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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Main Author: Kim Pham
Format: Article
Language:English
Published: Publishing House for Science and Technology 2017-09-01
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
description 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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publishDate 2017-09-01
publisher Publishing House for Science and Technology
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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
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