A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite
type: Item
instance of: scholarly article
title: A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite
zbMATH Open document ID: 0906.73006
DOI: 10.1016/S0020-7462(96)00130-8
published in: International Journal of Non-Linear Mechanics
publication date: 1997-10-28T00:00:00Z
review text: The authors present a rational one-dimensional model for the superelastic behavior of shape-memory alloys (SMA). A single scalar internal variable, the volume fraction of martensite, is considered for which an evolution equation in rate form is proposed. The simplicity of the modeling is rewarded by its efficiency, because various homogenization techniques (Voigt scheme (law of mixtures), Mori-Tanaka scheme, Reuss scheme, time-discrete model) allow the authors to determine the dependency of the elasticity coefficient upon the martensite contents. A numerical technique using a return-map algorithm is exploited to find sensible solutions of the time-discrete model. Simulations of the modeling for typical SMA superelastic stress-strain responses demonstrate excellent agreement with experimentally recorded stress-strain curves including hysteresis (Ni-Ti straight wires). The paper is well documented and proves that rather simple modelings completed by good applied mathematics and a safe numerical algorithm can provide a mathematically efficient and physically sound approach to a difficult problem.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 1081060
zbMATH Keywords: Ni-Ti straight wires
zbMATH Keywords: scalar internal variable
zbMATH Keywords: volume fraction of martensite
zbMATH Keywords: evolution equation in rate form
zbMATH Keywords: homogenization techniques
zbMATH Keywords: elasticity coefficient
zbMATH Keywords: return-map algorithm
zbMATH Keywords: time-discrete model
zbMATH Keywords: stress-strain curves
zbMATH Keywords: hysteresis
author: Ferdinando Auricchio
author: Elio Sacco
reviewed by: Gérard A. Maugin
MaRDI profile type: Publication
full work available at URL: s0020-7462(96)00130-8
OpenAlex ID: W2042257811
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description: scientific article; zbMATH DE number 1081060