On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples
Porous materials can be described either by Biot’s consolidation theory or the Theory of Porous Media (TPM). Depending on the loading regime, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the case of finite deformati...
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Elsevier
2024-12-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X24000338 |
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| author | Maximilian Brodbeck Franziska S. Egli Marlon Suditsch Seyed Morteza Seyedpour Tim Ricken |
| author_facet | Maximilian Brodbeck Franziska S. Egli Marlon Suditsch Seyed Morteza Seyedpour Tim Ricken |
| author_sort | Maximilian Brodbeck |
| collection | DOAJ |
| description | Porous materials can be described either by Biot’s consolidation theory or the Theory of Porous Media (TPM). Depending on the loading regime, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the case of finite deformation are prone to instabilities and computationally costly. Simplified models assuming small deformations increase stability of the solution process. Within this work, limitations of two simplified models in comparison with the fully non-linear TPM are studied. Therefore a Mandel-like problem is considered. Differences arise especially for rapid consolidation processes and for elongations larger than 3%. It can be further shown, that the simplified models have an inherent mass error. |
| format | Article |
| id | doaj-art-b5930cc76b164985aa96941bbdde7aaf |
| institution | Kabale University |
| issn | 2666-657X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-b5930cc76b164985aa96941bbdde7aaf2024-12-19T11:00:58ZengElsevierExamples and Counterexamples2666-657X2024-12-016100167On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamplesMaximilian Brodbeck0Franziska S. Egli1Marlon Suditsch2Seyed Morteza Seyedpour3Tim Ricken4Institute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, GermanyInstitute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, GermanyInstitute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, GermanyInstitute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, Germany; Porous Media Laboratory, Institute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, GermanyInstitute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, Germany; Porous Media Laboratory, Institute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, Germany; Corresponding author at: Institute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, Stuttgart, 70569, Germany.Porous materials can be described either by Biot’s consolidation theory or the Theory of Porous Media (TPM). Depending on the loading regime, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the case of finite deformation are prone to instabilities and computationally costly. Simplified models assuming small deformations increase stability of the solution process. Within this work, limitations of two simplified models in comparison with the fully non-linear TPM are studied. Therefore a Mandel-like problem is considered. Differences arise especially for rapid consolidation processes and for elongations larger than 3%. It can be further shown, that the simplified models have an inherent mass error.http://www.sciencedirect.com/science/article/pii/S2666657X24000338Poro-elasticityMandel like problemBiotTheory of Porous MediaNondimensionalisationMass conservation |
| spellingShingle | Maximilian Brodbeck Franziska S. Egli Marlon Suditsch Seyed Morteza Seyedpour Tim Ricken On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples Examples and Counterexamples Poro-elasticity Mandel like problem Biot Theory of Porous Media Nondimensionalisation Mass conservation |
| title | On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples |
| title_full | On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples |
| title_fullStr | On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples |
| title_full_unstemmed | On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples |
| title_short | On the influence of non-linearity within two-phase poro-elasticity: Numerical examples and counterexamples |
| title_sort | on the influence of non linearity within two phase poro elasticity numerical examples and counterexamples |
| topic | Poro-elasticity Mandel like problem Biot Theory of Porous Media Nondimensionalisation Mass conservation |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X24000338 |
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