Open Access
July, 2005 A model of 3D shape memory alloy materials
Toyohiko AIKI
J. Math. Soc. Japan 57(3): 903-933 (July, 2005). DOI: 10.2969/jmsj/1158241940


It is a crucial step how to describe the relationship between the strain, the stress and the temperature field, when we consider the mathematical modelling for shape memory alloy materials. From the experimental results we know that the relationship can be described by the hysteresis operators. In this paper we propose a new system consisting of differential equations as a mathematical model for shape memory alloy materials occupying the three dimensional domain. The key of the modelling is the characterization for the generalized stop operators by using the ordinary differential equations including the subdifferential of the indicator function for the closed interval. Also, we give a proof of the well-posedness of the system.


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Toyohiko AIKI. "A model of 3D shape memory alloy materials." J. Math. Soc. Japan 57 (3) 903 - 933, July, 2005.


Published: July, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1076.74041
MathSciNet: MR2139739
Digital Object Identifier: 10.2969/jmsj/1158241940

Primary: 34C55 , 35K45 , 74D10

Keywords: 3D shape memory alloy , Hysteresis , subdifferential

Rights: Copyright © 2005 Mathematical Society of Japan

Vol.57 • No. 3 • July, 2005
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