Abstract
The objective of this article is to investigate steady state solutions for the Fr'emond theory of shape memory alloys. Special attention is paid to the temperature range where both martensite and austenite appear. We will give a construction of solutions, which involves only elementary mathematical tools.
Similar content being viewed by others
References
Bénilan, Ph.; Blanchard, D.; Ghidouche, H.: On a nonlinear system for shape memory alloys. Continuum Mech. Thermodyn. 1 (1990) 65–76
Colli, P.; Frémond, M.; Visintin, A.: Thermo-mechanical evolution of shape memory alloys. Quart. Appl. Math. 158 (1990) 31–47
Falk, F.: Model free energy, mechanics and thermodynamics of shape memory alloys. Acta Metallurgica 28 (1980) 1773–1780
Falk, F.: Ginzburg-Landau Theory of Static Domain Walls in Shape-Memory Alloys, Z. Phys. B—Condensed Matter 51 (1983) 177–185
Frémond, M.: Shape memory alloys. A thermomechanical model. In: Free Boundary, Problems — Theory and Applications V–VI (K.-H. Hoffmann, J. Sprekels, eds.) Longman, London, 1990
Friedman, A.; Sprekels, J.: Steady states of austenitic-martensitic domains in the Ginzburg-Landau theory of shape memory alloys. Continuum Mech. Thermodyn. 2 (1990) 199–213
Hoffmann, K.-H.; Niezgódka, M.; Zheng, S.: Existence and Uniqueness of Global Solutions to an Extended Model of the Dynamical Developments in Shape Memory Alloys. Nonlinear Analysis TMA (in print)
Sprekels, J.: Shape Memory Alloys. Mathematical Models for a Class of First Order Solid-Solid Phase Transitions in Metals, preprint (1990)
Author information
Authors and Affiliations
Additional information
The author was supported by Deutsche Forschungsgemeinschaft (DFG), SPP “Anwendungsbezogene Optimierung und Steuerung”.
Rights and permissions
About this article
Cite this article
Horn, W. Stationary solutions for the one-dimensional Frémond model of shape memory Effects. Continuum Mech. Thermodyn 3, 277–292 (1991). https://doi.org/10.1007/BF01126411
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01126411