Homogenization of some variational problems connected to the theory of lubrication

An important problem in the theory of lubrication is to model and analyze the effects of surface roughness on the hydrodynamic performance. An efficient method to do this is homogenization. In this paper we prove a general homogenization result which allows us to consider unstationary variational problems, related to Reynolds type equations, where the lubricant may be Newtonian or non-Newtonian. Recently, the idea of finding upper and lower bounds on the effective behavior, obtained by homogenization, was applied for the first time in tribology. The homogenization result in this work may therefore also serve as a rigorous starting point for developing these successful results to unstationary problems.     

Prediction of fragment size and ejection distance of masonry wall under blast load using homogenized masonry material properties

The fragment hazard resulting from a nearby explosion is a major concern in the design of structures which may be subjected to blast loads. This paper presents a predictive method based on the theories of continuum damage mechanics and mechanics of micro-crack development, and numerical simulation to determine the probabilistic fragment size distribution and the launch distances. Theoretical derivations are presented to calculate fragment distribution. The fragmentation process is modeled according to the crack initiation and propagation, which depend on the material damage levels and are estimated using continuum damage mechanics theory. The proposed method involves two steps. First a finite element model is developed to estimate the material damage, fragment distribution and the ejection velocity. Then a simple algorithm is used to predict the fragment trajectory and the launch distance based on the fragment size and the ejection velocity. A masonry wall is used as an example in this study. The wall is modeled with both the distinctive consideration of the brick and mortar material properties and the homogenized masonry material properties. The reliability and efficiency of using the homogenized masonry material model in predicting the masonry wall damage and fragmentation are proven. The program AUTODYN is used in this study to conduct the numerical simulations with the proposed models linked to it as user subroutines. The numerical results indicate that the masonry fragments approximately follow the Weibull distribution, which is consistent with some empirical fragment distributions. The proposed method avoids using erosion technique, which inevitably results in a loss of fragment mass, and avoids discretizing the structure into particles or predefining the failure planes, which may lead to unrealistic prediction of damage propagation and evolution and therefore inaccurate fragmentation process and fragment size distributions.     

Statistical Characterization of Complex Random Media in Random Fields

The statistical macroscopic characterization of composite materials in simple and complex electromagnetic environments is addressed. Based on the central limit theorem applied to the random parameters that characterize the microscopic constituents, the probability density function, mean, uncertainty and confidence intervals of various macroscopic effective constitutive material and wave parameters are derived. The implications ofthe randomness of the external field on these parameters are also investigated.     

Homogenization of Carbides in Ni60/WC Composite Coatings Made by Fiber Laser Remelting

In the current study, the effect of laser remelting on homogenization of carbides in WC-reinforced Ni60 composite coatings was investigated. Ni60 + 50 wt% WC composite coatings were fabricated on the surface of Q550 steel by LDF4000-100 fiber laser device. First cladding layer was made by rectangle laser spot and then circular laser spot was utilized to remelt the coatings. Microstructure characteristics were investigated by optical microscope and scanning electron microscopy. Elemental distribution and phase constitution were analyzed by energy disperse spectroscopy and X-ray diffraction. The results showed that accumulation of residual WC particles was sufficiently eliminated under the effect of laser remelting. The irregularly shaped carbides in first cladding layer were transformed into well-distributed polygonal carbides by laser remelting. Statistical analysis indicated median size of reinforcement particles decreased from 35.40 to 5.62 µm. Microhardness of remelted region had a smooth profile and decreased by ?50 HV_0.1 than that of first cladding region. Homogenization of carbides in nickel composite coating was well realized by laser remelting.     

Improved rheological properties and shelf-life of wheat starch-lipid complex produced by the homogenization process

Physical homogenization was applied to the production of a starch-lipid complex formed through a hydrophobic interaction between amylose and fatty acid molecules. In addition, vegetable oils as a source of fatty acids and wheat starch as a source of amylose molecules were used to produce the starch-lipid complex. The complex index was significantly (p < 0.05) increased through the homogenization, leading to the release of the amylose molecules from the starch granules and a high dispersibility of the fatty acids. In particular, the viscosity characteristics clearly demonstrated a dramatic improvement in the structural stability and retrogradation behavior as a result of the homogenization treatment. Vegetable oils with homogenization can be utilized to produce the starch-lipid complex as a food ingredient with an extended shelf-life and the improved rheological properties.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10068-021-00889-w.     

Homogenization kinetics of a cast Ti48A12W0.5Si alloy

The homogenization kinetics of a cast Ti48A12W0.5Si alloy with a duplex microstructure was studied in terms of γ-phase dissolution and -grain growth. It was found that the measured volume fraction of remnant γ grains can be well simulated by a model of interface-controlled dissolution in a dislocation mechanism, instead of a diffusion-controlled one. The activation energy for the /γ interface reaction was found to be Q_int = 476 kJ mol⁻¹, which is much higher than the interdiffusion activation energy in TiAl alloy. The grain growth of phase during homogenization can be categorized into three stages. During the first stage, where the volume fraction of remnant γ grains is higher than about 10%, the growth of grains follows the parabolic law D = k₁t^0.2, and the activation energy for grain growth was calculated to be Q₁ = 442 kJ mol⁻¹, very close to the Q_int for /γ interface reaction. In the second stage, where few fine γ grains (1–10 vol.%) remained, a dramatic grain growth occurs. During the final stage, as the single phase is obtained, the coarsening of grains again satisfies the grain growth law D = k₃t^0.4, with the grain growth activation energy Q₃ of 147 kJ mol⁻¹, lower than the reported interdiffusion energy of γ phase.     

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.     

均匀化理论在多孔板结构优化中的应用研究

多尺度均匀化理论自从上世纪 70年代产生以来 ,就被认为是确定复合材料当量性能的一种不可替代的方法。本文将多尺度均匀化方法应用于基于有限元分析的多孔板结构优化设计中 ,简述了求解当量板有效弹性常数的均匀化理论 ,在此基础上 ,建立了基于有限元分析的多孔板结构优化流程 ,编写了FORTRAN程序 ,并将其与AN SYS软件相连接 ,完成了一个多孔板结构的优化设计 ,所得结果表明 ,它能够满足工程应用的需要 ,并为多孔板结构设计提供了一种新思路     

Trefftz approximations in complex media: Accuracy and applications

Approximations by Trefftz functions are rapidly gaining popularity in the numerical solution of boundary value problems of mathematical physics. By definition, these functions satisfy locally, in weak form, the underlying differential equations of the problem, which often results in high-order or even exponential accuracy with respect to the size of the basis set. We highlight two separate examples in applied electromagnetics and photonics: (i) homogenization of periodic structures, and (ii) numerical simulation of electromagnetic waves in slab geometries. Extensive numerical evidence and theoretical considerations show that Trefftz approximations can be applied much more broadly than is traditionally done: they are effective not only in physically homogeneous regions but also in complex inhomogeneous ones. Two mechanisms underlying the high accuracy of Trefftz approximations in such complex cases are pointed out. The first one is related to trigonometric interpolation and the second one – somewhat surprisingly – to well-posedness of random matrices.