A one dimensional variational model of superelasticity for shape memory alloys
In this paper we propose a variational framework for the modeling of superelasticity in shape memory alloys with softening behavior. This model is valid for a class of standard rate-independent materials with a single internal variable. The quasi-static evolution is based on two physical principles...
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| Language: | English |
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Publishing House for Science and Technology
2017-09-01
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| Series: | Vietnam Journal of Mechanics |
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| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/10750 |
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| author | Kim Pham |
| author_facet | Kim Pham |
| author_sort | Kim Pham |
| collection | DOAJ |
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In this paper we propose a variational framework for the modeling of superelasticity in shape memory alloys with softening behavior. This model is valid for a class of standard rate-independent materials with a single internal variable. The quasi-static evolution is based on two physical principles: a stability criterion which selects the local minima of the total energy and an energy balance condition which ensures the absolute continuity of the total energy. The stability criterion allows to bypass non-uniqueness issues associated to softening behaviour while the energy balance condition accounts for brutal evolutions at the local levels. We investigate properties of homogeneous and non-homogenous solutions towards this variational evolution problem. Specifically, we show how softening behaviour can lead to instability of the homogeneous states. In this latter case, we show that a stable solution would consist in following the Maxwell line given by the softening behaviour, then resulting in a non-homogeneous evolution.
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| format | Article |
| id | doaj-art-cbebafd7830a48a7b77836d1b0eb8a9c |
| institution | OA Journals |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-cbebafd7830a48a7b77836d1b0eb8a9c2025-08-20T02:11:16ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822017-09-0139310.15625/0866-7136/10750A one dimensional variational model of superelasticity for shape memory alloysKim Pham0Université Paris-Saclay, France In this paper we propose a variational framework for the modeling of superelasticity in shape memory alloys with softening behavior. This model is valid for a class of standard rate-independent materials with a single internal variable. The quasi-static evolution is based on two physical principles: a stability criterion which selects the local minima of the total energy and an energy balance condition which ensures the absolute continuity of the total energy. The stability criterion allows to bypass non-uniqueness issues associated to softening behaviour while the energy balance condition accounts for brutal evolutions at the local levels. We investigate properties of homogeneous and non-homogenous solutions towards this variational evolution problem. Specifically, we show how softening behaviour can lead to instability of the homogeneous states. In this latter case, we show that a stable solution would consist in following the Maxwell line given by the softening behaviour, then resulting in a non-homogeneous evolution. https://vjs.ac.vn/index.php/vjmech/article/view/10750shape memory alloys (SMA)superelasticitysofteningone dimensional modelenergetic approachstability criterion |
| spellingShingle | Kim Pham A one dimensional variational model of superelasticity for shape memory alloys Vietnam Journal of Mechanics shape memory alloys (SMA) superelasticity softening one dimensional model energetic approach stability criterion |
| title | A one dimensional variational model of superelasticity for shape memory alloys |
| title_full | A one dimensional variational model of superelasticity for shape memory alloys |
| title_fullStr | A one dimensional variational model of superelasticity for shape memory alloys |
| title_full_unstemmed | A one dimensional variational model of superelasticity for shape memory alloys |
| title_short | A one dimensional variational model of superelasticity for shape memory alloys |
| title_sort | one dimensional variational model of superelasticity for shape memory alloys |
| topic | shape memory alloys (SMA) superelasticity softening one dimensional model energetic approach stability criterion |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/10750 |
| work_keys_str_mv | AT kimpham aonedimensionalvariationalmodelofsuperelasticityforshapememoryalloys AT kimpham onedimensionalvariationalmodelofsuperelasticityforshapememoryalloys |