Z. Hashin and S. Shtrikman, A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials, Journal of Applied Physics, vol.70, issue.10, pp.3125-3131, 1962.
DOI : 10.1063/1.1702301

D. R. Talbot and J. R. Willis, Variational Principles for Inhomogeneous Non-linear Media, IMA Journal of Applied Mathematics, vol.35, issue.1, pp.39-54, 1985.
DOI : 10.1093/imamat/35.1.39

P. Castañeda, The effective mechanical properties of nonlinear isotropic composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.45-71, 1991.
DOI : 10.1016/0022-5096(91)90030-R

G. W. Milton, On characterizing the set of possible effective tensors of composites: The variational method and the translation method, Communications on Pure and Applied Mathematics, vol.25, issue.1, pp.43-63, 1990.
DOI : 10.1002/cpa.3160430104

K. Lurie and A. Cherkaev, Synopsis, Proc. R. Soc. Edinb. A 99, pp.71-87, 1984.
DOI : 10.1063/1.1728579

F. Murat, L. Tartar, D. Bergman, J. Lions, G. Papanicolaou et al., Calcul des variations et homogénéisation Les méthodes de l'homogénéisation: théorie et applications en physique, École d'été d'analyse numérique, Collection Direction des études et recherches d, 1985.

K. Bhattacharya and R. V. Kohn, Elastic Energy Minimization and the Recoverable Strains of Polycrystalline Shape-Memory Materials, Archive for Rational Mechanics and Analysis, vol.139, issue.2, pp.99-180, 1997.
DOI : 10.1007/s002050050049

G. W. Milton and S. K. Serkov, Bounding the current in nonlinear conducting composites, Journal of the Mechanics and Physics of Solids, vol.48, issue.6-7, pp.1295-1324, 2000.
DOI : 10.1016/S0022-5096(99)00083-6

D. R. Talbot and J. R. Willis, Bounds for the effective constitutive relation of a nonlinear composite, Proc. R. Soc. Lond. A 460, pp.2705-2723, 2004.
DOI : 10.1098/rspa.2004.1309

M. Peigney, A pattern-based method for bounding the effective response of a nonlinear composite, Journal of the Mechanics and Physics of Solids, vol.53, issue.4, pp.923-948, 2005.
DOI : 10.1016/j.jmps.2004.11.001

M. Peigney, Recoverable strains in composite shape memory alloys, Journal of the Mechanics and Physics of Solids, vol.56, issue.2, pp.360-375, 2008.
DOI : 10.1016/j.jmps.2007.05.016

M. Peigney, Improved bounds on the energy-minimizing strains in martensitic polycrystals, Continuum Mechanics and Thermodynamics, vol.39, issue.1, pp.923-946, 2016.
DOI : 10.1007/s00161-014-0360-y
URL : https://hal.archives-ouvertes.fr/hal-01254058

V. Nesi, D. R. Talbot, and J. R. Willis, Translation and related bounds for the response of a nonlinear composite conductor, Proc. R. Soc. Lond. A, pp.455-3687, 1999.
DOI : 10.1098/rspa.1999.0472

A. Garroni and R. V. Kohn, Some three-dimensional problems related to dielectric breakdown and polycrystal plasticity, Proc. R. Soc. Lond. A 459, pp.2613-2625, 2003.
DOI : 10.1098/rspa.2003.1152

P. Ponte-castañeda and J. R. Willis, The Effective Behavior of Nonlinear Composites: A Comparison between Two Methods, Materials Science Forum, vol.123, issue.125, pp.351-360, 1993.
DOI : 10.4028/www.scientific.net/MSF.123-125.351

R. Hill, Elastic properties of reinforced solids: Some theoretical principles, Journal of the Mechanics and Physics of Solids, vol.11, issue.5, pp.357-372, 1963.
DOI : 10.1016/0022-5096(63)90036-X

J. R. Willis, Variational Estimates for the Overall Response of an Inhomogeneous Nonlinear Dielectric, Homogenization and Effective Moduli of Materials and Media, 1986.
DOI : 10.1007/978-1-4613-8646-9_12

P. and P. Castañeda, Bounds and Estimates for the Properties of Nonlinear Heterogeneous Systems, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.340, issue.1659, pp.531-567, 1992.
DOI : 10.1098/rsta.1992.0079

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

H. Brézis, Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland, 1972.

B. E. Peigney and M. Peigney, Bounds for nonlinear composite conductors via the translation method, Journal of the Mechanics and Physics of Solids, vol.101, pp.93-117, 2017.
DOI : 10.1016/j.jmps.2017.01.017
URL : https://hal.archives-ouvertes.fr/hal-01477382