Determination of the size of the representative volume element for random composites: statistical and numerical approach
01 Jun 2003-International Journal of Solids and Structures (Pergamon)-Vol. 40, Iss: 13, pp 3647-3679
TL;DR: In this article, a quantitative definition of the representative volume element (RVE) size is proposed, which can be associated with a given precision of the estimation of the overall property and the number of realizations of a given volume V of microstructure that one is able to consider.
About: This article is published in International Journal of Solids and Structures.The article was published on 2003-06-01. It has received 1772 citations till now. The article focuses on the topics: Representative elementary volume.
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TL;DR: Vonoi tessellations are used and are shown to include morphological properties that make them particularly challenging to mesh with high element quality, and the results are mainly illustrated by the high-quality meshing of polycrystals with large number of grains.
815 citations
TL;DR: In this article, various formats of gradient elasticity and their performance in static and dynamic applications are discussed and an overview of length scale identification and quantification procedures is given, together with the variationally consistent boundary conditions.
723 citations
Cites background from "Determination of the size of the re..."
...In this approach, the question ‘‘how large is the length scale?’’ is in fact rephrased as ‘‘how large is the RVE size?’’ Many studies have been devoted to the quantification of RVE sizes for randomly heterogeneous materials, and the general trends are that the RVE size increases with increased contrast in material properties, see for instance (Kanit et al., 2003; Gitman et al., 2006)....
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TL;DR: In this paper, the concept of representative volume element (RVE) is analyzed for elastic materials and the results were based on a statistical analysis of numerical experiments, where tests have been performed on a random heterogeneous material.
587 citations
TL;DR: In this paper, the authors focus on the scale over which homogenization is being carried out, called the mesoscale, separating the microscale (level of microheterogeneities) from the macroscale (Level of RVE).
515 citations
Cites methods from "Determination of the size of the re..."
...Various quantitative estimates of d-dependence—or, what is called finite-size scaling in condensed matter physics—were computed for many different materials by Huet and co-workers, this author and co-workers; see also [26], and [27]....
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TL;DR: An overview of the results obtained with lattice models of the fracture, highlighting the relations with statistical physics theories and more conventional fracture mechanics approaches is presented.
Abstract: Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in which a network of elastic beams, bonds, or electrical fuses with random failure thresholds are subject to an increasing external load. These models describe on a qualitative level the failure processes of real, brittle, or quasi-brittle materials. This has been particularly important in solving the classical engineering problems of material strength: the size dependence of maximum stress and its sample-to-sample statistical fluctuations. At the same time, lattice models pose many new fundamental questions in statistical physics, such as the relation between fracture and phase transitions. Experimental results point out to the existence of an intriguing crackling noise in the acoustic emission and of self-affine fractals in the crack surface morphology. Recent advances ...
464 citations
References
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Book•
11 Feb 1984
TL;DR: This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.
Abstract: Image Processing and Mathematical Morphology-Frank Y. Shih 2009-03-23 In the development of digital multimedia, the importance and impact of image processing and mathematical morphology are well documented in areas ranging from automated vision detection and inspection to object recognition, image analysis and pattern recognition. Those working in these ever-evolving fields require a solid grasp of basic fundamentals, theory, and related applications—and few books can provide the unique tools for learning contained in this text. Image Processing and Mathematical Morphology: Fundamentals and Applications is a comprehensive, wide-ranging overview of morphological mechanisms and techniques and their relation to image processing. More than merely a tutorial on vital technical information, the book places this knowledge into a theoretical framework. This helps readers analyze key principles and architectures and then use the author’s novel ideas on implementation of advanced algorithms to formulate a practical and detailed plan to develop and foster their own ideas. The book: Presents the history and state-of-the-art techniques related to image morphological processing, with numerous practical examples Gives readers a clear tutorial on complex technology and other tools that rely on their intuition for a clear understanding of the subject Includes an updated bibliography and useful graphs and illustrations Examines several new algorithms in great detail so that readers can adapt them to derive their own solution approaches This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.
9,566 citations
"Determination of the size of the re..." refers background in this paper
...If this limit is reached before h !1 , for example, for a value h ¼ A, the points of the structure with a distance larger than A are not correlated (Matheron, 1971; Jeulin, 1981; Serra, 1982; Jeulin, 2001)....
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...To describe the geometrical dispersion, the state of two points x1 and x2 with the separation h can be tested, without considering what happens between the two points (Matheron, 1971; Jeulin, 1981; Serra, 1982; Coster and Chermant, 1989; Jeulin, 2001)....
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TL;DR: In this paper, the authors derived upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry.
Abstract: Variational principles in the linear theory of elasticity, involving the elastic polarization tensor, have been applied to the derivation of upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry. When the ratios between the different phase moduli are not too large the bounds derived are close enough to provide a good estimate for the effective moduli. Comparison of theoretical and experimental results for a two-phase alloy showed good agreement.
5,224 citations
"Determination of the size of the re..." refers background in this paper
...Hashin and Shtrikmans bounds incorporate the notion of isotropic distribution of phases ( Hashin and Shtrikman, 1963 )....
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...Hashin and Shtrikman s bounds incorporate the notion of isotropic distribution of phases (Hashin and Shtrikman, 1963)....
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Book•
01 Jul 1993TL;DR: In this paper, the authors introduce basic elements of elasticity theory: foundations geometric foundations, kinematic foundations, dynamic foundations, constitutive relations elastostatic problems of linear elasticity boundary value problems and extremum principles three-dimensional problems solution of singular problems.
Abstract: Part 1 Overall properties of heterogeneous solids: aggregate properties and averaging methods aggregate properties, averaging methods elastic solids with microcavities and microcracks linearly elastic solids, elastic solids with traction-free defects, elastic solids with micrcavities, elastic solids with microcracks elastic solids with micro-inclusions overall elastic modulus and compliance tensors, examples o elastic solids with elastic micro-inclusions, upper and lower bounds for overall elastic moduli, self-consistent differential and related averaging methods, Eshelby's tensor and related topics solids with periodic microstructure general properties and field equations, overall properties of solids with periodic microstructure, mirror-image decomposition of periodic fields. Part 2 Introduction to basic elements of elasticity theory: foundations geometric foundations, kinematic foundations, dynamic foundations, constitutive relations elastostatic problems of linear elasticity boundary-value problems and extremum principles three-dimensional problems solution of singular problems. Appendix: references.
2,544 citations
"Determination of the size of the re..." refers background in this paper
...Theycan be found in reference extended papers and textbooks like Willis (1981), Sanchez-Palencia and Zaoui (1987) and Nemat-Nasser and Hori (1993) or, more recently, Suquet (1997), Ponte Casta~ n neda and Suquet (1987), Bornert et al. (2001), Besson et al. (2001) and Jeulin and Ostoja-Starzewski (2001), where extensions to nonlinear properties are also proposed....
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TL;DR: In this article, anwendungsmoglichkeiten der Methode werden besprochen, in which experimentelle Vergleichswerte weichen von den berechneten etwas ab, was beweist, das die Experimente nicht den von der Theorie geforderten idealen Bedingungen genugt haben.
Abstract: Mit Hilfe des Begriffes der elastischen Polarisierbarkeit konnen die elastischen Konstanten des makroskopisch isotropen Vielkristalls aus den Einkristallkonstanten exakt ausgerechnet werden. Im Falle des Aggregats aus kubischen Kristalliten, in dem die Bestimmung des Kompressionsmoduls trivial ist, folgt der Schubmodul aus einer Gleichung 3. Grades [Gl. (22)], in der Kombinationen der Einkristallhauptkonstanten als Koeffizienten auftreten. Die experimentellen Vergleichswerte weichen von den berechneten etwas ab, was beweist, das die Experimente nicht den von der Theorie geforderten idealen Bedingungen genugt haben. Weitere Anwendungsmoglichkeiten der Methode werden besprochen.
1,433 citations
"Determination of the size of the re..." refers background in this paper
...In contrast, the self-consistent (SC) scheme, presented by Beran (1968) for thermal conductivity and by Hershey (1954) and Kr€oner (1958) for linear polycrystals, refers to a disordered distribution of phases....
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