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International Journal for Multiscale Computational Engineering
Jacob Fish (open in a new tab) Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA
J. Tinsley Oden (open in a new tab) Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
Somnath Ghosh (open in a new tab) Departments of Civil & Systems Engineering, Mechanical Engineering, and Material Science Engineering, Johns Hopkins University, Baltimore, MD, USA
Arif Masud (open in a new tab) Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 3129E Newmark Civil Engineering Laboratory, MC-250, Urbana, Illinois 61801-2352, USA
Klaus Hackl (open in a new tab) Institute of Mechanics of Materials, Ruhr-University Bochum, Bochum, 44721, Germany
Karel Matous (open in a new tab) Department of Aerospace and Mechanical Engineering, Center for Shock Wave-Processing of Advanced Reactive Materials, University of Notre Dame, Notre Dame, Indiana 46556, USA
Thomas J.R. Hughes (open in a new tab) Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 East 24th Street, C0200, Austin, TX 78712-1229, USA
Caglar Oskay (open in a new tab) Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, Tennessee 37235, USA
Tamar Schlick (open in a new tab) Department of Chemistry, New York University, New York, New York 10003, USA; Courant Institute of Mathematical Sciences, New York University, New York, New York, 10012, USA; NYU-ECNU Center for Computational Chemistry, NYU Shanghai, China
The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.4 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.3 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 2.2 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00034 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.46 SJR: 0.333 SNIP: 0.606 CiteScore™:: 3.1 H-Index: 31

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APPLICATION OF THE MULTISCALE FEM TO THE MODELING OF NONLINEAR COMPOSITES WITH A RANDOM MICROSTRUCTURE

pages 213-227
DOI: 10.1615/IntJMultCompEng.2012002059
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RÉSUMÉ

In this contribution the properties and application of the multiscale finite element program MSFEAP are presented. This code is developed on basis of coupling the homogenization theory with the finite element method. According to this concept, the investigation of an appropriately chosen representative volume element yields the material parameters needed for the simulation of a macroscopic body. The connection of scales is based on the principle of volume averaging and the Hill-Mandel macrohomogeneity condition. The latter leads to the determination of different types of boundary conditions for the representative volume element and in this way to the postulation of a well-posed problem at this level. The numerical examples presented in the contribution investigate the effective material behavior of microporous media. An isotropic and a transversally anisotropic microstructure are simulated by choosing an appropriate orientation and geometry of the representative volume element in each Gauss point. The results are verified by comparing them with Hashin-Shtrikman's analytic bounds. However, the chosen examples should be understood as simply an illustration of the program application, while its main feature is a modular structure suitable for further development.

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