Free Access
Issue |
ESAIM: M2AN
Volume 44, Number 6, November-December 2010
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Page(s) | 1239 - 1253 | |
DOI | https://doi.org/10.1051/m2an/2010024 | |
Published online | 17 March 2010 |
- T. Aiki, A model of 3D shape memory alloy materials. J. Math. Soc. Jpn. 57 (2005) 903–933. [CrossRef] [Google Scholar]
- M. Arndt, M. Griebel and T. Roubíček, Modelling and numerical simulation of martensitic transformation in shape memory alloys. Contin. Mech. Thermodyn. 15 (2003) 463–485. [Google Scholar]
- F. Auricchio and L. Petrini, Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations. Int. J. Numer. Methods Eng. 55 (2002) 1255–1284. [Google Scholar]
- F. Auricchio and L. Petrini, A three-dimensional model describing stress-temperature induced solid phase transformations. Part I: Solution algorithm and boundary value problems. Int. J. Numer. Methods Eng. 61 (2004) 807–836. [Google Scholar]
- F. Auricchio and L. Petrini, A three-dimensional model describing stress-temperature induced solid phase transformations. Part II: Thermomechanical coupling and hybrid composite applications. Int. J. Numer. Methods Eng. 61 (2004) 716–737. [CrossRef] [Google Scholar]
- F. Auricchio and E. Sacco, A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite. Int. J. Non-Linear Mech. 32 (1997) 1101–1114. [CrossRef] [Google Scholar]
- F. Auricchio, A. Reali and U. Stefanelli, A phenomenological 3D model describing stress-induced solid phase transformations with permanent inelasticity, in Topics on Mathematics for Smart Systems (Rome, 2006), World Sci. Publishing (2007) 1–14. [Google Scholar]
- F. Auricchio, A. Reali and U. Stefanelli, A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity. Int. J. Plast. 23 (2007) 207–226. [CrossRef] [Google Scholar]
- F. Auricchio, A. Mielke and U. Stefanelli, A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Math. Models Meth. Appl. Sci. 18 (2008) 125–164. [CrossRef] [MathSciNet] [Google Scholar]
- F. Auricchio, A. Reali and U. Stefanelli, A macroscopic 1D model for shape memory alloys including asymmetric behaviors and transformation-dependent elastic properties. Comput. Methods Appl. Mech. Eng. 198 (2009) 1631–1637. [CrossRef] [Google Scholar]
- A.-L. Bessoud and U. Stefanelli, A three-dimensional model for magnetic shape memory alloys. Preprint IMATI-CNR 27PV09/20/0 (2009). [Google Scholar]
- M. Brokate and J. Sprekels, Hysteresis and phase transitions, Applied Mathematical Sciences 121. Springer-Verlag, New York (1996). [Google Scholar]
- P. Colli, Global existence for the three-dimensional Frémond model of shape memory alloys. Nonlinear Anal. 24 (1995) 1565–1579. [CrossRef] [MathSciNet] [Google Scholar]
- P. Colli and J. Sprekels, Global existence for a three-dimensional model for the thermodynamical evolution of shape memory alloys. Nonlinear Anal. 18 (1992) 873–888. [CrossRef] [MathSciNet] [Google Scholar]
- T.W. Duerig, A.R. Pelton, Eds., SMST-2003 Proceedings of the International Conference on Shape Memory and Superelastic Technology Conference. ASM International (2003). [Google Scholar]
- T.W. Duerig, K.N. Melton, D. Stökel and C.M. Wayman, Eds., Engineering aspects of shape memory alloys. Butterworth-Heinemann (1990). [Google Scholar]
- F. Falk, Martensitic domain boundaries in shape-memory alloys as solitary waves. J. Phys. C4 Suppl. 12 (1982) 3–15. [Google Scholar]
- F. Falk and P. Konopka, Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys. J. Phys. Condens. Matter 2 (1990) 61–77. [Google Scholar]
- M. Frémond, Matériaux à mémoire de forme. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 304 (1987) 239–244. [Google Scholar]
- M. Frémond, Non-smooth Thermomechanics. Springer-Verlag, Berlin (2002). [Google Scholar]
- S. Govindjee and C. Miehe, A multi-variant martensitic phase transformation model: formulation and numerical implementation. Comput. Methods Appl. Mech. Eng. 191 (2001) 215–238. [Google Scholar]
- D. Helm and P. Haupt, Shape memory behaviour: modelling within continuum thermomechanics. Int. J. Solids Struct. 40 (2003) 827–849. [CrossRef] [Google Scholar]
- M. Hilpert, On uniqueness for evolution problems with hysteresis, in Mathematical Models for Phase Change Problems, J.F. Rodrigues Ed., Birkhäuser, Basel (1989) 377–388. [Google Scholar]
- K.H. Hoffmann, M. Niezgódka and S. Zheng, Existence and uniqueness to an extended model of the dynamical developments in shape memory alloys. Nonlinear Anal. 15 (1990) 977–990. [Google Scholar]
- P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, GAKUTO Int. Series Math. Sci. Appl. 8. Gakkotosho, Tokyo (1996). [Google Scholar]
- P. Krejčí and U. Stefanelli, Existence and nonexistence for the full thermomechanical Souza-Auricchio model of shape memory wires. Preprint, IMATI-CNR, 12PV09/10/0 (2009). [Google Scholar]
- D.C. Lagoudas, P.B. Entchev, P. Popov, E. Patoor, L.C. Brinson and X. Gao, Shape memory alloys, Part II: Modeling of polycrystals. Mech. Materials 38 (2006) 391–429. [CrossRef] [Google Scholar]
- V.I. Levitas, Thermomechanical theory of martensitic phase transformations in inelastic materials. Int. J. Solids Struct. 35 (1998) 889–940. [CrossRef] [Google Scholar]
- G.A. Maugin, The thermomechanics of plasticity and fracture, Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (1992). [Google Scholar]
- A. Mielke and A. Petrov, Thermally driven phase transformation in shape-memory alloys. Adv. Math. Sci. Appl. 17 (2007) 160–182. [Google Scholar]
- A. Mielke, L. Paoli and A. Petrov, On existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys. SIAM J. Math. Anal. 41 (2009) 1388–1414. [CrossRef] [MathSciNet] [Google Scholar]
- A. Mielke, L. Paoli, A. Petrov and U. Stefanelli, Error estimates for discretizations of a rate-independent variational inequality. WIAS Preprint n. 1407 (2009). [Google Scholar]
- A. Mielke, L. Paoli, A. Petrov and U. Stefanelli, Error control for space-time discretizations of a 3D model for shape-memory materials, in Proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials (Bochum 2008), IUTAM Bookseries, Springer (2009). [Google Scholar]
- I. Pawłow, Three-dimensional model of thermomechanical evolution of shape memory materials. Control Cybernet. 29 (2000) 341–365. [Google Scholar]
- B. Peultier, T. Ben Zineb and E. Patoor, Macroscopic constitutive law for SMA: Application to structure analysis by FEM. Materials Sci. Eng. A 438–440 (2006) 454–458. [Google Scholar]
- P. Popov and D.C. Lagoudas, A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite. Int. J. Plast. 23 (2007) 1679–1720. [Google Scholar]
- B. Raniecki and Ch. Lexcellent, RL models of pseudoelasticity and their specification for some shape-memory solids. Eur. J. Mech. A Solids 13 (1994) 21–50. [Google Scholar]
- S. Reese and D. Christ, Finite deformation pseudo-elasticity of shape memory alloys – Constitutive modelling and finite element implementation. Int. J. Plast. 28 (2008) 455–482. [CrossRef] [Google Scholar]
- T. Roubíček, Models of microstructure evolution in shape memory alloys, in Nonlinear Homogenization and its Appl. to Composites, Polycrystals and Smart Materials, P. Ponte Castaneda, J.J. Telega, B. Gambin Eds., NATO Sci. Series II/170, Kluwer, Dordrecht (2004) 269–304. [Google Scholar]
- A.C. Souza, E.N. Mamiya and N. Zouain, Three-dimensional model for solids undergoing stress-induced phase transformations. Eur. J. Mech. A Solids 17 (1998) 789–806. [CrossRef] [Google Scholar]
- U. Stefanelli, Analysis of a variable time-step discretization for the Penrose-Fife phase relaxation problem. Nonlinear Anal. 45 (2001) 213–240. [CrossRef] [MathSciNet] [Google Scholar]
- P. Thamburaja and L. Anand, Polycrystalline shape-memory materials: effect of crystallographic texture. J. Mech. Phys. Solids 49 (2001) 709–737. [CrossRef] [Google Scholar]
- F. Thiebaud, Ch. Lexcellent, M. Collet and E. Foltete, Implementation of a model taking into account the asymmetry between tension and compression, the temperature effects in a finite element code for shape memory alloys structures calculations. Comput. Materials Sci. 41 (2007) 208–221. [CrossRef] [Google Scholar]
- A. Visintin, Differential Models of Hysteresis, Applied Mathematical Sciences 111. Springer, Berlin (1994). [Google Scholar]
- S. Yoshikawa, I. Pawłow and W.M. Zajączkowski, Quasi-linear thermoelasticity system arising in shape memory materials. SIAM J. Math. Anal. 38 (2007) 1733–1759. [CrossRef] [MathSciNet] [Google Scholar]
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