zbMATH — the first resource for mathematics

Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi. (English) Zbl 1106.74048
Summary: A continuum-mechanical description of the stored energy in shape-memory alloys is presented, with its multi-well character giving rise to a microstructure described, with a certain approximation, by special gradient Young measures. A rate-independent phenomenological dissipation is then considered to model a hysteretic response. Isothermal simulations for CuAlNi single crystal are presented.

74N05 Crystals in solids
74G65 Energy minimization in equilibrium problems in solid mechanics
Full Text: DOI
[3] Arndt, M., Upscaling from Atomistic Models to Higher Order Gradient Continuum Models for Crystalline Solids. PhD.Thesis, Inst. für Numer. Simulation, Universitä t Bonn, 2004.
[24] Govindjee, S., Mielke, A., Hall, G.J. and Miehe, C., ’Application of notions of quasi-convexity to the modeling and simulation of martensitic and shape memory phase transformations’, in: Mang, H.A., Rammerstorfer, F.G. and Eberhardsteiner, J. (eds) Proceeding 5th World Congress on Computational Mechanics., Vienna University of Technology, Austria, (2002).
[26] Hall, G.J. and Govindjee, S., ’Application of the relaxed free energy of mixing to problems in shape memory alloy simulation’, J. Intelligent Mater. Systems. & Struct., in print. · Zbl 1116.74400
[34] Kruží k, M. and Roubíček, T., Mesoscopic model of microstructure evolution in shape memory alloys with applications to NiMnGa. Preprint IMA No.2003, University of Minnesota, Minneapolis, November 2004.
[35] Landa, M., Plešek, J., Urbánek, P. and Novák, V., ’Evaluation of anisotropic elastic properties by ultrasonic methods’, in: Proceedings 40th Intl. Conf. Experimental Stress Anal., Prague, June 3–6, 2002, pp. 141–146.
[39] Lubliner J., ’A maximum dissipation principle in generalized plasticity’, Acta Mech. 52. (1984) 225–237. 39. Mainik, A. and Mielke, A., ’Existence results for energetic models for rate-independent systems’, Calc. Var. 22. (2005) 73–99.
[42] Mielke, A., ’Evolution of rate-independent systems’, in: Dafermos, C. and Feireisl, E. (eds.) Handbook of Differential Equations: Evolutionary Diff. Eqs., North-Holland, Amsterdam, 2005, in press.
[64] Roubíček, T., ’Models of microstructure evolution in shape memory materials’, in: Ponte Castaneda, P., Telega, J.J. and Gambin, B. (eds) NATO Workshop Nonlinear Homogenization and its Appl. to Composites, Polycrystals and Smart Mater,. NATO Sci. Series II/170. , Kluwer, Dordrecht, 2004, pp.269–304. · Zbl 1320.74087
[65] Roubíček, T. and Kruží k, M., ’Mesoscopic model of microstructure evolution in shape memory alloys, its numerical analysis and computer implementation’, in: Miehe, C. (ed) 3rd GAMM Seminar on microstructures. , GAMM Mitteilungen., J.Wiley, in press. · Zbl 1157.74032
[66] Sedlák, P., Seiner, H., Landa, M., Novák, V., Šittner, P. and Manosa, Ll., ’Elastic constants of bcc austenite and 2H orthorhombic martensite in CuAlNi shape memory alloy’, Acta Mat. (2005).
[68] Simo, J.C., ’A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition’, Comp. Math. Appl. Mech. Engrg. 66. (1988) 199–219, 68. (1988) 1–31. · Zbl 0611.73057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.