A polygonal finite element formulation for modeling nearly incompressible materials
The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the...
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| Published in | Meccanica (Milan) Vol. 55; no. 4; pp. 701 - 723 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.04.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0025-6455 1572-9648 |
| DOI | 10.1007/s11012-019-01121-0 |
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| Abstract | The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements. |
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| AbstractList | The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements. The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements. |
| Author | Jabareen, Mahmood |
| Author_xml | – sequence: 1 givenname: Mahmood surname: Jabareen fullname: Jabareen, Mahmood email: cvjmah@technion.ac.il organization: Faculty of Civil and Environmental Engineering, Technion - Israel Institute of Technology |
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| CitedBy_id | crossref_primary_10_1007_s42102_021_00058_x crossref_primary_10_1016_j_compstruc_2023_107244 crossref_primary_10_1016_j_ijmecsci_2023_108160 crossref_primary_10_1007_s11012_020_01150_0 crossref_primary_10_1007_s00466_024_02558_1 crossref_primary_10_1002_nme_6698 crossref_primary_10_1002_nme_7358 crossref_primary_10_1115_1_4055670 crossref_primary_10_1016_j_enganabound_2023_07_024 crossref_primary_10_1016_j_enganabound_2023_07_003 |
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| SubjectTerms | Automotive Engineering beyond the Finite Elements Civil Engineering Classical Mechanics Computational fluid dynamics Computational Models for 'Complex' Materials and Structures Eigenvalues Finite element method Locking Mechanical Engineering Nonlinear analysis Patch tests Physics Physics and Astronomy Polygons Potential energy Shape functions |
| Title | A polygonal finite element formulation for modeling nearly incompressible materials |
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