Abstract
In our previous works we have proposed a mathematical model for dynamics of shape memory alloy materials. In the model the relationship between the strain and the stress is given as the generalized stop operator described by the ordinary differential equation including the subdifferential of the indicator function for the closed interval depending on the temperature. Here, we adopt the Duhem type of hysteresis operators as the mathematical description of the relationship in order to deal with the more realistic mathematical model. The aims of this paper are to show our new model and to establish the well-posedness of the model.
This work is partially supported by a grant in aid of JSPS ((C)16540146).
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Aiki, T., Okazaki, T. (2006). One-dimensional Shape Memory Alloy Problem with Duhem Type of Hysteresis Operator. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_1
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DOI: https://doi.org/10.1007/978-3-7643-7719-9_1
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