Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law
Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a for...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/10/4637 |
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| author | Gildas Yaovi Amouzou Azzeddine Soulaïmani |
| author_facet | Gildas Yaovi Amouzou Azzeddine Soulaïmani |
| author_sort | Gildas Yaovi Amouzou |
| collection | DOAJ |
| description | Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model. |
| first_indexed | 2024-03-10T11:16:39Z |
| format | Article |
| id | doaj.art-f0a3fc346a9c4f1caed439ea26228005 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T11:16:39Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-f0a3fc346a9c4f1caed439ea262280052023-11-21T20:23:38ZengMDPI AGApplied Sciences2076-34172021-05-011110463710.3390/app11104637Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb LawGildas Yaovi Amouzou0Azzeddine Soulaïmani1Departement of Mechanical Engineering, École de Technologie Supérieure, 1100 Notre-Dame W., Montréal, QC H3C 1K3, CanadaDepartement of Mechanical Engineering, École de Technologie Supérieure, 1100 Notre-Dame W., Montréal, QC H3C 1K3, CanadaTwo numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model.https://www.mdpi.com/2076-3417/11/10/4637plasticityMohr–Coulombreturn mappingconsistent tangent operator |
| spellingShingle | Gildas Yaovi Amouzou Azzeddine Soulaïmani Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law Applied Sciences plasticity Mohr–Coulomb return mapping consistent tangent operator |
| title | Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law |
| title_full | Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law |
| title_fullStr | Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law |
| title_full_unstemmed | Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law |
| title_short | Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law |
| title_sort | numerical algorithms for elastoplacity finite elements code development and implementation of the mohr coulomb law |
| topic | plasticity Mohr–Coulomb return mapping consistent tangent operator |
| url | https://www.mdpi.com/2076-3417/11/10/4637 |
| work_keys_str_mv | AT gildasyaoviamouzou numericalalgorithmsforelastoplacityfiniteelementscodedevelopmentandimplementationofthemohrcoulomblaw AT azzeddinesoulaimani numericalalgorithmsforelastoplacityfiniteelementscodedevelopmentandimplementationofthemohrcoulomblaw |