A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties
In this work a spectral stochastic computational scheme is proposed that links the global properties of multi‐phase periodic composites to the geometry and random material properties of their microstructural components. To propagate the uncertainties associated with the material properties to the mi...
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| Veröffentlicht in: | International journal for numerical methods in engineering 2010-07, Vol.83 (1), p.59-90 |
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| container_title | International journal for numerical methods in engineering |
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| creator | Tootkaboni, M. Graham-Brady, L. |
| description | In this work a spectral stochastic computational scheme is proposed that links the global properties of multi‐phase periodic composites to the geometry and random material properties of their microstructural components. To propagate the uncertainties associated with the material properties to the microstructural response the scheme benefits from a combination of homogenization theory built into a finite element framework and the spectral representation of uncertainty based on Hermite Chaos where a probabilistic characterization of the solutions to a set of local problems defined on the period cell is first sought. A full stochastic description of the global (effective) properties is then obtained by averaging the solutions to the forgoing set of local problems over the unit cell. A representative subset of results is compared with the results obtained using Monte Carlo simulation to demonstrate the accuracy of the proposed procedure. Copyright © 2010 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/nme.2829 |
| format | Article |
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J. Numer. Meth. Engng</addtitle><description>In this work a spectral stochastic computational scheme is proposed that links the global properties of multi‐phase periodic composites to the geometry and random material properties of their microstructural components. To propagate the uncertainties associated with the material properties to the microstructural response the scheme benefits from a combination of homogenization theory built into a finite element framework and the spectral representation of uncertainty based on Hermite Chaos where a probabilistic characterization of the solutions to a set of local problems defined on the period cell is first sought. A full stochastic description of the global (effective) properties is then obtained by averaging the solutions to the forgoing set of local problems over the unit cell. A representative subset of results is compared with the results obtained using Monte Carlo simulation to demonstrate the accuracy of the proposed procedure. Copyright © 2010 John Wiley & Sons, Ltd.</description><subject>Computer simulation</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Hermite Chaos expansion</subject><subject>homogenization theory</subject><subject>Homogenizing</subject><subject>Karhunen-Loeve transform</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Methods of scientific computing (including symbolic computation, algebraic computation)</subject><subject>Microstructure</subject><subject>Monte Carlo methods</subject><subject>multi-phase composites</subject><subject>Numerical analysis. Scientific computation</subject><subject>Physics</subject><subject>Sciences and techniques of general use</subject><subject>Solid mechanics</subject><subject>solids</subject><subject>Spectra</subject><subject>stochastic Galerkin</subject><subject>Stochasticity</subject><subject>Structural and continuum mechanics</subject><subject>Uncertainty</subject><issn>0029-5981</issn><issn>1097-0207</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp10LtuFDEUBmALgcQSkHgEN0g0E3yZi11GIQmXzdKAKK0TzzFrGI8H26sQCp4drzIKFZWL853f9k_IS85OOWPizRzwVCihH5ENZ3pomGDDY7KpI910WvGn5FnO3xnjvGNyQ_6c0XCYim-yhQlpXtCWBBPNJdo95OItDVj2caQuJrqPIX7D2f-G4uNMo1uXl0qRLph8HOuGjWGJ2RfM9NaXPU0wjzHQAKWKGr6kWG3xmJ-TJw6mjC_W84R8ubz4fP6u2X66en9-tm2s7HvdgKyv7bTusXO8k3p0TjvVAdxIUG3LgEnegh4VqxM1MhBCazYqPSh-w7WUJ-T1fW69-ucBczHBZ4vTBDPGQza8H7hs20Hyf9SmmHNCZ5bkA6Q7w5k5VmxqxeZYcaWv1lQ41ufqP63PD14IpTkTXXXNvbv1E979N8_sri_W3NX7XPDXg4f0w_SDHDrzdXdlttcfd2_Fh53R8i_q55tp</recordid><startdate>20100702</startdate><enddate>20100702</enddate><creator>Tootkaboni, M.</creator><creator>Graham-Brady, L.</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20100702</creationdate><title>A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties</title><author>Tootkaboni, M. ; Graham-Brady, L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3669-a31505996e5f1539dff9f85aab3a8440a0314a9d80dff8d0a22990d89781b1933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Computer simulation</topic><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Hermite Chaos expansion</topic><topic>homogenization theory</topic><topic>Homogenizing</topic><topic>Karhunen-Loeve transform</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Methods of scientific computing (including symbolic computation, algebraic computation)</topic><topic>Microstructure</topic><topic>Monte Carlo methods</topic><topic>multi-phase composites</topic><topic>Numerical analysis. Scientific computation</topic><topic>Physics</topic><topic>Sciences and techniques of general use</topic><topic>Solid mechanics</topic><topic>solids</topic><topic>Spectra</topic><topic>stochastic Galerkin</topic><topic>Stochasticity</topic><topic>Structural and continuum mechanics</topic><topic>Uncertainty</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tootkaboni, M.</creatorcontrib><creatorcontrib>Graham-Brady, L.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tootkaboni, M.</au><au>Graham-Brady, L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties</atitle><jtitle>International journal for numerical methods in engineering</jtitle><addtitle>Int. J. Numer. Meth. Engng</addtitle><date>2010-07-02</date><risdate>2010</risdate><volume>83</volume><issue>1</issue><spage>59</spage><epage>90</epage><pages>59-90</pages><issn>0029-5981</issn><issn>1097-0207</issn><eissn>1097-0207</eissn><coden>IJNMBH</coden><abstract>In this work a spectral stochastic computational scheme is proposed that links the global properties of multi‐phase periodic composites to the geometry and random material properties of their microstructural components. To propagate the uncertainties associated with the material properties to the microstructural response the scheme benefits from a combination of homogenization theory built into a finite element framework and the spectral representation of uncertainty based on Hermite Chaos where a probabilistic characterization of the solutions to a set of local problems defined on the period cell is first sought. A full stochastic description of the global (effective) properties is then obtained by averaging the solutions to the forgoing set of local problems over the unit cell. A representative subset of results is compared with the results obtained using Monte Carlo simulation to demonstrate the accuracy of the proposed procedure. Copyright © 2010 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/nme.2829</doi><tpages>32</tpages></addata></record> |
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| identifier | ISSN: 0029-5981 |
| ispartof | International journal for numerical methods in engineering, 2010-07, Vol.83 (1), p.59-90 |
| issn | 0029-5981 1097-0207 1097-0207 |
| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Computer simulation Exact sciences and technology Fundamental areas of phenomenology (including applications) Hermite Chaos expansion homogenization theory Homogenizing Karhunen-Loeve transform Mathematical models Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Microstructure Monte Carlo methods multi-phase composites Numerical analysis. Scientific computation Physics Sciences and techniques of general use Solid mechanics solids Spectra stochastic Galerkin Stochasticity Structural and continuum mechanics Uncertainty |
| title | A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties |
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