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==1 Title, abstract and keywords==
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==Abstract==
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The methods of two-scale analysis based on the method of numerical material testing (NMT) [<span id='cite-1'></span>[[#1|1]]] and plate testing (NPT) [<span id='cite-2'></span>[[#2|2]]] have indisputable superiority over FE2 -type micro-macro coupling schemes, though there are some issues to be resolved or examined. In particular, the decoupling of micro- and macroscopic analyses makes the homogenization-based two-scale analysis methods computationally law-cost and thus practical in view of industrial applications, but at the same time requires us to prepare reliable macroscopic constitutive models. To identify promising research directions for two-scale analyses, we introduce three selected topics described below to discuss the advantages and challenges of NMT and NPT.
  
Your paper should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.
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A major advantage in the first topic is that macroscopic inelastic constitutive models for a variety of composite materials can easily be determined with reference to the material models assumed for periodic microstructures (unit cells), if the small strain assumption is valid. However, NMTs with finite deformation of resins often cause some trouble. That is, even though isotropic multiplicative finite visco-plastic models is originally developed and introduced for NMTs, the formulation of the corresponding anisotropic model for macroscopic analyses is not always possible.
  
Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
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The second topic arises from the method of NPT for composite plates, which enables us to evaluate the relationship between macroscopic resultant stresses and generalized strains. The originally formulated microscopic problem is featured by the in-plane periodic boundary conditions, which properly reproduces all the plate’s deformation modes. If we confine ourselves to linearly elastic material behavior, even the topology optimization of microscopic plate’s cross-sections is successfully conducted to maximize the performance at macro-scale. Nonetheless, we may not meet a macroscopic plate model that can accommodate the NPT results of nonlinear material behavior assumed for the in-plane unit cell.
  
An abstract is required for every paper; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself.
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The third subject of study is related to the method of isogeometric analyses (IGA) [<span id='cite-3'></span>[[#3|3]]] for NMT and NPT. Since the treatment of the combination of different materials in IGA models is not trivial especially along with periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex-full property of IGA and the in-plane periodicity. A promising coping technique is proposed and numerically demonstrated.  
  
==2 The main text==
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== Recording of the presentation ==
 
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|- style="text-align: center;"  
 
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| Location: Technical University of Catalonia (UPC), Vertex Building.  
===2.1 Subsections===
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|- style="text-align: center;"
 
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| Date: 1 - 3 September 2015, Barcelona, Spain.
Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.
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<span id='_Ref382560620'></span>
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{| style="margin: 1em auto 1em auto;border: 1pt solid black;border-collapse: collapse;"
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|-
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| style="text-align: center;"|Thickness
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| style="text-align: center;"|3.175 mm
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|-
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| style="text-align: center;"|Young Modulus
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| style="text-align: center;"|12.74 MPa
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| style="text-align: center;"|Poisson coefficient
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| style="text-align: center;"|0.25
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| style="text-align: center;"|Density
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| style="text-align: center;"|1107 kg/m<sup>3</sup>
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 
<span style="text-align: center; font-size: 75%;">Table 1: Material properties</span></div>
 
  
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== General Information ==
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* Location: Technical University of Catalonia (UPC), Barcelona, Spain.
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* Date: 1 - 3 September 2015
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{| style="width: 100%;"
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| style="vertical-align: top;"| <math>{\nabla }^{2}\phi =0</math>
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| style="text-align: right;"|<span id='_Ref424030152'></span>
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(1)
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|}
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===2.4 Supplementary material===
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==3 Bibliography==
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==4 Acknowledgments==
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Acknowledgments should be inserted at the end of the paper, before the references section.
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==5 References==
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<span id='_Ref449083719'></span>
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[[#cite-1|[1]]] Author, A. and Author, B. (Year) Title of the article. Title of the Journal. Article code. Available: [http://www.scipedia.com/ucode. http://www.scipedia.com/ucode.]
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[[#cite-1|[1]]] K. Terada, J. Kato, N. Hirayama, T. Inugai and K. Yamamoto, “A method of two-scale analysis
 
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with micro-macro decoupling scheme: application to hyperelastic composite materials”, Comput.
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Mech. 52, 1199-1219, (2013).
 
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[[#cite-2|[2]]] Author, A. and Author, B. (Year) Title of the article. Title of the Journal. Volume number, first page-last page.
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[[#cite-2|[2]]] K. Terada, N. Hirayama, K. Yamamoto, M. Muramatsu, S. Matsubara and S. Nishi, “Numerical
 
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plate testing for linear two-scale analyses of composite plates with in-plane periodicity”, Int. J.
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Num. Meth. Engng, in press.
 
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[[#cite-3|[3]]] Author, C. (Year). Title of work: Subtitle (edition.). Volume(s). Place of publication: Publisher.
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[[#cite-3|[3]]] T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, “Isogeometric analysis: CAD, finite elements,
 
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NURBS, exact geometry and mesh refinement”, Comput. Meth. Appl. Mech. Engng. 194.
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[[#cite-4|[4]]] Author of Part, D. (Year). Title of chapter or part. In A. Editor & B. Editor (Eds.), Title: Subtitle of book (edition, inclusive page numbers). Place of publication: Publisher.
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[[#cite-6|[6]]] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: [http://www.scipedia.com/document.pdf http://www.scipedia.com/document.pdf]. [Accessed day, month and year].
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Latest revision as of 15:39, 19 July 2016

Abstract

The methods of two-scale analysis based on the method of numerical material testing (NMT) [1] and plate testing (NPT) [2] have indisputable superiority over FE2 -type micro-macro coupling schemes, though there are some issues to be resolved or examined. In particular, the decoupling of micro- and macroscopic analyses makes the homogenization-based two-scale analysis methods computationally law-cost and thus practical in view of industrial applications, but at the same time requires us to prepare reliable macroscopic constitutive models. To identify promising research directions for two-scale analyses, we introduce three selected topics described below to discuss the advantages and challenges of NMT and NPT.

A major advantage in the first topic is that macroscopic inelastic constitutive models for a variety of composite materials can easily be determined with reference to the material models assumed for periodic microstructures (unit cells), if the small strain assumption is valid. However, NMTs with finite deformation of resins often cause some trouble. That is, even though isotropic multiplicative finite visco-plastic models is originally developed and introduced for NMTs, the formulation of the corresponding anisotropic model for macroscopic analyses is not always possible.

The second topic arises from the method of NPT for composite plates, which enables us to evaluate the relationship between macroscopic resultant stresses and generalized strains. The originally formulated microscopic problem is featured by the in-plane periodic boundary conditions, which properly reproduces all the plate’s deformation modes. If we confine ourselves to linearly elastic material behavior, even the topology optimization of microscopic plate’s cross-sections is successfully conducted to maximize the performance at macro-scale. Nonetheless, we may not meet a macroscopic plate model that can accommodate the NPT results of nonlinear material behavior assumed for the in-plane unit cell.

The third subject of study is related to the method of isogeometric analyses (IGA) [3] for NMT and NPT. Since the treatment of the combination of different materials in IGA models is not trivial especially along with periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex-full property of IGA and the in-plane periodicity. A promising coping technique is proposed and numerically demonstrated.

Recording of the presentation

Location: Technical University of Catalonia (UPC), Vertex Building.
Date: 1 - 3 September 2015, Barcelona, Spain.

General Information

External Links

References

[1] K. Terada, J. Kato, N. Hirayama, T. Inugai and K. Yamamoto, “A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials”, Comput. Mech. 52, 1199-1219, (2013).

[2] K. Terada, N. Hirayama, K. Yamamoto, M. Muramatsu, S. Matsubara and S. Nishi, “Numerical plate testing for linear two-scale analyses of composite plates with in-plane periodicity”, Int. J. Num. Meth. Engng, in press.

[3] T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement”, Comput. Meth. Appl. Mech. Engng. 194.

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