A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element Implementation
In this paper, a three-dimensional model of nonlinear elastic material is proposed. The model is formulated in the framework of Green elasticity, which is based on the specific elastic energy potential. Equivalently, this model can be associated to the deformation theory of plasticity. The constitut...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Materials |
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| Online Access: | https://www.mdpi.com/1996-1944/14/23/7351 |
| _version_ | 1797507517748609024 |
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| author | Aleksander Szwed Marcin D. Gajewski |
| author_facet | Aleksander Szwed Marcin D. Gajewski |
| author_sort | Aleksander Szwed |
| collection | DOAJ |
| description | In this paper, a three-dimensional model of nonlinear elastic material is proposed. The model is formulated in the framework of Green elasticity, which is based on the specific elastic energy potential. Equivalently, this model can be associated to the deformation theory of plasticity. The constitutive relationship, derived from the assumed specific energy, divides the material’s behavior into two stages: the first one starts with an initial almost linear stress–strain relation which, for higher strain, smoothly turns into the second stage of hardening. The proposed relation mimics the experimentally observed response of ductile metals, aluminum alloys in particular. In contrast to the classic deformation theory of plasticity or the plastic flow theory, the presented model can describe metal compressibility in both stages of behavior. The constitutive relationship is non-reversible expressing stress as a function of strain. Special attention is given to the calibration process, in which a one-dimensional analog of the three-dimensional model is used. Various options of calibration based on uniaxial stress test are extensively discussed. A finite element code is written and verified in order to validate the model. Solutions of selected problems, obtained via ABAQUS, confirm the correctness of the model and its usefulness in numerical simulations, especially for buckling. |
| first_indexed | 2024-03-10T04:49:34Z |
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| id | doaj.art-a1748f81596b4a30897c983ca4f58d74 |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T04:49:34Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
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| series | Materials |
| spelling | doaj.art-a1748f81596b4a30897c983ca4f58d742023-11-23T02:42:08ZengMDPI AGMaterials1996-19442021-11-011423735110.3390/ma14237351A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element ImplementationAleksander Szwed0Marcin D. Gajewski1Faculty of Civil Engineering, Warsaw University of Technology, 00-637 Warsaw, PolandFaculty of Civil Engineering, Warsaw University of Technology, 00-637 Warsaw, PolandIn this paper, a three-dimensional model of nonlinear elastic material is proposed. The model is formulated in the framework of Green elasticity, which is based on the specific elastic energy potential. Equivalently, this model can be associated to the deformation theory of plasticity. The constitutive relationship, derived from the assumed specific energy, divides the material’s behavior into two stages: the first one starts with an initial almost linear stress–strain relation which, for higher strain, smoothly turns into the second stage of hardening. The proposed relation mimics the experimentally observed response of ductile metals, aluminum alloys in particular. In contrast to the classic deformation theory of plasticity or the plastic flow theory, the presented model can describe metal compressibility in both stages of behavior. The constitutive relationship is non-reversible expressing stress as a function of strain. Special attention is given to the calibration process, in which a one-dimensional analog of the three-dimensional model is used. Various options of calibration based on uniaxial stress test are extensively discussed. A finite element code is written and verified in order to validate the model. Solutions of selected problems, obtained via ABAQUS, confirm the correctness of the model and its usefulness in numerical simulations, especially for buckling.https://www.mdpi.com/1996-1944/14/23/7351nonlinear elasticityGreen elasticitydeformation theory of plasticityinfinitesimal strainspecific energystress–strain relations |
| spellingShingle | Aleksander Szwed Marcin D. Gajewski A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element Implementation Materials nonlinear elasticity Green elasticity deformation theory of plasticity infinitesimal strain specific energy stress–strain relations |
| title | A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element Implementation |
| title_full | A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element Implementation |
| title_fullStr | A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element Implementation |
| title_full_unstemmed | A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element Implementation |
| title_short | A Nonlinear Elastic Model for Compressible Aluminum Alloys with Finite Element Implementation |
| title_sort | nonlinear elastic model for compressible aluminum alloys with finite element implementation |
| topic | nonlinear elasticity Green elasticity deformation theory of plasticity infinitesimal strain specific energy stress–strain relations |
| url | https://www.mdpi.com/1996-1944/14/23/7351 |
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