. Depending on the conditions of tests, in terms of surface roughness, special instrumentation is capable of recording local as well as global response. Three tests on Hostun gravel at different confining radial pressures have been conducted and a deviatoric hardening model with nonassociated flow rule has been adopted for their numerical simulations. The point of inception of strain localization based on various theoretical considerations has been discussed and experimentally verified. The post‐peak behavior is simulated by employing a homogenization technique in which the soil sample is treated as a composite material consisting of a shear band surrounded by intact material. A deviatoric strain softening model has been adopted for the shear band. It is shown that the mechanism of failure and the response of the soil sample is reasonably well simulated. Although there are some concerns regarding the homogeneity of the sample, the post‐peak stage and the overall mechanical response of gravel‐steel interface are rather well reproduced.     

Tailoring materials with prescribed elastic properties

This paper describes a method to design the periodic microstructure of a material to obtain prescribed constitutive properties. The microstructure is modelled as a truss or thin frame structure in 2 and 3 dimensions. The problem of finding the simplest possible microstructure with the prescribed elastic properties can be called an inverse homogenization problem, and is formulated as an optimization problem of finding a microstructure with the lowest possible weight which fulfils the specified behavioral requirements. A full ground structure known from topology optimization of trusses is used as starting guess for the optimization algorithm. This implies that the optimal microstructure of a base cell is found from a truss or frame structure with 120 possible members in the 2-dimensional case and 2016 possible members in the 3-dimensional case. The material parameters are found by a numerical homogenization method, using Finite-Elements to model the representative base cell, and the optimization problem is solved by an optimality criteria method.

Numerical examples in two and three dimensions show that it is possible to design materials with many different properties using base cells modelled as truss or frame works. Hereunder is shown that it is possible to tailor extreme materials, such as isotropic materials with Poisson's ratio close to − 1, 0 and 0.5, by the proposed method. Some of the proposed materials have been tested as macro models which demonstrate the expected behaviour.