no. 2
Geometrically nonlinear shape-memory polycrystals made from a two-variant material
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 2, pp. 377-398. 
@article{M2AN_2000__34_2_377_0,
     author = {Kohn, Robert V. and Niethammer, Barbara},
     title = {Geometrically nonlinear shape-memory polycrystals made from a two-variant material},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {377--398},
     publisher = {Dunod},
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     volume = {34},
     number = {2},
     year = {2000},
     mrnumber = {1765665},
     zbl = {0978.74015},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_2_377_0/}
}
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Kohn, Robert V.; Niethammer, Barbara. Geometrically nonlinear shape-memory polycrystals made from a two-variant material. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 2, pp. 377-398. http://www.numdam.org/item/M2AN_2000__34_2_377_0/

[1] J.M. Bail and R.D. James, Proposed experimental test of a theory of fine microstructures and the two-well problem. Phil. Trans. R. Soc. Lond. A 338 (1992) 389-450. | Zbl

[2] J.M. Ball and F. Murat, Wlp-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225-253. | MR | Zbl

[3] K. Bhattacharya, Theory of martensitic microstructure and the shape-memory effect, unpublished lecture notes.

[4] K. Bhattacharya and R.V. Kohn, Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials. Arch. Rat Mech. Anal. 139 (1998) 99-180. | MR | Zbl

[5] A. Braides, Homogenization of some almost periodic coercive functional. Rend. Accad. Naz. Sci. Detta XL, V. Ser., Mem. Mat. 9 (1985) 313-322. | MR | Zbl

[6] O.P. Bruno and G.H. Goldsztein, A fast algorithm for the simulation of polycrystalline misfïts: martensitic transformations in two space dimensions, Proc. Roy. Soc. Lond. Ser. A (to appear). | MR | Zbl

[7] O.P. Bruno and G.H. Goldsztein, Numerical simulation of martensitic transformations in two- and three-dimensional polycrystals, J. Mech. Phys. Solids (to appear). | MR | Zbl

[8] F. John and L. Nirenberg, On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14 (1961) 415-426. | MR | Zbl

[9] F. John, Rotation and strain. Comm. Pure Appl. Math. 14 (1961) 391-413. | MR | Zbl

[10] F. John Bounds for deformations in terms of average strains, in Inequalities III, O. Shisha Ed., Academic Press (1972) 129-143. | MR | Zbl

[11] F. John, Uniqueness of Non-Linear Elastic Equilibrium for Prescribed Boundary Displacements and Sufficiently Small Strains. Comm. Pure Appl. Math. 25 (1972) 617-635. | MR | Zbl

[12] R. V. Kohn, The relaxation of a double-well energy. Continuum Mech Thermodyn. 3 (1991) 193-236. | MR | Zbl

[13] R. V. Kohn and V. Lods, in preparation (1999).

[14] R. V. Kohn and G. Strang, Optimal design and relaxation of variational problems II. Comm. Pure. Appl. Math. 34 (1986) 139-182. | MR | Zbl

[15] S. Müller, Homogenization of nonconvex integral functionals and cellular elastic materials. Arch. Rat. Mech. Anal.99 (1987) 189-212. | MR | Zbl

[16] Y. C. Shu and K. Bhattacharya, The influence of texture on the shape-memory effect in polycrystals. Acta. Mater. 46 (1998) 5457-5473.