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Some numerical simulations of pseudoelastic hysteresis in shape memory alloys. (English) Zbl 0785.73032

Summary: Recently, B. Fedelich and G. Zanzotto [Contin. Mech. Thermodyn. 3, 215-276 (1991)] have developed a model for the nonisothermal pseudoelastic behaviour of a shape memory material and have conducted some numerical simulation experiments. We present a different method for the numerical solution and discuss it in comparison with their results.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74C99 Plastic materials, materials of stress-rate and internal-variable type
74A15 Thermodynamics in solid mechanics
80A22 Stefan problems, phase changes, etc.
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References:

[1] Sprekels, J.: Shape memory alloys: Mathematical models for a class of first order solid-solid phase transition in metals, Control and Cybernetics 19 (1990) 287-308 · Zbl 1229.49048
[2] Niezgódka, M., Sprekels, J.: Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys, Numer. Math. 58 (1991) 759-778 · Zbl 0715.65099 · doi:10.1007/BF01385653
[3] Müller, I., Xu, H.: On the pseudo-elastic hysteresis, Acta Metall. 39 (1991) 263-271 · doi:10.1016/0956-7151(91)90305-K
[4] Fedelich, B., Zanzotto, G.: One-dimensional quasistatic nonisothermal evolution of shape-memory material inside the hysteresis loop, Continuum Mech. Thermodyn. 3 (1991) 215-276 · Zbl 0825.73049 · doi:10.1007/BF01126410
[5] Fu, S., Müller, I., Xu, H.: Experimental and theoretical investigation of the pseudoelastic hysteresis, to appear
[6] Krasnoselskii, M. A., Pokrovskii, A. V.: Systems with hysteresis, Springer 1989. Russian edition: Nauka, Moscow, 1983
[7] Wilmanski, K.: A model of stress-induced patterns in shape memory alloys, submitted · Zbl 0774.73016
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