Zeitschriftenartikel: „Homogenization structure“

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Krejčí, Tomáš, Aleš Jíra, Luboš Řehounek, Michal Šejnoha, Jaroslav Kruis und Tomáš Koudelka. „Homogenization of trabecular structures“. MATEC Web of Conferences 310 (2020): 00041. http://dx.doi.org/10.1051/matecconf/202031000041.

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Numerical modeling of implants and specimens made from trabecular structures can be difficult and time-consuming. Trabecular structures are characterized as spatial truss structures composed of beams. A detailed discretization using the finite element method usually leads to a large number of degrees of freedom. It is attributed to the effort of creating a very fine mesh to capture the geometry of beams of the structure as accurately as possible. This contribution presents a numerical homogenization as one of the possible methods of trabecular structures modeling. The proposed approach is based on a multi-scale analysis, where the whole specimen is assumed to be homogeneous at a macro-level with assigned effective properties derived from an independent homogenization problem at a meso-level. Therein, the trabecular structure is seen as a porous or two-component medium with the metal structure and voids filled with the air or bone tissue at the meso-level. This corresponds to a two-level finite element homogenization scheme. The specimen is discretized by a reasonable coarse mesh at the macro-level, called the macro-scale problem, while the actual microstructure represented by a periodic unit cell is discretized with sufficient accuracy, called the meso-scale problem. Such a procedure was already applied to modeling of composite materials or masonry structures. The application of this multi-scale analysis is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.

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Chen, Wei, Pi Zhi Zhao, Yu Li Zhou und Yan Feng Pan. „Effects of Homogenization Conditions on the Microstructures of Twin-Roll Cast Foil Stock of AA8021 Aluminum Alloy“. Materials Science Forum 877 (November 2016): 296–302. http://dx.doi.org/10.4028/www.scientific.net/msf.877.296.

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AA8021 aluminum alloy twin-roll cast strips with 7mm gauge were rolled to 3.8mm gauge sheets and given homogenization, further rolled into 0.55mm gauge foil stocks with intermediate annealing. This paper investigated the influence of homogenization conditions on microstructures of foil stocks in detail. The results show that, for the foil stock made from the sheet without homogenization, the grain structure is partially recrystallized. While the grain structure of foil stock made from the sheet with medium temperature homogenization is fully recrystallized, but it is coarse near sheet surface. However, foil stock made from the sheet with high temperature homogenization has fine and uniform recrystallized grain structures. The differences of grain structures among these three kinds of foil stocks can be understood by the variation in solid solution content of Fe, Si, Mn and distribution of intermetallic compounds. The optimized homogenization condition was adopted by our plant to produce foil stock, and its grain structure was fine and uniform. The surface quality of final aluminum foil rolled from the foil stock could meet high grade requirements of customers.

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BRAIDES, ANDREA, und DAG LUKKASSEN. „REITERATED HOMOGENIZATION OF INTEGRAL FUNCTIONALS“. Mathematical Models and Methods in Applied Sciences 10, Nr. 01 (Februar 2000): 47–71. http://dx.doi.org/10.1142/s0218202500000057.

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We consider the homogenization of sequences of integral functionals defined on media with several length-scales. Our general results connected to the corresponding homogenized functional are used to analyze new types of structures and to illustrate the wide range of effective properties achievable through reiteration. In particular, we consider a two-phase structure which is optimal when the integrand is a quadratic form and point out examples where the macroscopic behavior of this structure underlines an effective energy density which is lower than that of the best possible multirank laminate. We also present some results connected to a reiterated structure where the effective property is extremely sensitive of the growth of the integrand.

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Aftandiliants, Ye G. „Modelling of structure forming in structural steels“. Naukovij žurnal «Tehnìka ta energetika» 11, Nr. 4 (10.09.2020): 13–22. http://dx.doi.org/10.31548/machenergy2020.04.013.

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The study showed that the influence of alloying elements on the secondary structure formation of the steels containing from 0.19 to 0.37 wt. % carbon; 0.82-1.82 silicon; 0.63-3.03 manganese; 1.01-3.09 chromium; 0.005-0.031 nitrogen; up to 0.25 wt.% vanadium and austenite grain size is determined by their change in the content of vanadium nitride phase in austenite, its alloying and overheating above tac3, and the dispersion of ferrite-pearlite, martensitic and bainitic structures is determined by austenite grain size and thermal kinetic parameters of phase transformations. Analytical dependencies are defined that describe the experimental data with a probability of 95% and an error of 10% to 18%. An analysis results of studying the structure formation of structural steel during tempering after quenching show that the dispersion and uniformity of the distribution of carbide and nitride phases in ferrite is controlled at complete austenite homogenization by diffusion mobility and the solubility limit of carbon and nitrogen in ferrite, and secondary phase quantity in case of the secondary phase presence in austenite more than 0.04 wt. %. Equations was obtained which, with a probability of 95% and an error of 0.7 to 2.6%, describe the real process.

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Griso, Georges, Larysa Khilkova, Julia Orlik und Olena Sivak. „Homogenization of Perforated Elastic Structures“. Journal of Elasticity 141, Nr. 2 (05.06.2020): 181–225. http://dx.doi.org/10.1007/s10659-020-09781-w.

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Abstract The paper is dedicated to the asymptotic behavior of $\varepsilon$ ε -periodically perforated elastic (3-dimensional, plate-like or beam-like) structures as $\varepsilon \to 0$ ε → 0 . In case of plate-like or beam-like structures the asymptotic reduction of dimension from $3D$ 3 D to $2D$ 2 D or $1D$ 1 D respectively takes place. An example of the structure under consideration can be obtained by a periodic repetition of an elementary “flattened” ball or cylinder for plate-like or beam-like structures in such a way that the contact surface between two neighboring balls/cylinders has a non-zero measure. Since the domain occupied by the structure might have a non-Lipschitz boundary, the classical homogenization approach based on the extension cannot be used. Therefore, for obtaining Korn’s inequalities, which are used for the derivation of a priori estimates, we use the approach based on interpolation. In case of plate-like and beam-like structures the proof of Korn’s inequalities is based on the displacement decomposition for a plate or a beam, respectively. In order to pass to the limit as $\varepsilon \to 0$ ε → 0 we use the periodic unfolding method.

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Marsan, A. L., und D. Dutta. „Construction of a Surface Model and Layered Manufacturing Data From 3D Homogenization Output“. Journal of Mechanical Design 118, Nr. 3 (01.09.1996): 412–18. http://dx.doi.org/10.1115/1.2826901.

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A homogenization method has been recently developed to optimize the topology of a structure. This method will suggest a structural topology, but the results will be in finite element form. Most engineering applications, however, require smooth structures, whether the faces of the structures be planar or curved. Given the topology of a three-dimensional structure as suggested by the homogenization method, an algorithm is developed to interpret the structure and generate a smooth, manufacturable surface representation of the structure. Structures designed by the homogenization method can be quite complex and traditional manufacturing technique may not be well suited for constructing them. Layered manufacturing is adopted for producing such structures and it is shown how to generate the necessary data for this novel manufacturing technique from the surface model of the structure. Some steps of the algorithm require designer inputs. Examples are given which demonstrates this algorithm.

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Armstrong, Scott, Tuomo Kuusi und Jean-Christophe Mourrat. „The additive structure of elliptic homogenization“. Inventiones mathematicae 208, Nr. 3 (17.11.2016): 999–1154. http://dx.doi.org/10.1007/s00222-016-0702-4.

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Tsalis, Dimitrios, Nicolas Charalambakis, Kevin Bonnay und George Chatzigeorgiou. „Effective properties of multiphase composites made of elastic materials with hierarchical structure“. Mathematics and Mechanics of Solids 22, Nr. 4 (07.12.2015): 751–70. http://dx.doi.org/10.1177/1081286515612142.

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In this paper, the analytical solution of the multi-step homogenization problem for multi-rank composites with generalized periodicity made of elastic materials is presented. The proposed homogenization scheme may be combined with computational homogenization for solving more complex microstructures. Three numerical examples are presented, concerning locally periodic stratified materials, matrices with wavy layers and wavy fiber-reinforced composites.

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Jin, Ji-Won, Byung-Wook Jeon, Chan-Woong Choi und Ki-Weon Kang. „Multi-Scale Probabilistic Analysis for the Mechanical Properties of Plain Weave Carbon/Epoxy Composites Using the Homogenization Technique“. Applied Sciences 10, Nr. 18 (18.09.2020): 6542. http://dx.doi.org/10.3390/app10186542.

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Probabilistic analyses of carbon fabric composites were conducted using the Monte Carlo simulation based on a homogenization technique to evaluate the mechanical properties of composites and their stochastic nature. First, the homogenization analysis was performed for a micro-level structure, which fiber and matrix are combined. The effective properties obtained from this analysis were compared with the results from the rule of mixture theory to verify the homogenization analysis. And, tensile tests were conducted to clearly evaluate the result and the reliability was verified by comparing the results of the tensile tests and homogenization analysis. In addition, the Monte Carlo simulation was performed based on homogenization analyses to consider the uncertainties of the micro-level structure combined of fiber and matrix. Next, the results of this simulation were applied to the macro-level structure combined of the tow and matrix to perform the Monte Carlo simulation based on the homogenization technique. Finally, the sensitivity analysis was conducted to identify the effect of constituents of the carbon plain weave composite and the linear correlation of the micro- and macro-level structures combined of the fiber/matrix and tow/matrix, respectively. The findings of this study verified that the effective properties of the plain weave carbon/epoxy composite and their uncertainties depended on the properties of the carbon fiber and epoxy, which are the basic constituents of plain weave carbon/epoxy composites.

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Sherniyozov, A., und Sh Payziyev. „FOCAL SPOT STRUCTURE OF FRESNEL LENS AND ITS HOMOGENIZATION“. «Узбекский физический журнал» 21, Nr. 4 (21.08.2019): 245–49. http://dx.doi.org/10.52304/.v21i4.113.

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Using statistical Monte-Carlo photon-tracing method, we numerically studied focal spot structure of flat Fresnel lens. It has been shown that due to dispersion effect, focal spot structure changes considerably. In addition, we demonstrated homogenization of strongly focused photons. Rectangular prism can be applied to achieve the homogenization.

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Meunier, Gérard, Christophe Guérin, Vincent Charmoille und Patrice Labie. „Frequency‐domain homogenization for periodic electromagnetic structure“. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 29, Nr. 6 (16.11.2010): 1416–24. http://dx.doi.org/10.1108/03321641011078481.

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Meunier, Gérard, Vincent Charmoille, Christophe Guerin, Patrice Labie und Yves Marechal. „Homogenization for Periodical Electromagnetic Structure: Which Formulation?“ IEEE Transactions on Magnetics 46, Nr. 8 (August 2010): 3409–12. http://dx.doi.org/10.1109/tmag.2010.2044386.

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Duerinckx, Mitia, Antoine Gloria und Felix Otto. „The Structure of Fluctuations in Stochastic Homogenization“. Communications in Mathematical Physics 377, Nr. 1 (17.03.2020): 259–306. http://dx.doi.org/10.1007/s00220-020-03722-3.

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Woźnicki, A., D. Leśniak, G. Włoch, B. Leszczyńska-Madej und A. Wojtyna. „The Effect Of Homogenization Conditions On The Structure And Properties Of 6082 Alloy Billets“. Archives of Metallurgy and Materials 60, Nr. 3 (01.09.2015): 1763–72. http://dx.doi.org/10.1515/amm-2015-0303.

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Abstract The paper presents the results of laboratory homogenization investigations of the 6082 grade alloys, differing in Mg and Si content. At the first stage, the microstructure of alloys was analysed after homogenization finished with water quenching. SEM/EDS investigations and DSC tests were applied to evaluate the dissolution of the Mg2Si particles and concentration of the main alloying additions in the grains interiors, depending on soaking conditions. In the case of alloy with lower Mg and Si content, homogenization the temperature of 535ºC for 8h is sufficient for significant Mg2Si particles dissolution. For the alloy with higher Mg and Si content, after homogenization the temperature of 550ºC for 8h, the amount of undissolved Mg2Si particles decreases visibly, compared to homogenization at 535ºC for 8h. However, an unfavourable tendency of dispersoids growth is observed and these soaking conditions are not found to be recommended. At the second research stage, the influence of homogenization cooling rate on the size and distribution of the Mg2Si particles observed in the alloys microstructure was analysed. The ability of the Mg2Si particles, precipitated during various homogenization coolings, to rapid dissolution was estimated. For this purpose, the hardness after solution heat treatment with short annealing and ageing was determined and the DSC tests were performed. It was found, that cooling after homogenization at 315ºC/h is sufficient for precipitation of fine Mg2Si particles, which dissolve during subsequent rapid heating. Cooling at 40ºC/h, causes precipitation of Mg2Si phase in the form of large particles, unable for further fast dissolution.

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Vončina, Maja, Irena Paulin, Ana Debevec und Aleš Nagode. „MODIFICATION OF THE CAST STRUCTURE OF AN EN AW 2011 ALLOY WITH HOMOGENIZATION“. Materiali in tehnologije 55, Nr. 2 (15.04.2021): 327–33. http://dx.doi.org/10.17222/mit.2020.215.

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Aluminium alloys of group 2xxx contain copper as the main alloying element. Copper increases the strength and workability of the alloy, but also reduces the corrosion resistance and weldability. During casting, a nonequilibrium solidification occurs. Therefore, the cast alloy needs to be heat treated with a so-called homogenization process. Homogenization allows us to eliminate crystalline segregations and low-melting eutectics, and also causes changes in the morphology of intermetallic phases. The forming ability is in this way increased. In this research the subject of the investigations was the aluminium alloy with designation EN AW 2011 (AlCuBiPb), whereas the comparative analysis before and after homogenization annealing was made. Homogenization was conducted at 520 °C for 6 h. First, slices from two rods before and after homogenization were cut out, where three samples from each slice of the rod, namely in the middle, on D/4 and at the edge of the slice were prepared. Differential scanning calorimetry (DSC) was performed on all six samples, the results were compared with each other in order to establish the structure homogeneity before and after the homogenization process through the cross-section of the rod. Samples for light (LM) and scanning electron microscopy (SEM) were also prepared, whereas the phase composition and chemical homogeneity were analysed. Using the Thermo-Calc program, the nonequilibrium solidification was simulated and the phase formation during solidification was examined. From the obtained results, it was concluded that the homogenization was carried out successfully, due to a homogeneous chemical distribution in the examined phases and to a fairly homogeneous chemical composition throughout the cross-section of the rod slice.

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Meng, Xi Hui, Xiao Yu Ma und Xiao Ya Zheng. „Numerical Computation for Effective Mechanical Properties of Honeycomb Core Structure“. Advanced Materials Research 912-914 (April 2014): 460–65. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.460.

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This paper combined the homogenization method with finite element method. The equivalent mechanical coefficients of the hexagonal aluminum honeycomb core were computed on ABAQUS platform by developing the user subroutine UEXPAN ( ) and Python script file. The results obtained with homogenization method were compared with those obtained with energy method, and it showed the feasibility of homogenization method. Then the effects of thickness-to-length ratio t/l on equivalent mechanical coefficients were taken into account. The results suggested that the equivalent in-plane mechanical parameters vary non-linearly with respect to t/l, while the equivalent out-of-plane mechanical parameters vary linearly with respect to t/l, which will provide reference for optimizing the design of honeycomb core structure.

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Nguyen, Anh Vu, Karine Charlet, Belhassen Chedli Bouzgarrou, Ky Nam Pham, Trong Dai Vu und Alexis Béakou. „Hybrid Effect on Hybrid Composite Reinforced Carbon Fibers and Flax Fibers“. Key Engineering Materials 801 (Mai 2019): 101–6. http://dx.doi.org/10.4028/www.scientific.net/kem.801.101.

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In this paper, hybrid composite made of carbon woven fibers and flax woven fibers is studied. This hybrid composite structure takes advantages of high resistance, high stiffness of carbon fibers and high damping and low density of flax fibers. Different structures of flax woven composites, carbon woven composites and hybrid composites were fabricated and tested experimentally. With aim of predicting the properties of the hybrid composite, a homogenization model of the composite is established. The homogenization model is based on the rule-of-mixture and iso-strain assumption. The results of the analytical homogenization model (AHM) are then compared with the results of experimental tests. The results show a good agreement between the AHM and the experimental results at the homogenization level of the woven composite. However, at the hybrid composite homogenization level, the experimental results present considerably higher stiffness than analytical results that is explained by hybrid effect on the hybrid composite.

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Zou, Yong Zhi, Zheng Bin Xu und Jian Min Zeng. „Effect of SDAS on Homogenization of Al-Si-Mg Casting Alloys“. Advanced Materials Research 97-101 (März 2010): 1041–44. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.1041.

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Aluminum alloy A357 can be heat treated in order to obtain optimum mechanical properties. Moreover, SDAS (Second dendrite arm spacing) is an important structure feature in cast aluminum alloys. The effects of SDAS on the homogenization of Al-Si-Mg alloy are investigated through measurement of SDAS and hardness analysis. The results show that the homogenization time increases as the value of SDAS increases and the homogenization temperature decreases in the homogenization process. The homogenization kinetics equation is: . In addition, the hardness after homogenization treatment at 540°C for 6 hours is advanced with the reduction of SDAS.

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Li, Xing Gang, Kui Zhang, Yong Jun Li, Xin Zhao und Xu Jun Mi. „Mechanical Properties and Microstructures of Mg-Al-Zn Alloys with High Aluminum Contents“. Materials Science Forum 610-613 (Januar 2009): 801–5. http://dx.doi.org/10.4028/www.scientific.net/msf.610-613.801.

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The effect of Al contents on the properties and structures of AZ80, AZ91，AZ131 and AZ151 magnesium alloys has been studied. The experiments of homogenization treatment, hot extrusion, and annealing treatment are carried out in order to study the effects of these processes to the properties and structure of AZ80, AZ91, AZ131 and AZ151 magnesium alloys. The parameters of homogenization treatment (420°C×24h, 420°C×36h) determined by DSC and metallurgical photo are sufficient which ensure the eutectic phase melt into magnesium matrix greatly. The strength of extruded bars shortly after homogenization treatment increase (Rp0.2 from 232 to 310MPa), but elongation decrease (A from 12 to 2.5%) with Al contents. The differences and causes of structure and mechanical properties of extruded bar after the process of aging are analyzed in detail by tensile experiments, hardness measurement, and optical observation.

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Hassani, B., und E. Hinton. „A review of homogenization and topology optimization I—homogenization theory for media with periodic structure“. Computers & Structures 69, Nr. 6 (Dezember 1998): 707–17. http://dx.doi.org/10.1016/s0045-7949(98)00131-x.

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Hua, Xiao, Shanan Xu, Mingming Wang, Ying Chen, Hui Yang und Ruijin Yang. „Effects of high-speed homogenization and high-pressure homogenization on structure of tomato residue fibers“. Food Chemistry 232 (Oktober 2017): 443–49. http://dx.doi.org/10.1016/j.foodchem.2017.04.003.

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Xu, Yao, und Weisheng Niu. „Periodic homogenization of elliptic systems with stratified structure“. Discrete & Continuous Dynamical Systems - A 39, Nr. 4 (2019): 2295–323. http://dx.doi.org/10.3934/dcds.2019097.

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Shinoda, Yoshikatsu, und Akihiro Matsuda. „Homogenization Analysis of Porous Polymer Considering Microscopic Structure“. Procedia Engineering 60 (2013): 343–48. http://dx.doi.org/10.1016/j.proeng.2013.07.027.

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Xu, Yao, und Weisheng Niu. „Homogenization of elliptic systems with stratified structure revisited“. Communications in Partial Differential Equations 45, Nr. 7 (11.01.2020): 655–89. http://dx.doi.org/10.1080/03605302.2019.1709871.

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Poli[sbreve]evski, Dan. „Basic Homogenization Results for a Biconnectedε-Periodic Structure“. Applicable Analysis 82, Nr. 4 (April 2003): 301–9. http://dx.doi.org/10.1080/0003681031000094870.

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Mourrat, Jean-Christophe, und Felix Otto. „Correlation structure of the corrector in stochastic homogenization“. Annals of Probability 44, Nr. 5 (September 2016): 3207–33. http://dx.doi.org/10.1214/15-aop1045.

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Mascarenhas, M. L., und Dan Poliševski. „Homogenization of the torsion problem with quasiperiodic structure“. Numerical Functional Analysis and Optimization 13, Nr. 5-6 (Januar 1992): 475–85. http://dx.doi.org/10.1080/01630569208816493.

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Fusco, N., und G. Moscariello. „On the homogenization of quasilinear divergence structure operators“. Annali di Matematica Pura ed Applicata 146, Nr. 1 (Dezember 1986): 1–13. http://dx.doi.org/10.1007/bf01762357.

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AMIRAT, YOUCEF, und VLADIMIR V. SHELUKHIN. „Homogenization of composite electrets“. European Journal of Applied Mathematics 28, Nr. 2 (13.06.2015): 261–83. http://dx.doi.org/10.1017/s0956792516000255.

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We study the two-scale homogenization of the diffraction interfacial condition for the diffusion equation relevant to a composite medium which has a periodic structure. The results are applied to the electric field potential within a dielectric composite body when there is a difference in dielectric permittivity between the composite components in the presence of interfacial static charges. The principal result is that the interfacial charge distribution is equivalent to an apparent bulk charge which can be calculated starting from the composite geometry. We perform the corrector analysis and establish that the corrector terms strongly depend on the interfacial charge.

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Khanh, Trinh Duy. „Second gradient substitution model for high contrast bi-phase structure“. Journal of Science and Technology in Civil Engineering (STCE) - NUCE 14, Nr. 2 (17.04.2020): 116–26. http://dx.doi.org/10.31814/stce.nuce2020-14(2)-11.

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Lightweight structures with soft inclusion material, such as hollow core slabs, foam sandwich wall, pervious pavement ... are widely used in construction engineering for sustainable goals. Voids and soft inclusion can be modeled as a very soft material, while the main material is modeled with its original rigidity, which is so much higher than inclusion's one. In consequence, highly contrast bi-phase structure attracts the interests of scientists and engineers. One important demand is how to build a homogeneous equivalent model to replace the multi-phase structure which requires much resources and time to perform structure analysis. Various homogenization schemes have succeeded in establishing a homogeneous substitution model for composite materials which fulfill the scale separation condition (characteristic length of heterogeneity is very small in comparison to structure dimensions). Herein, elastic stiffness matrix of a homogeneous model which replaces a bi-phase material is computed by a higher-order homogenization scheme. A non-homogeneous boundary condition (a polynomial inspired from Taylor series expansion) is used in computation. Homogeneous substitution model constructed from this computation process, can give engineers a fast and effective tool to predict the behavior of bi-phase structure. Instead of a classical Cauchy continuum, second gradient model is selected as a potential candidate for substituting the composite material behavior because of the separation scale (volume ratio of inclusion to matrix phase reaches unit). Keywords: generalized continuum; second-gradient medium; higher-order homogenization; non-homogeneous boundary conditions; representative volume element.

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Vlădulescu, Florian, und Dan Mihai Constantinescu. „Lattice structure optimization and homogenization through finite element analyses“. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 234, Nr. 12 (29.07.2020): 1490–502. http://dx.doi.org/10.1177/1464420720945744.

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Lattice topology optimization can stimulate the design of new materials with spatially dependent properties with composite parts or three-dimensional printed components. The present work considers a mounting bracket for an industrial robotic arm as a case study, having as the main objective the increase of the fundamental frequency and secondly its mass reduction. Two design approaches were considered by using the ANSYS software: the first stage optimized the orthotropic lattice material by establishing an optimal variable cubic cell lattice density distribution in the geometric model; the second stage used a homogenized model based on the lattice optimization resulted from the previous stage and considered different volume fractions and variable density for four different types of cells. Homogenization increased the stiffness of the bracket by using the same cubic lattice cell and the fundamental frequency increased from 1227 Hz obtained with lattice optimization to 1366 Hz after homogenization. For the unoptimized bracket the fundamental frequency was only 839 Hz. The mass was reduced to more than half. The most effective proved to be the midpoint lattice cell as by homogenization the mass was reduced from 45.5 kg to 18.22 kg.

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Bryantsev, P. Yu, V. S. Zolotorevskiy und V. K. Portnoy. „The Effect of Heat Treatment and Mn, Cu and Cr Additions on the Structure of Ingots of Al-Mg-Si-Fe Alloys“. Materials Science Forum 519-521 (Juli 2006): 401–6. http://dx.doi.org/10.4028/www.scientific.net/msf.519-521.401.

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Phase transformations in 6XXX alloys with Mn, Cu and Cr additions have been studied in the process of homogenization annealing at different temperatures. The continuous cooling transformation diagrams of decomposition of solid solution during the cooling of ingots from the homogenization temperature have been plotted. The effect of the cooling rate after homogenization on the properties of ingots during extrusion has been studied.

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Zhang, Kehong, Yuhang Su und Hui Xiao. „Preparation and characterization of nanofibrillated cellulose from waste sugarcane bagasse by mechanical force“. BioResources 15, Nr. 3 (09.07.2020): 6636–47. http://dx.doi.org/10.15376/biores.15.3.6636-6647.

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The effect of different mechanical force application methods was investigated relative to the structure and properties of nanofibrillated cellulose (NFC) from sugarcane bagasse. The NFC was prepared by grinding, high pressure homogenization, and ultrasonication with chemical pretreatment. Fiber morphology, crystalline, chemical structures, and tensile property were analyzed to reveal the mechanisms of NFC production behind different mechanical treatments. The results showed that compared with grinding treatment, high pressure homogenization and ultrasonic treatment can obviously increase the aspect ratio and size uniformity of NFC. Ultrasonic treatment gave the best results. The combination of grinding, high pressure homogenization, and ultrasonic treatment resulted in NFC with the average diameter of 23.18 nm. With the shearing action of grinding, high pressure homogenization, and ultrasonic treatment, the mechanical properties, crystallinity and thermal stability of NFC were gradually enhanced. This results demonstrated that a very low-value agricultural waste product can be easily converted to a high performance nanocomposite with tensile strength of 153.6 MPa and strain at break of 8.83%.

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Staszak, Natalia, Tomasz Garbowski und Anna Szymczak-Graczyk. „Solid Truss to Shell Numerical Homogenization of Prefabricated Composite Slabs“. Materials 14, Nr. 15 (23.07.2021): 4120. http://dx.doi.org/10.3390/ma14154120.

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The need for quick and easy deflection calculations of various prefabricated slabs causes simplified procedures and numerical tools to be used more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Based on the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on the RVE boundary and generalized strains.

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Jalagonia, Natia, Fernand Marqui, Karlo Barbakadze, Ekaterine Sanaia, Guram Bokuchava und Tinatin Kuchukhidze. „Obtaining of Graphene Structure Containing Ceramic Composites in High Temperature Vacuum Furnace“. Materials Science Forum 900 (Juli 2017): 101–4. http://dx.doi.org/10.4028/www.scientific.net/msf.900.101.

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We have obtained ceramic composites containing graphene structure, where homogenization process of powdery composite was improved. At first, α-alumina was obtained from local row, which is cheap and available. The obtaining method was developed by our group. Graphene oxide was synthesized from natural graphite. Homogenization was carried out in nanomill with organic binder, which provides for equal distribution and separation of graphene oxide layers (Organic binder behaves as “scotch tape”) during grinding. Some characteristics of ceramic materials have been improved.

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Zengin, Huseyin, Yunus Turen, Hayrettin Ahlatci, Yavuz Sun und Ismail Hakkı Kara. „Microstructure and Corrosion Properties of Homogenized Mg-4Zn-1La Magnesium Alloy“. Key Engineering Materials 750 (August 2017): 118–23. http://dx.doi.org/10.4028/www.scientific.net/kem.750.118.

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In this study, microstructure and corrosion behaviour of homogenized Mg-4Zn-1La magnesium alloy was investigated. Mg-4Zn-1La alloy was produced by low-pressure die casting method. Homogenization treatments were performed at 350 °C and 400 °C for 12, 18, 24 and 48 hours, followed by rapid cooling in water at room temperature. Microstructure characterizations showed that La addition led to a formation of semi-continuous network structure and islands of second phases which identified as T-phase (Mg7Zn3RE). A significant amount of second phase dissolution and an increase in a-Mg grain size with increasing both homogenization time and temperature was observed. Homogenization treatment led to an improvement in corrosion resistance of Mg-4Zn-1La alloy. Homogenization at 400 °C resulted in better corrosion resistance than homogenization at 350 °C for all homogenization duration.

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Agić, Ante. „Multiscale Modeling Electrospun Nanofiber Structures“. Materials Science Forum 714 (März 2012): 33–40. http://dx.doi.org/10.4028/www.scientific.net/msf.714.33.

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The carbon nanotube (CNT) structure is a promising building block for future nanocomposite structures. Mechanical properties of the electrospun butadiene elastomer reinforced with CNT are analyzed by multiscale method. Effective properties of the fiber at microscale determined by homogenization procedure using modified shear-lag model, while on the macro scale effective properties for the point-bonded stochastic fibrous network determined by volume homogenization procedure using multilevel finite element. Random fibrous network was generated according experimentally determined stochastic quantificators. Influence of CNT reinforcement on elastic modulus of electrospun sheet on macroscopic level is determined.

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Cheng, Lin, Pu Zhang, Emre Biyikli, Jiaxi Bai, Joshua Robbins und Albert To. „Efficient design optimization of variable-density cellular structures for additive manufacturing: theory and experimental validation“. Rapid Prototyping Journal 23, Nr. 4 (20.06.2017): 660–77. http://dx.doi.org/10.1108/rpj-04-2016-0069.

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Purpose The purpose of the paper is to propose a homogenization-based topology optimization method to optimize the design of variable-density cellular structure, in order to achieve lightweight design and overcome some of the manufacturability issues in additive manufacturing. Design/methodology/approach First, homogenization is performed to capture the effective mechanical properties of cellular structures through the scaling law as a function their relative density. Second, the scaling law is used directly in the topology optimization algorithm to compute the optimal density distribution for the part being optimized. Third, a new technique is presented to reconstruct the computer-aided design (CAD) model of the optimal variable-density cellular structure. The proposed method is validated by comparing the results obtained through homogenized model, full-scale simulation and experimentally testing the optimized parts after being additive manufactured. Findings The test examples demonstrate that the homogenization-based method is efficient, accurate and is able to produce manufacturable designs. Originality/value The optimized designs in our examples also show significant increase in stiffness and strength when compared to the original designs with identical overall weight.

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Lukkassen, Dag, Gabriel Nguetseng, Hubert Nnang und Peter Wall. „Reiterated homogenization of nonlinear monotone operators in a general deterministic setting“. Journal of Function Spaces and Applications 7, Nr. 2 (2009): 121–52. http://dx.doi.org/10.1155/2009/102486.

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We study reiterated homogenization of a nonlinear non-periodic elliptic differential operator in a general deterministic setting as opposed to the usual stochastic setting. Our approach proceeds from an appropriate notion of convergence termed reiterated Σ-convergence. A general deterministic homogenization theorem is proved and several concrete examples are studied under various structure hypotheses ranging from the classical periodicity hypothesis to more complicated, but realistic, structure hypotheses.

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Li, Yong Jun, und Kui Zhang. „Study on Processing Technique in Engineering Tests of Mg-7.1Gd-4.6Y-1.3Nd-0.5Zr Alloy“. Applied Mechanics and Materials 423-426 (September 2013): 811–15. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.811.

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Combined with the pre-test results, homogenization, plastic deformation, aging and other processes of Mg-7.1Gd-4.6Y-1.3Nd-0.5Zr (EW75) magnesium alloy was studied in engineering tests. The results show that in engineering test the large ingots (Φ500×800~900mm) of the EW75 alloy using two-stage homogenization treatment had perfect homogenization effect and no burnt structure. After multi-directional forging and extruded deformation, the homogenized residual second phase particles were fully broken, and the structure was refined and uniform. The peak aged craft was 230°C×6h, with the aging time increasing, the tensile strength and elongation remained unchanged, showing a strong anti-aging ability. The two-stage homogenization treatment + multi-directional forging + direct extrusion deformation + peak aging treatment was used to prepare a high performance EW75 alloy and at longitudinal direction its ultimate tensile strength, yield strength and elongation were 450MPa, 385MPa, 12.0% respectively.

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Yan, Jun, Haitao Hu, Zhixun Yang, Rui Wan und Yang Li. „Multi-scale analysis for helically wound structures with one-dimensional periodicity“. Engineering Computations 36, Nr. 8 (07.10.2019): 2911–28. http://dx.doi.org/10.1108/ec-10-2018-0489.

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Purpose The purpose of this study is to present a multi-scale analysis methodology for calculating the effective stiffnesses and the micro stresses of helically wound structures efficiently and accurately. The helically wound structure is widely applied in ocean and civil engineering as load-bearing structures with high flexibility, such as wire ropes, umbilical cables and flexible risers. Their structures are usually composed of a number of twisted subcomponents with relatively large slender ratio and have the one-dimensional periodic characteristic in the axial direction. As the huge difference between the axial length and the cross-section size of this type of structures, the finite element modeling and theoretical analysis based on some assumption are usually unavailable leading to the reduction of computability; even the optimization design becomes infeasible. Design/methodology/approach Based on the asymptotic homogenization theory, the one-dimensional periodic helically wound structure is equivalent to the one-dimensional homogeneous beam. A novel implementation of the homogenization is derived for the analysis of the effective mechanical properties of the helically wound structure, and the tensile, bending, torsional and coupling stiffness properties of the effective beam model are obtained. On this basis, a downscaling analysis formation for the micro-component stress in the one-dimensional periodic wound structure is constructed. The stress of micro-components in the specified geometry position of the helically wound structure is obtained basing on the asymptotic homogenization theory simultaneously. Findings By comparing with the result from finite element established accurately, the established multi-scale calculation method of the one-dimensional periodic helically wound structure is verified. The influence of size effects on the macro effective performance and the micro-component stress is discussed. Originality/value This paper will provide the theoretical basis for the efficient elastoplastic analysis of the helically wound structure, even the fatigue analysis. In addition, it is necessary to point out that the axial length of the helically wound structure in the general engineering problems that such as deep-sea risers and submarine cables.

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Yuan, Wei, Cheng Xu, Li Xue, Hui Pang, Axiu Cao, Yongqi Fu und Qiling Deng. „Integrated Double-Sided Random Microlens Array Used for Laser Beam Homogenization“. Micromachines 12, Nr. 6 (09.06.2021): 673. http://dx.doi.org/10.3390/mi12060673.

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Double microlens arrays (MLAs) in series can be used to divide and superpose laser beam so as to achieve a homogenized spot. However, for laser beam homogenization with high coherence, the periodic lattice distribution in the homogenized spot will be generated due to the periodicity of the traditional MLA, which greatly reduces the uniformity of the homogenized spot. To solve this problem, a monolithic and highly integrated double-sided random microlens array (D-rMLA) is proposed for the purpose of achieving laser beam homogenization. The periodicity of the MLA is disturbed by the closely arranged microlens structures with random apertures. And the random speckle field is achieved to improve the uniformity of the homogenized spot by the superposition of the divided sub-beams. In addition, the double-sided exposure technique is proposed to prepare the rMLA on both sides of the same substrate with high precision alignment to form an integrated D-rMLA structure, which avoids the strict alignment problem in the installation process of traditional discrete MLAs. Then the laser beam homogenization experiments have been carried out by using the prepared D-rMLA structure. The laser beam homogenized spots of different wavelengths have been tested, including the wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B). The experimental results show that the uniformity of the RGB homogenized spots is about 91%, 89%, and 90%. And the energy utilization rate is about 89%, 87%, 86%, respectively. Hence, the prepared structure has high laser beam homogenization ability and energy utilization rate, which is suitable for wide wavelength regime.

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Sigrist, Jean-François, Daniel Broc und Christian Lainé. „Fluid-Structure Interaction Effects Modeling for the Modal Analysis of a Nuclear Pressure Vessel“. Journal of Pressure Vessel Technology 129, Nr. 1 (17.03.2006): 1–6. http://dx.doi.org/10.1115/1.2389025.

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The present paper deals with the modal analysis of a nuclear reactor with fluid-structure interaction effects. The proposed study aims at describing various fluid-structure interaction effects using several numerical approaches. The modeling lies on a classical finite element discretization of the coupled fluid-structure equation, enabling the description of added mass and added stiffness effects. A specific procedure is developed in order to model the presence of internal structures within the nuclear reactor, based on periodical homogenization techniques. The numerical model of the nuclear pressure vessel is developed in a finite element code in which the homogenization method is implemented. The proposed methodology enables a convenient analysis from the engineering point of view and gives an example of the fluid-structure interaction effects, which are expected on an industrial structure. The modal analysis of the nuclear pressure vessel is then performed and highlights of the relative importance of FSI effects for the industrial case are evaluated: the analysis shows that added mass effects and confinement effects are of paramount importance in comparison to added stiffness effects.

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Asada, Takashi, und Nobutada Ohno. „Implicit Formulation of Homogenization Method for Periodic Elastoplastic Solids“. Key Engineering Materials 340-341 (Juni 2007): 1055–60. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.1055.

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In this study, to determine incremental, perturbed displacement fields in periodic elastoplastic solids, an incremental homogenization problem is fully implicitly formulated, and an algorithm is developed to solve the homogenization problem. It is shown that the homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increments in unit cells, and that the present formulation allows versatility in the initial setting of strain increments in contrast to previous studies. The homogenization algorithm developed is then examined by analyzing a holed plate, with an elastoplastic micro-structure, subjected to tensile loading. It is thus demonstrated that the convergence in iteratively solving the homogenization problem strongly depends on the initial setting of strain increments in unit cells, and that quick convergences can be attained if the initial setting of strain increments is appropriate.

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Guerra, Valentina, Chaoying Wan, Volkan Degirmenci, Jeremy Sloan, Dimitris Presvytis und Tony McNally. „2D boron nitride nanosheets (BNNS) prepared by high-pressure homogenisation: structure and morphology“. Nanoscale 10, Nr. 41 (2018): 19469–77. http://dx.doi.org/10.1039/c8nr06429f.

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Trinh, Duy Khanh, und Samuel Forest. „Generalized continuum overall modelling of periodic composite structures“. Vietnam Journal of Mechanics 33, Nr. 4 (12.12.2011): 245–58. http://dx.doi.org/10.15625/0866-7136/33/4/258.

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Classical homogenization methods fail to reproduce the overall response of composite structures when macroscopic strain gradients become significant. Generalized continuum models like Cosserat, strain gradient and micromorphic media, can be used to enhance the overall description of heterogeneous materials when the hypothesis of scale separation is not fulfilled. We show in the present work how the higher order elasticity moduli can be identified from suitable loading conditions applied to the unit cell of a periodic composite. The obtained homogeneous substitution generalized continuum is used then to predict the response of a composite structure subjected to various loading conditions. Reference finite element computations are performed on the structure taking all the heterogeneities into account. The overall substitution medium is shown to provide improved predictions compared to standard homogenization. In particular the additional boundary conditions required by generalized continua makes it possible to better represent the clamping conditions on the real structure.

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Braides, Andrea, und Nicola A. Nodargi. „Homogenization of cohesive fracture in masonry structures“. Mathematics and Mechanics of Solids 25, Nr. 2 (30.08.2019): 181–200. http://dx.doi.org/10.1177/1081286519870222.

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We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist of (i) a linear elastic contribution within the blocks, (ii) a Barenblatt’s cohesive contribution at contact surfaces between blocks, and (iii) a suitable unilateral condition on the strain across contact surfaces, and are governed by a small parameter representing the typical ratio between the length of the blocks and the dimension of the structure. Using the terminology of [Formula: see text]-convergence and within the functional setting supplied by the functions of bounded deformation, we analyze the asymptotic behavior of such energy functionals when the parameter tends to zero, and derive a simple homogenization formula for the limit energy. Furthermore, we highlight the main mathematical and mechanical properties of the homogenized energy, including its non-standard growth conditions under tension or compression. The key point in the limit process is the definition of macroscopic tensile and compressive stresses, which are determined by the unilateral conditions on contact surfaces and the geometry of the blocks.

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Shao, Zhu Feng, Ya Nan Jia, Chuan Dong Rao, Zai Kui Xiang, Mei Sui, Yu Fen Wang und Yi Wang Bao. „Analysis of Influence of High Temperature Homogenizing on UV Transmittance of Quartz Glass“. Key Engineering Materials 680 (Februar 2016): 285–88. http://dx.doi.org/10.4028/www.scientific.net/kem.680.285.

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Synthetic quartz glass is an excellent transmittance material in ultraviolet (UV), visible and near-infrared bands. Homogenization process to synthetic quartz glass optical elements is done in order to make the composition and structure more uniform. The homogenization temperature is above 1800°C. After high-temperature homogenization, the UV transmittance of quartz glass appears a certain extent of decline in the edge partition., After high temperature homogenization process, it is found that the closer the layer to the graphite vessel, the stronger influence on UV transmittance will be. This conclusion is made by comparing the UV transmission of the quartz glass in different layers. Furthermore, the factors affecting the UV transmittance is also analyzed in this article.

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Tian, Ni, Gang Zhao, Chun Ming Liu und Liang Zuo. „Microstructural Evolvement of Al-1.5Si-1.1Mg-0.5Cu Alloy Ingot during Homogenization Treatment“. Materials Science Forum 546-549 (Mai 2007): 1037–42. http://dx.doi.org/10.4028/www.scientific.net/msf.546-549.1037.

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The kinds, morphologies and distributions, enclosed the micro-structural evolvement of Al-1.5Si-1.1Mg-0.5Cu alloy during homogenization treatment were investigated by means of optical microscopy, XRD, SEM/EDS and TEM/EDS. The results show that there were mainly three kinds of morphologically distinct constituents in as-cast Al-1.5Si-1.1Mg-0.5Cu alloy for automotive panels, such as coarse Mg2Si and Al8(FeMn)2Si, and multiphase eutectic structure consisted of AlMgSiFeCu elements, except the α-Al matrix phase. The coarse Mg2Si and Al8(FeMn)2Si were distributed in the α-Al interdentritic regions or at grain boundaries, the former sometimes appears more obvious eutectic characteristics than the later one. The multiphase eutectic products distributed both inside grains with agglomerate aspects and along the α-Al interdentritic regions or at grain boundaries, which is contained with Si and Al2Cu. Coarse binary eutectic structure Mg2Si partly dissolved into matrix and the eutectic characteristics disappeared, whereas Al8(FeMn)2Si changed a little during homogenization. Agglomerate multi-eutectic structures were non-equilibrium products, some of them fully dissolved into matrix and the others partially dissolved and left the discrete blocky Si behind after homogenization.

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TELEGA, JÓZEF JOACHIM. „JUSTIFICATION OF A REFINED SCALING OF STIFFNESSES OF REISSNER PLATES WITH FINE PERIODIC STRUCTURE“. Mathematical Models and Methods in Applied Sciences 02, Nr. 04 (Dezember 1992): 375–406. http://dx.doi.org/10.1142/s0218202592000235.

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The aim of this paper is a rigorous justification of the model of linear elastic plates proposed in Ref. 19. Such a model is obtained by rescaling stiffnesses and performing homogenization of a Reissner plate exhibiting fine periodic structure. To prove convergence, when the periodicity parameter tends to zero, the epi-convergence method is applied; the proof of convergence essentially exploits duality arguments. The dual homogenization, based on the principle of the complementary energy, is also studied; the properties of the macroscopic potential are investigated and the dual homogenized (macroscopic) potential is derived.

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