FFT based numerical homogenization method for porous conductive materials
The Fourier series method is used to solve the periodic homogenization problem for conductive materials containing voids. The problems involving voids are special cases of infinite contrast whose full field solution is not unique, causing convergence issues when iteration schemes are used. In this p...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering 2020-08, Vol.368, p.113160, Article 113160 |
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| container_title | Computer methods in applied mechanics and engineering |
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| creator | To, Quy-Dong Bonnet, Guy |
| description | The Fourier series method is used to solve the periodic homogenization problem for conductive materials containing voids. The problems involving voids are special cases of infinite contrast whose full field solution is not unique, causing convergence issues when iteration schemes are used. In this paper, we reformulate the problem based on the temperature field in the skeleton and derive an equation where the temperature field is connected to values on the pore boundary. Iteration schemes based on the new equation show that the convergence is fast, yielding good results both in terms of local fields and effective conductive properties.
•Fast Fourier Transform techniques to compute effective conductivity of porous material.•Fast convergence iterative scheme for the infinite contrast problem involving voids.•Analytical form factors for polygons which can be applied to void of arbitrary shape. |
| doi_str_mv | 10.1016/j.cma.2020.113160 |
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•Fast Fourier Transform techniques to compute effective conductivity of porous material.•Fast convergence iterative scheme for the infinite contrast problem involving voids.•Analytical form factors for polygons which can be applied to void of arbitrary shape.</description><subject>Conductivity</subject><subject>Convergence</subject><subject>Engineering Sciences</subject><subject>Fast Fourier transform</subject><subject>Fourier series</subject><subject>Homogenization</subject><subject>Iteration scheme</subject><subject>Iterative methods</subject><subject>Mechanics</subject><subject>Numerical homogenization method</subject><subject>Porous conductive media</subject><subject>Porous materials</subject><subject>Solid mechanics</subject><subject>Temperature distribution</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWKsfwNuCJw9b83ezi6dSrC0UvNRzyCazNqW7qcluQT-9KSsenctjhvcbZh5C9wTPCCbF035mWj2jmKaeMFLgCzQhpaxySlh5iSYYc5HLkoprdBPjHqcqCZ2g9XK5zWodwWbd0EJwRh-ynW_9B3TuW_fOd1kL_c7brPEhO_rgh5gZ39nB9O4EWav7ROlDvEVXTRK4-9Upel--bBerfPP2ul7MN7nhmPa51BSwBq6hqqAAimuJbUN1IZigpKhFpY0BbWthsZVYlEIzWpOaGmMZk5xN0eO4d6cP6hhcq8OX8tqp1XyjzjNMZcUZFyeSvA-j9xj85wCxV3s_hC6dpyjnlDHMuEwuMrpM8DEGaP7WEqzO6aq9Sumqc7pqTDcxzyMD6dWTg6CicdAZsC6A6ZX17h_6B1HqgWY</recordid><startdate>20200815</startdate><enddate>20200815</enddate><creator>To, Quy-Dong</creator><creator>Bonnet, Guy</creator><general>Elsevier B.V</general><general>Elsevier BV</general><general>Elsevier</general><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><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0001-9257-835X</orcidid></search><sort><creationdate>20200815</creationdate><title>FFT based numerical homogenization method for porous conductive materials</title><author>To, Quy-Dong ; Bonnet, Guy</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c402t-7a2e0ae4ae99e6e20b70df2a6535216b59acceadb5d0d70585a32b1b2ccd33743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Conductivity</topic><topic>Convergence</topic><topic>Engineering Sciences</topic><topic>Fast Fourier transform</topic><topic>Fourier series</topic><topic>Homogenization</topic><topic>Iteration scheme</topic><topic>Iterative methods</topic><topic>Mechanics</topic><topic>Numerical homogenization method</topic><topic>Porous conductive media</topic><topic>Porous materials</topic><topic>Solid mechanics</topic><topic>Temperature distribution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>To, Quy-Dong</creatorcontrib><creatorcontrib>Bonnet, Guy</creatorcontrib><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><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>To, Quy-Dong</au><au>Bonnet, Guy</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>FFT based numerical homogenization method for porous conductive materials</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2020-08-15</date><risdate>2020</risdate><volume>368</volume><spage>113160</spage><pages>113160-</pages><artnum>113160</artnum><issn>0045-7825</issn><eissn>1879-2138</eissn><abstract>The Fourier series method is used to solve the periodic homogenization problem for conductive materials containing voids. The problems involving voids are special cases of infinite contrast whose full field solution is not unique, causing convergence issues when iteration schemes are used. In this paper, we reformulate the problem based on the temperature field in the skeleton and derive an equation where the temperature field is connected to values on the pore boundary. Iteration schemes based on the new equation show that the convergence is fast, yielding good results both in terms of local fields and effective conductive properties.
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| ispartof | Computer methods in applied mechanics and engineering, 2020-08, Vol.368, p.113160, Article 113160 |
| issn | 0045-7825 1879-2138 |
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| source | Elsevier ScienceDirect Journals |
| subjects | Conductivity Convergence Engineering Sciences Fast Fourier transform Fourier series Homogenization Iteration scheme Iterative methods Mechanics Numerical homogenization method Porous conductive media Porous materials Solid mechanics Temperature distribution |
| title | FFT based numerical homogenization method for porous conductive materials |
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