A micromechanically consistent energy estimate for polycrystalline shape-memory alloys. I - General formulation

Andersen, 1990, The structural phase diagram and oxygen equilibrium partial pressure of YBa2Cu3O6+x studied by neutron powder diffraction and gas volumetry, Physica C, 172, 31, 10.1016/0921-4534(90)90639-V Ball, 1992, Proposed experimental tests of a theory of fine microstructure and the two-well problem, Phil. Trans. R. Soc. A, 338, 389 Bhattacharya, 2003 Bhattacharya, 1997, Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials, Arch. Ration. Mech. Anal., 139, 99, 10.1007/s002050050049 Boussaid, 2019, Characterizations of symmetric polyconvexity, Arch. Ration. Mech. Anal., 234, 417, 10.1007/s00205-019-01395-4 Bunge, 2013 Castaneda, 1997, Nonlinear composites, 171, 10.1016/S0065-2156(08)70321-1 Churchill, 2009, Tips and tricks for characterizing shape memory alloy wire: Part 3-localization and propagation phenomena, Exp. Tech., 33, 70, 10.1111/j.1747-1567.2009.00558.x Cisse, 2016, A review of constitutive models and modeling techniques for shape memory alloys, Int. J. Plast., 76, 244, 10.1016/j.ijplas.2015.08.006 Dacorogna, 2007 Daly, 2007, Stress-induced martensitic phase transformation in thin sheets of Nitinol, Acta Mater., 55, 3593, 10.1016/j.actamat.2007.02.011 Eucken, 1990, The effect of textures on shape memory behaviour, 487 Govindjee, 2007, An upper bound to the free energy of mixing by twin-compatible lamination for n-variant martensitic phase transformations, Contin. Mech. Thermodyn., 18, 443, 10.1007/s00161-006-0038-1 Govindjee, 2001, A multi-variant martensitic phase transformation model: Formulation and numerical implementation, Comput. Methods Appl. Mech. Engrg., 191, 215, 10.1016/S0045-7825(01)00271-7 Govindjee, 2003, The free energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis, J. Mech. Phys. Solids, 4, 763, 10.1016/S0022-5096(02)00105-9 Hackl, 2008, An upper bound to the free energy of n−variant polycrystalline shape memory alloys, J. Mech. Phys. Solids, 56, 2832, 10.1016/j.jmps.2008.04.005 Hackl, 2008, Experimental verification of a micromechanical model for polycrystalline shape memory alloys in dependence of martensite orientation distributions, Mater. Sci. Eng. A, 481, 347, 10.1016/j.msea.2006.10.218 Kachanov, 2004 Kohn, 1991, The relaxation of a double-well energy, Contin. Mech. Thermodyn., 3, 193, 10.1007/BF01135336 Lurie, 1984, Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion, Proc. R. Soc. Edinburgh A, 99, 71, 10.1017/S030821050002597X Milton, 2002 Murat, 1985, Calcul des variations et homogénéisation, 319 Nam, 1990, Cu-content dependence of shape memory characteristics in Ti–Ni–Cu alloys, Mater. Trans. JIM, 31, 959, 10.2320/matertrans1989.31.959 Otsuka, 1974, Morphology and crystallography of thermoelastic Cu–Al–Ni martensite analyzed by the phenomenological theory, Trans. Japan Inst. Met., 15, 103, 10.2320/matertrans1960.15.103 Peigney, 2008, Recoverable strains in composite shape memory alloys, J. Mech. Phys. Solids, 56, 360, 10.1016/j.jmps.2007.05.016 Peigney, 2009, A non-convex lower bound on the effective free energy of polycrystalline shape memory alloys, J. Mech. Phys. Solids, 57, 970, 10.1016/j.jmps.2009.02.003 Peigney, 2013, On the energy-minimizing strains in martensitic microstructures-part 2: Geometrically linear theory, J. Mech. Phys. Solids, 61, 1511, 10.1016/j.jmps.2012.12.011 Peigney, 2013, An incremental variational approach to coupled thermo-mechanical problems in anelastic solids. Application to shape-memory alloys, Int. J. Sol. Struct., 50, 4043, 10.1016/j.ijsolstr.2013.08.013 Peigney, 2011, Numerical simulation of shape memory alloys structures using interior-point methods, Int. J. Sol. Struct., 48, 2791, 10.1016/j.ijsolstr.2011.05.017 Pipkin, 1991, Elastic materials with two preferred states, Quart. J. Mech. Appl. Math., 44, 1, 10.1093/qjmam/44.1.1 Shaw, 1997, On the nucleation and propagation of phase transformation fronts in a NiTi alloy, Acta Mater., 45, 683, 10.1016/S1359-6454(96)00189-9 Shu, 1998, The influence of texture on the shape-memory effect in polycrystals, Acta Mater., 46, 5457, 10.1016/S1359-6454(98)00184-0 Smyshlyaev, 1998, A ‘non-local’ variational approach to the elastic energy minimalization of martensitic polycrystals, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 454, 1573, 10.1098/rspa.1998.0222 Smyshlyaev, 1999, On the relation of a three-well energy, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 455, 779, 10.1098/rspa.1999.0335 Willis, 1977, Bounds and self-consistent estimates for the overall properties of anisotropic composites, J. Mech. Phys. Solids, 25, 185, 10.1016/0022-5096(77)90022-9 Willis, 1981, Variational and related methods for the overall properties of composites, 1, 10.1016/S0065-2156(08)70330-2 Zhan, 2002 Zhang, 2009, Energy barriers and hysteresis in martensitic phase transformations, Acta Mater., 57, 4332, 10.1016/j.actamat.2009.05.034 Zhao, 1998, Texture development and transformation strain of a cold-rolled Ti50–Ni45-Cu5 alloy, Scr. Mater., 39, 1317, 10.1016/S1359-6462(98)00291-7