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==1 Title, abstract and keywords==
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==Abstract==
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Spatial coarse-graining techniques are powerful methods to overcome the computational limits of molecular dynamics. In order to extend atomistic simulations of crystalline materials to the micronscale and beyond, the quasicontinuum (QC) approximation [<span id='cite-1'></span>[[#1|1]]-<span id='cite-3'></span>[[#3|3]]] reduces large crystalline atomistic ensembles to a significantly smaller number of representative atoms with suitable interpolation schemes to infer the motion of all particles. In contrast to most other concurrent multiscale techniques, this allows for the simulation of large systems solely based on interatomic potentials and thus without the need for (oftentimes phenomenological) continuum constitutive models. This promises superior accuracy for predictive simulations at the meso- and macroscales.
  
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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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Here, we will discuss one such coarse-graining scheme, viz. a fully-nonlocal energy-based QC technique [<span id='cite-4'></span>[[#4|4]],<span id='cite-5'></span>[[#5|5]]] which excels by minimal approximation errors and vanishing force artefacts (a common problem in concurrent scale-coupling methods) [<span id='cite-6'></span>[[#6|6]]]. Our model is equipped with automatic adaptation techniques to effectively tie atomistic resolution to regions of interest while efficiently coarse-graining the remaining solid. We review both mesh-based and meshless formulations. The former adopts methods from finite elements (using an affine interpolation on a Delaunay triangulation), whereas the latter is based on local maximum-entropy interpolation schemes. In both cases, the result is a computational toolbox for coarse-grained atomistic simulations, whose computational challenges are quite similar to those of molecular dynamics. Finite temperature extensions as well as coarse-graining in time can be incorporated in the presented framework [<span id='cite-7'></span>[[#7|7]]].
  
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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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We will review the underlying theory and give an overview of the state of the art, followed by a suite of numerical examples demonstrating the benefits and limitations of the nonlocal energy-based QC method. Examples range from nanoindentation and material failure to defect interactions and nanoscale mechanical size effects.
  
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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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== Recording of the presentation ==
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{| style="font-size:120%; color: #222222; border: 1px solid darkgray; background: #f3f3f3; table-layout: fixed; width:100%;"
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==2 The main text==
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| {{#evt:service=youtube|id=https://youtu.be/_-uI-s5Uo78 alignment=center}}
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You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
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|- style="text-align: center;"  
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| Location: Technical University of Catalonia (UPC), Vertex Building.  
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Most of the papers in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific journals in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.
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|- style="text-align: center;"
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| Date: 28 - 30 September 2015, Barcelona, Spain.
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===2.1 Subsections===
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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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===2.2 General guidelines===
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:*  Use decimal points (not commas); use a space for thousands (10 000 and above).
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:*  Follow internationally accepted rules and conventions. In particular use the international system of units (SI). If other quantities are mentioned, give their equivalent in SI.
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Please insert tables as editable text and not as images. Tables should be placed next to the relevant text in the article. Number tables consecutively in accordance with their appearance in the text (<span id='cite-_Ref382560620'></span>[[#_Ref382560620|table 1]], table 2, etc.) and place any table notes below the table body. Be sparing in the use of tables and ensure that the data presented in them do not duplicate results described elsewhere in the article.
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{| style="margin: 1em auto 1em auto;border: 1pt solid black;border-collapse: collapse;"
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| style="text-align: center;"|Thickness
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| style="text-align: center;"|3.175 mm
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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;"|1107 kg/m<sup>3</sup>
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<span style="text-align: center; font-size: 75%;">Table 1: Material properties</span></div>
 
  
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Graphics may be inserted directly in the document and positioned as they should appear in the final manuscript.
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== General Information ==
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* Location: Technical University of Catalonia (UPC), Barcelona, Spain.
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* Date: 28 - 30 September 2015
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* Secretariat: [//www.cimne.com/ International Center for Numerical Methods in Engineering (CIMNE)].
  
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== External Links ==
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* [//congress.cimne.com/particles2015/frontal/default.asp Particles 2015] Official Website of the Conference.
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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<span style="text-align: center; font-size: 75%;">Figure 1. Scipedia logo.</span></div>
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Number the figures according to their sequence in the text (<span id='cite-_Ref448852946'></span>[[#_Ref448852946|figure 1]], figure 2, etc.). Ensure that each illustration has a caption. A caption should comprise a brief title. Keep text in the illustrations themselves to a minimum but explain all symbols and abbreviations used. Try to keep the resolution of the figures to a minimum of 300 dpi. If a finer resolution is required, the figure can be inserted as supplementary material
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==References==
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For tabular summations that do not deserve to be presented as a table, lists are often used. Lists may be either numbered or bulleted. Below you see examples of both.
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(1)
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===2.4 Supplementary material===
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Supplementary material can be inserted to support and enhance your article. This includes video material, animation sequences, background datasets, computational models, sound clips and more. In order to ensure that your material is directly usable, please provide the files with a preferred maximum size of 50 MB. Please supply a concise and descriptive caption for each file.
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==3 Bibliography==
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Citations in text will follow a citation-sequence system (i.e. sources are numbered by order of reference so that the first reference cited in the paper is [<span id='cite-1'></span>[[#1|1]]], the second [<span id='cite-2'></span>[[#2|2]]], and so on) with the number of the reference in square brackets. Once a source has been cited, the same number is used in all subsequent references. If the numbers are not in a continuous sequence, use commas (with no spaces) between numbers. If you have more than two numbers in a continuous sequence, use the first and last number of the sequence joined by a hyphen (e.g. [<span id='cite-1'></span>[[#1|1]], <span id='cite-3'></span>[[#3|3]]] or [<span id='cite-2'></span>[[#2|2]]-<span id='cite-2'></span>[[#4|4]]]).
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You should ensure that all references are cited in the text and that the reference list. References should preferably refer to papers published in Scipedia. Unpublished results should not be included in the reference list, but can be mentioned in the text. The reference data must be updated once publication is ready. Complete bibliographic information for all cited references must be given following the standards in the field (IEEE and ISO 690 standards are recommended). If possible, a hyperlink to the referenced publication should be given. See examples for Scipedia’s articles [<span id='cite-1'></span>[[#1|1]]], other journal articles [<span id='cite-2'></span>[[#2|2]]], books [<span id='cite-3'></span>[[#3|3]]], book chapter [<span id='cite-4'></span>[[#4|4]]], conference proceedings [<span id='cite-5'></span>[[#5|5]]], and online documents [<span id='cite-6'></span>[[#6|6]]], shown in references section below.
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==4 Acknowledgments==
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==5 References==
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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]]] E. Tadmor, M. Ortiz, and R. Phillips, “Quasicontinuum analysis of defects in solids”, Philos.
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Mag. A 73, 1529-1563 (1996).
 
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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]]] V. Shenoy, R. Miller, E. Tadmor, D. Rodney, R. Phillips and M. Ortiz, “An adaptive finite
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element approach to atomic-scale mechanics – the quasicontinuum method”, J. Mech. Phys.
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Solids 47, 611-642 (1999).
 
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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]]] J. Knap and M. Ortiz, “An analysis of the quasicontinuum method”, J. Mech. Phys. Solids 49,
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1899–1923 (2001).
 
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[[#cite-4|[4]]] D. M. Kochmann and G. N. Venturini, “A meshless quasicontinuum method based on local
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maximum-entropy interpolation”, Mod. Sim. Mat. Sci. Eng. 22, 034007 (2014).
 
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[[#cite-5|[5]]] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.
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[[#cite-5|[5]]] M. Espanol, D. M. Kochmann, S. Conti and M. Ortiz, “A Γ-convergence analysis of the
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quasicontinumm method”, Multiscale Model. Simul. 11, 766–794 (2013).
 
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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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[[#cite-6|[6]]] J. S. Amelang, G. N. Venturini and D. M. Kochmann, “Summation rules for a fully-nonlocal
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energy-based quasicontinuum method”, J. Mech. Phys. Solids, under review (2014).
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<div id="7"></div>
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[[#cite-7|[7]]] G. Venturini, K. Wang, I. Romero, P. Ariza and M. Ortiz, “Atomistic long-term simulation of
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heat and mass transport”, J. Mech. Phys. Solids 73, 242-268 (2014).

Latest revision as of 12:21, 20 July 2016

Abstract

Spatial coarse-graining techniques are powerful methods to overcome the computational limits of molecular dynamics. In order to extend atomistic simulations of crystalline materials to the micronscale and beyond, the quasicontinuum (QC) approximation [1-3] reduces large crystalline atomistic ensembles to a significantly smaller number of representative atoms with suitable interpolation schemes to infer the motion of all particles. In contrast to most other concurrent multiscale techniques, this allows for the simulation of large systems solely based on interatomic potentials and thus without the need for (oftentimes phenomenological) continuum constitutive models. This promises superior accuracy for predictive simulations at the meso- and macroscales.

Here, we will discuss one such coarse-graining scheme, viz. a fully-nonlocal energy-based QC technique [4,5] which excels by minimal approximation errors and vanishing force artefacts (a common problem in concurrent scale-coupling methods) [6]. Our model is equipped with automatic adaptation techniques to effectively tie atomistic resolution to regions of interest while efficiently coarse-graining the remaining solid. We review both mesh-based and meshless formulations. The former adopts methods from finite elements (using an affine interpolation on a Delaunay triangulation), whereas the latter is based on local maximum-entropy interpolation schemes. In both cases, the result is a computational toolbox for coarse-grained atomistic simulations, whose computational challenges are quite similar to those of molecular dynamics. Finite temperature extensions as well as coarse-graining in time can be incorporated in the presented framework [7].

We will review the underlying theory and give an overview of the state of the art, followed by a suite of numerical examples demonstrating the benefits and limitations of the nonlocal energy-based QC method. Examples range from nanoindentation and material failure to defect interactions and nanoscale mechanical size effects.

Recording of the presentation

Location: Technical University of Catalonia (UPC), Vertex Building.
Date: 28 - 30 September 2015, Barcelona, Spain.

General Information

External Links

References

[1] E. Tadmor, M. Ortiz, and R. Phillips, “Quasicontinuum analysis of defects in solids”, Philos. Mag. A 73, 1529-1563 (1996).

[2] V. Shenoy, R. Miller, E. Tadmor, D. Rodney, R. Phillips and M. Ortiz, “An adaptive finite element approach to atomic-scale mechanics – the quasicontinuum method”, J. Mech. Phys. Solids 47, 611-642 (1999).

[3] J. Knap and M. Ortiz, “An analysis of the quasicontinuum method”, J. Mech. Phys. Solids 49, 1899–1923 (2001).

[4] D. M. Kochmann and G. N. Venturini, “A meshless quasicontinuum method based on local maximum-entropy interpolation”, Mod. Sim. Mat. Sci. Eng. 22, 034007 (2014).

[5] M. Espanol, D. M. Kochmann, S. Conti and M. Ortiz, “A Γ-convergence analysis of the quasicontinumm method”, Multiscale Model. Simul. 11, 766–794 (2013).

[6] J. S. Amelang, G. N. Venturini and D. M. Kochmann, “Summation rules for a fully-nonlocal energy-based quasicontinuum method”, J. Mech. Phys. Solids, under review (2014).

[7] G. Venturini, K. Wang, I. Romero, P. Ariza and M. Ortiz, “Atomistic long-term simulation of heat and mass transport”, J. Mech. Phys. Solids 73, 242-268 (2014).

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