Stochastic finite elements: Where is the physics?
The micromechanics based on the Hill-Mandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF) models of material properties (such as Hooke’s law) having no physical content, or even at odds with physics. At the same time, that condition allows...
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| Format: | Article |
| Language: | English |
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Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2011-01-01
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| Series: | Theoretical and Applied Mechanics |
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| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-5584/2011/1450-55841104379O.pdf |
| _version_ | 1811279478308995072 |
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| author | Ostoja-Starzewski Martin |
| author_facet | Ostoja-Starzewski Martin |
| author_sort | Ostoja-Starzewski Martin |
| collection | DOAJ |
| description | The micromechanics based on the Hill-Mandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF) models of material properties (such as Hooke’s law) having no physical content, or even at odds with physics. At the same time, that condition allows one to set up the RFs of stiffness and compliance tensors in function of the mesoscale and actual random microstructure of the given material. The mesoscale is defined through a Statistical Volume Element (SVE), i.e. a material domain below the Representative Volume Element (RVE) level. The paper outlines a procedure for stochastic scale-dependent homogenization leading to a determination of mesoscale one-point and two-point statistics and, thus, a construction of analytical RF models. |
| first_indexed | 2024-04-13T00:55:20Z |
| format | Article |
| id | doaj.art-72d146c9b6fb475aa55a0bbed9440cf4 |
| institution | Directory Open Access Journal |
| issn | 1450-5584 |
| language | English |
| last_indexed | 2024-04-13T00:55:20Z |
| publishDate | 2011-01-01 |
| publisher | Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade |
| record_format | Article |
| series | Theoretical and Applied Mechanics |
| spelling | doaj.art-72d146c9b6fb475aa55a0bbed9440cf42022-12-22T03:09:41ZengSerbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, BelgradeTheoretical and Applied Mechanics1450-55842011-01-0138437939610.2298/TAM1104379OStochastic finite elements: Where is the physics?Ostoja-Starzewski MartinThe micromechanics based on the Hill-Mandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF) models of material properties (such as Hooke’s law) having no physical content, or even at odds with physics. At the same time, that condition allows one to set up the RFs of stiffness and compliance tensors in function of the mesoscale and actual random microstructure of the given material. The mesoscale is defined through a Statistical Volume Element (SVE), i.e. a material domain below the Representative Volume Element (RVE) level. The paper outlines a procedure for stochastic scale-dependent homogenization leading to a determination of mesoscale one-point and two-point statistics and, thus, a construction of analytical RF models.http://www.doiserbia.nb.rs/img/doi/1450-5584/2011/1450-55841104379O.pdfrandom mediarandom fieldsmesoscaleanisotropystochastic finite elementsmultiscale methodsuncertainty quantification |
| spellingShingle | Ostoja-Starzewski Martin Stochastic finite elements: Where is the physics? Theoretical and Applied Mechanics random media random fields mesoscale anisotropy stochastic finite elements multiscale methods uncertainty quantification |
| title | Stochastic finite elements: Where is the physics? |
| title_full | Stochastic finite elements: Where is the physics? |
| title_fullStr | Stochastic finite elements: Where is the physics? |
| title_full_unstemmed | Stochastic finite elements: Where is the physics? |
| title_short | Stochastic finite elements: Where is the physics? |
| title_sort | stochastic finite elements where is the physics |
| topic | random media random fields mesoscale anisotropy stochastic finite elements multiscale methods uncertainty quantification |
| url | http://www.doiserbia.nb.rs/img/doi/1450-5584/2011/1450-55841104379O.pdf |
| work_keys_str_mv | AT ostojastarzewskimartin stochasticfiniteelementswhereisthephysics |