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1
Content available remote Micromechanical analysis of glass fiber reinforced epoxy composites and case study of macro-mechanical observation
Alam Shahinoor, Chowdhury Mohammad Asaduzzaman
Composites Theory and Practice
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2020
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R. 20, nr 1
23--34
EN
This paper was written and formulated based on the micromechanical analysis of unidirectional glass fiber reinforced epoxy composite lamina. To simplify the calculations and achieve acceptable results, a few assumptions like idealized packing,the representative volume element (RVE), uniform strain boundary condition, statistically homogeneous unidirectional fiber reinforced composites, etc. are taken into consideration. Translational symmetric transformation was applied and established mathematical models are presented to obtain the values of the effective material properties by means of the simple strength of materials approach so that they can be compared with the semi-empirical model. In addition, a parametric study was carried out to verify the dependency of the fiber and matrix on the overall effective material properties. This will ultimately helpto develop the required glass fiber reinforced epoxy composites for their specific applications.
2
Content available remote Influence of RVE geometrical parameters on elastic response of woven flax-epoxy composite materials
Ryzińska Grażyna, Janowski Grzegorz
Composites Theory and Practice
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2020
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R. 20, nr 2
51--59
EN
In the case of polymer composites reinforced with natural fiber woven fabrics, microstructural calculations are extremely difficult to perform due to their characteristic variability, among others their mechanical properties. The aforementioned scientific problem has not been thoroughly investigated, hence the purpose of this work was to assess the possibilities of predicting the properties of a composite reinforced with flax woven fabric by micromechanical calculations using the Mori-Tanaka and the double inclusion homogenization models. In addition, the second important utilitarian problem that was undertaken in the work was assessment of the impact of the size of the representative volume element (RVE) on the obtained results. The analyses were carried out for composites based on epoxy resin reinforced with flax fabrics: plain, 2x2 twill and 3x1 twill types. Based on the performed calculations, it was found that the obtained results depend on the type of weave in the fabric used, the size of the RVE, the number of yarn bands in the RVE and the appropriately selected homogenization method. Guidelines useful for evaluating the optimal RVE size depending on the type of weave were formulated.
PL
W przypadku kompozytów polimerowych zbrojonych tkaninami z włókien naturalnych przeprowadzanie obliczeń mikrostrukturalnych jest wyjątkowo trudne do wykonania z uwagi na charakterystyczną dla nich zmienność, m.in. właściwości mechanicznych. Wspomniany problem naukowy nie jest dokładnie zbadany, stąd celem niniejszej pracy była ocena możliwości prognozowania właściwości kompozytu wzmacnianego tkaniną lnianą poprzez obliczenia mikromechaniczne z wykorzystaniem modelu homogenizacji Mori-Tanaka oraz Double Inclusion. Ponadto drugim istotnym problemem utylitarnym, który podjęto w pracy, była ocena wpływu wielkości reprezentatywnego elementu objętościowego (REO) na uzyskane wyniki. Analizy przeprowadzono dla kompozytów o osnowie żywicy epoksydowej zbrojnej tkaninami lnianymi o splocie: płóciennym, skośnym 2x2 oraz skośnym 3x1. Na podstawie przeprowadzonych obliczeń stwierdzono, że uzyskane wyniki zależą od rodzaju splotu w zastosowanej tkaninie, wielkości REO, ilości pasm przędzy w REO oraz odpowiednio dobranej metody homogenizacji. Sformułowano wskazówki przydatne do oceny optymalnego wymiaru REO w zależności od rodzaju splotu.
3
Content available Near-surface mass defect in models of locally heterogeneous solid mechanics
Nahirnyj Taras, Tchervinka Kostiantyn
Acta Mechanica et Automatica
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2019
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Vol. 13, no. 3
205--210
EN
This article deals with the model of the locally heterogeneous elastic body. The model accounts for long-range interaction and describes near-surface non-homogeneity and related size effects. The key systems of model equations are presented. From the viewpoint of the representative volume element, the boundary condition for density and the limits of applicability of the model are discussed. The difference of mass density in the near-surface body region from the reference value (near-surface mass defect) causes a non-zero stressed state. It is indicated on the strong dependence of the surface value of density from the curvature of the surface of thin fibres. The effect of the near-surface mass defect on the stressed state and the size effect of surface stresses have been investigated on an example of a hollow cylinder. Size effect of its strength has been studied as well.
4
Content available Effect of Microstructural Morphology on Microscale Deformation Behavior of Al-4.5Cu-2Mg Alloy
Biswas P., Bhandari R., Mondal M. K., Mandal D.
Archives of Metallurgy and Materials
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2018
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Vol. 63, iss. 4
1575--1586
EN
The microscale deformation behaviour of the Al-4.5Cu-2Mg alloy has been studied to understand the influence of various processing routes and conditions, i.e. the gravity casting with and without grain refiner, the rheocast process and the strain induced melt activation (SIMA) process. The micromechanics based simulations have been carried out on the optical microstructures of the alloy by 2D representative volume elements (RVEs) employing two different boundary conditions. Microstructural morphology, such as the grain size, the shape and the volume fraction of α-Al and binary eutectic phases have a significant effect on the stress and strain distribution and the plastic strain localization of the alloy. It is found that the stress and strain distribution became more uniform with increasing the globularity of the α-Al grain and the α-Al phase volume fraction. The simulated RVEs also reveals that the eutectic phase carries more load, but least ductility with respect to the α-Al phase. The SIMA processed alloy contains more uniform stress distribution with less stress localization which ensures better mechanical property than the gravity cast, grain refined and rheocast alloy.
5
Content available Minimal kinematic boundary conditions for computational homogenization of the permeability coefficient
Wojciechowski M.
Acta Mechanica et Automatica
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2017
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Vol. 11, no. 3
199--203
EN
In the paper, computational homogenization approach is used for recognizing the macroscopic permeability from the microscopic representative volume element (RVE). Flow of water, at both macro and micro level, is assumed to be ruled by Darcy law. A special averaging constraint is used for numerical flow analysis in RVE, which allows to apply macroscopic pressure gradient without the necessity to use directly Dirichlet or Neumann boundary conditions. This approach allows arbitrarily shaped representative volumes and eliminates undesirable boundary effects. Generated effective permeability takes into account the structuring effects, what is an advantage over other homogenization methods, like self-consistent one.
6
Content available remote On the static nature of minimal kinematic boundary conditions for computational homogenisation
Wojciechowski M., Lefik M.
Engineering Transactions
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2016
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Vol. 64, iss. 4
581--587
EN
In the paper, the concept of minimal kinematic boundary conditions (MKBC) for computational homogenisation is considered. In the presented approach, the strain averaging equation is applied to the microscopic representative volume element (RVE) via Lagrange multipliers, which are, in turn, interpreted as macroscopic stresses. It is shown that this formulation fulfil automatically Hill-Mandel macrohomogeneity condition. Also, it is demonstrated, that MKBCs are in fact static, Neumann kind boundary conditions. As a consequence the effective parameters computed with this approach are lower bounds of the true effective values. Numerical analysis illustrating these results is also provided.
7
Content available remote Microstructure measures and the minimum size of a representative volume element: 2D numerical study
Łydżba D., Różański A.
Acta Geophysica
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2014
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Vol. 62, no. 5
1060--1086
EN
In the paper, a numerical study of the size of a representative volume element (RVE) for both the heat flow as well as the linear elasticity problems is presented. A particular two-phase random microstructure is studied and the method is applied to the digital image of reconstructed 2D realization of random media. The minimum size of RVE is deter-mined by the investigation of the convergence of apparent properties as the size of RVE is increasing. Then, two estimates of the minimum RVE size are proposed and it is shown that the estimates are in a good agreement with the results determined by the investigation of the convergence of apparent properties. The minimum size of RVE can be successfully predicted based only on the microstructure morphology. The statistical measures used in this work are: the two-point probability and the lineal-path functions.
8
Content available Two-scale modelling of reactive powder concrete. Part I: representative volume element and solution of the corresponding boundary value problem
Denisiewicz A., Kuczma M.
Civil and Environmental Engineering Reports
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2013
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No. 10
41--61
EN
The article is the first part of a series concerned with the modelling of reactive powder concrete by using a numerical homogenization technique. This technique is a multi-scale modelling approach. Specifically, in this paper a two scale modelling concept was applied. A model of reactive powder concrete (RPC) is considered whose behaviour on the macro scale is described on the basis of the phenomena occurring in the microstructure of the material. This approach provides the ability to take into account some complex phenomena occurring in the microstructure and their influence on the macroscopic physical and mechanical properties of the material. The method does not require knowledge of the constitutive equation parameters at the macro level. These are determined implicitly for each load increment on the basis of numerical model of a representative volume element,(RVE), which reflects the geometrical layout of particular material phases, their constitutive relations and mutual interactions. In this paper the linearly elastic behaviour of each constituent material is assumed within the small strain range. In solving the boundary value problems formulated on the RVE for RPC, the finite element method was utilized. A number of numerical test examples were solved which illustrate the influence of inhomogeneities on the overall response.
PL
Artykuł jest pierwszą częścią pracy dotyczącej modelowaniu betonów z proszków reaktywnych przy zastosowaniu numerycznej homogenizacji. Technika ta jest podejściem wielkoskalowego modelowania. W tym konkretnym przypadku modelowania dwuskalowego. Zachowanie modelu betonu typu RPC w skali makro (skala punktu materialnego, poziom opisu fenomenologicznego) opisywane jest na podstawie zjawisk zachodzących w mikrostrukturze materiału (mikroskala). Takie podejście daje możliwość uwzględnienia szeregu zjawisk zachodzących w mikrostrukturze na właściwości fizyczne i mechaniczne materiału. Na przykład wpływ mikropęknięć na wytrzymałość betonu. Nie bez znaczenia jest fakt, że metoda nie wymaga znajomości równań konstytutywnych w skali makro, związki te są wyznaczane w sposób niejawny dla każdego przyrostu obciążenia na podstawie numerycznego modelu reprezentatywnego elementu objętościowego RVE. Do wyznaczenia niejawnych związków fizycznych w makroskali niezbędna jest znajomość geometrii mikrostruktury, równań konstytutywnych na poziomie skali mikro oraz ich parametrów. W tej pierwszej części pracy ograniczono się do sformułowania i rozwiązania zagadnienia brzegowego na poziomie mikroskali dla zadanych makronaprężeń na brzegu RVE. Opracowano własny program komputerowy, który generuje w sposób losowy mikrostrukturę RPC i rozwiązuje problem brzegowy zdyskretyzowany metodą elementów skończonych. Praca zawiera wyniki obliczeń zadań testowych.
9
Content available remote Multiscale modelling of stress and strain partitioning in high strength dual phase steels
Asgari A., Ghadbeigi H., Pinna C., Hodgson P.D.
Computer Methods in Materials Science
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2012
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Vol. 12, No. 3
163--174
EN
Multiscale modelling of stress and strain partitioning in DP steel was carried out using both realistic microstructure-based RVE models as well as stochastic microstructures generated by Monte Carlo method. The stochastic microstructure models were shown to resemble that of realistic microstructures, enabling research on the specific aspects of the microstructure that could be difficult to control and study during experimental work. One such feature of the realistic microstructures studied in this work was the grain size and microstructure morphology. The microstructures were generated with varying average grain sizes while all other parameters, such as boundary conditions, material properties and volume fractions of martensite and ferrite were kept constant. It is found that the effect of grain size is much more pronounced during the initial localisation of the plastic deformation at and around the interface of the phases. In addition, the decrease in ductility and increase in strength of the DP steels are directly related to the refinement of grain sizes of each phase and the stress-strain partitioning in between them.
PL
Wieloskalowe modelowanie rozdziału naprężeń i odkształceń w stalach dwufazowych (DP) przeprowadzono wykorzystując zarówno reprezentatywny element objętości (ang. representative volume element RVE) z rzeczywistą mikrostrukturą jak i stochastyczną mikrostrukturę wygenerowaną metodą Monte Carlo. Stochastycznie wygenerowane mikrostruktury przypominały te rzeczywiste, umożliwiając badanie specyficznych cech mikrostruktury trudnych do analizowania metodami doświadczalnymi. Jedną z takich cech była wielkość ziarna i morfologia ziaren. Mikrostruktury wygenerowano stosując różne średnie wielkości ziarna podczas gdy pozostałe parametry, takie jak warunki brzegowe, własności materiału oraz ułamek objętości martenzytu i ferrytu pozostawały niezmienione. W konsekwencji zaobserwowano, że wpływ wielkości ziarna jest bardzie widoczny w czasie inicjalizacji lokalizacji odkształcenia plastycznego oraz wokół powierzchni międzyfazowych. Dodatkowo stwierdzono, że spadek plastyczności i wzrost wytrzymałości stali DP są związane z rozdrobnieniem ziarna każdej z faz oraz z rozdziałem naprężeń i odkształceń między fazami.
10
Content available remote Numerical modelling and verification of Polish ventricular assist device
Milenin A., Kopernik M., Jurkojć D., Gawlikowski M., Rusin T., Darłak M., Kustosz R.
Acta of Bioengineering and Biomechanics
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2012
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Vol. 14, no. 3
49-57
EN
The developed multiscale model of blood chamber of POLVAD (Polish ventricular assist device) was introduced. The tension test for polymer and digital image correlation (DIC) were performed for verification of the strains and displacements obtained in the numerical model of POLVAD_EXT. The numerical simulations were carried out in conditions given in the experiment to compare the results obtained on external surfaces of blood chamber of the POLVAD_EXT. The examined polymer applied in the POLVADs is sensitive to changes of temperature and this observation is considered in all prepared numerical models. The comparison of experimental and numerical results shows acceptable coincidence. There are some heterogeneous distributions of strains in experiment with respect to analysis of computed parameters. The comparison of two versions of blood chambers (POLVAD and POLVAD_EXT) in numerical analysis shows that POLVAD_EXT construction is better with respect to analysis of strain and stress. The maximum values of computed parameters are located in the regions between connectors on the internal surfaces of blood chambers of POLVAD.
11
Content available remote From digital image of microstructure to the size of representative volume element: B4C/Al composite
Różański A., Łydżba D.
Studia Geotechnica et Mechanica
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2011
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Vol. 33, nr 1
55-68
EN
In the field of micromechanics, the notion of representative volume element (RVE) and its quantitative definition are of the paramount importance. The definitions of RVE, used by scientists for different purposes, are mathematically strict but do not quantify its size. Furthermore, all the methods of RVE size determination (available in a voluminous literature) require a large number of numerical calculations like, for instance, those of finite element or other numerical techniques. In this paper, it is shown that the size of RVE can be evaluated based only on the morphology of microstructure that is involved in the statistical microstructure descriptor, namely the two-point correlation function. A methodology is applied to the digital image of the reconstructed 2D realization of the boron-carbide/aluminum (B4C/Al) composite. The condition for the minimum size of RVE used in the numerical procedure has been formulated in previous work of authors. The size of RVE is determined for different values of estimation error and the contrast in phase properties. The method is verified by performing numerical calculations of effective thermal conductivity coefficient.
12
Content available Numerical calculations of RVE dimensions for two-phase material
Miedzińska D., Niezgoda T.
Journal of KONES
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2011
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Vol. 18, No. 2
303-310
EN
A representative volume element (RVE) is a statistical representation of typical material properties. It should contain enough information on the microstructure thereby be sufficiently smaller than the macroscopic structural dimensions. The paper deals with the numerical calculations of the dimensions of the RVE for a two-phase material microstructure. Two and three dimensional models are taken into consideration. The structure of the samples are developed on the base of randomization of elements belonging to one of the phases. The phases volume share is 50/50%. The following series of the models are analyzed: from 10 x 10 to 100 x 100 elements for 2D samples and from 10 x 10 x 10 to 100 x 100 x 100 elements for 3D samples. The element characteristic dimension is 10 jm. The elastic behavior of the base materials (magnesium and alumina) is taken into account. The quasi-static compression tests of the developed structures are carried out with the use of LS-DYNA computer code. The results are presented as the equivalent Young modulus values and compared to the calculations based on the rule of mixtures. The stabilization of the achieved results allows to assess the dimensions of the RVE for two-phase material with random distribution.
13
Content available remote Microscale analysis of strain-stress state for TiN nanocoating of POLVAD and POLVAD_EXT
Milenin A., Kopernik M.
Acta of Bioengineering and Biomechanics
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2011
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Vol. 13, no. 4
11-19
EN
The main purpose of the research was to develop the micromodel of biocompatible titanium nitride nanocoating deposited on polymer by pulsed laser deposition method in blood chambers of Polish ventricular assist devices: POLVAD and POLVAD_EXT. The analysis of the parameters of micromodel crucial for the phenomenon of loss of cohesion occurring between coating and substrate was carried out as well. The micromodel takes into account residual stress, material model of nanocoating, stress resulting from blood pressure in chamber, the thickness of coating and wave parameters of nanocoating (wavelength and antinode). The investigation shows that thickness and residual stress are the most influential parameters. The phenomenon of the loss of cohesion will be observed more frequently for thicker coatings with higher residual stresses.
14
Content available remote Mesoscopic modelling of strain localization in concrete
Skarżyński Ł., Tejchman J.
Archives of Civil Engineering
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2009
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Vol. 55, nr 4
503-526
EN
The paper deals with strain localization in concrete subjected to uniaxial tension. The material was described at the meso-scale as a random heterogeneous three-phase one. All three phases were modelled with an isotropic scalar damage constitutive model. To ensure the mesh-independent numerical results, to preserve the well-posedness of the boundary value problem, and to describe properly strain localization in concrete, the model was enhanced by a characteristic length of micro-structure by means of the non-local theory. The effect of a specimen size, random distribution of aggregate, aggregate density, characteristic length and non-locality range on both strain localization and stress-strain curves was numerically investigated. The existence of a representative volume element (RVE) was discussed.
PL
Artykuł omawia lokalizacje odkształceń w betonie podczas jednoosiowego rozciągania. Materiał został opisany na poziomie skali mezo jako losowy niejednorodny materiał trójfazowy. Wszystkie fazy były modelowane przy zastosowaniu izotropowego modelu zniszczeniowego z degradacją sztywności. W celu zapewnienia niezależności wyników numerycznych od siatki, poprawnego postawienia problemu brzegowego i właściwego opisu lokalizacji odkształceń w betonie, model został rozszerzony o długość charakterystyczną mikrostruktury za pomocą teorii nielokalnej. Wykonano analizę wpływu wielkości próbki, losowego rozkładu kruszywa, zagęszczenia kruszywa, długości charakterystycznej oraz zakresu nielokalności na lokalizację odkształceń oraz krzywą naprężenia w funkcji odkształcenia. Przedyskutowano istnienie wielkości reprezentatywnej objętości materiału (RVE).
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