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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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Computational Evaluation of Strain Gradient Elasticity Constants

page 21
DOI: 10.1615/IntJMultCompEng.v2.i4.60
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RESUMO

Classical effective descriptions of heterogeneous materials fail to capture the influence of the spatial scale of the heterogeneity on the overall response of components. This influence may become important when the scale at which the effective continuum fields vary approaches that of the microstructure of the material and may then give rise to size effects and other deviations from the classical theory. These effects can be successfully captured by continuum theories that include a material length scale, such as strain gradient theories. However, the precise relation between the microstructure, on the one hand, and the length scale and other properties of the effective modeling, on the other, are usually unknown. A rigorous link between these two scales of observation is provided by an extension of the classical asymptotic homogenization theory, which was proposed by Smyshlyaev and Cherednichenko (J. Mech. Phys. Solids 48:1325−1358, 2000) for the scalar problem of antiplane shear. In the present contribution, this method is extended to three-dimensional linear elasticity. It requires the solution of a series of boundary value problems on the periodic cell that characterizes the microstructure. A finite element solution strategy is developed for this purpose. The resulting fields can be used to determine the effective higher-order elasticity constants required in the Toupin-Mindlin strain gradient theory. The method has been applied to a matrix-inclusion composite, showing that higher-order terms become more important as the stiffness contrast between inclusion and matrix increases.

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