EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 46 / No 5 (September-October 2012) ESAIM: M2AN, 46 5 (2012) 1121-1146 References
Free Access
Issue
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
Page(s) 1121 - 1146
DOI https://doi.org/10.1051/m2an/2011049
Published online 13 February 2012
  1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23, (1992) 1482–1518. [Google Scholar]
  2. M. Avellaneda and F.-H. Lin, Compactness methods in the theory of homogenization. Comm. Pure Appl. Math. 40 (1987) 803–847. [Google Scholar]
  3. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, Studies in Mathematics and its Applications 5. North-Holland, Amsterdam (1978) [Google Scholar]
  4. E. Bonnetier and M. Vogelius, An elliptic regularity result for a composite medium with “touching” fibers of circular cross-section. SIAM J. Math. Anal. 31 (2000) 651–677. [CrossRef] [MathSciNet] [Google Scholar]
  5. B.V. Boyarsky, Generalized solutions of a system of differential equations of the first order of elliptic type with discontinuous coefficients. Mat. Sb. N. S. 43 (1957) 451–503. [MathSciNet] [Google Scholar]
  6. L.A. Caffarelli and I. Peral, On W1,p estimates for elliptic equations in divergence form, Comm. Pure Appl. Math. 51 (1998) 1–21. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Carlos-Bellido, A. Donoso and P. Pedregal, Optimal design in conductivity under locally constrained heat flux. Arch. Rational Mech. Anal. 195 (2010) 333–351. [CrossRef] [Google Scholar]
  8. J. Casado-Diaz, J. Couce-Calvo and J.D. Martin-Gomez, Relaxation of a control problem in the coefficients with a functional of quadratic growth in the gradient. SIAM J. Control Optim. 47 (2008) 1428–1459. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Chipot, D. Kinderlehrer and L. Vergara-Caffarelli, Smoothness of linear laminates. Arch. Rational Mech. Anal. 96 (1985) 81–96. [Google Scholar]
  10. E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell’ energia peroperatori ellittici del secondo ordine. Boll. UMI 8 (1973) 391–411. [Google Scholar]
  11. P. Duysinx and M.P. Bendsoe, Topology optimization of continuum structures with local stress constraints. Internat. J. Numer. Math. Engrg. 43 (1998) 1453–1478. [Google Scholar]
  12. D. Faraco, Milton’s conjecture on the regularity of solutions to isotropic equations. Ann. Inst. Henri Poincare, Nonlinear Analysis 20 (2003) 889–909. [CrossRef] [Google Scholar]
  13. D. Fujii, B.C. Chen and N. Kikuchi, Composite material design of two-dimensional structures using the homogenization design method. Internat. J. Numer. Methods Engrg. 50 (2001) 2031–2051. [CrossRef] [MathSciNet] [Google Scholar]
  14. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Berlin, New York (2001). [Google Scholar]
  15. J.H. Gosse and S. Christensen, Strain invariant failure criteria for polymers in composite materials. AIAA (2001) 1184. [Google Scholar]
  16. V.V. Jikov, S.M. Kozlov and O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin, New York (1994). [Google Scholar]
  17. S. Jimenez and R. Lipton, Correctors and field fluctuations for the pϵ(x)-Laplacian with rough exponents. J. Math. Anal. Appl. 372 (2010) 448–469. [CrossRef] [Google Scholar]
  18. A. Kelly and N.H. Macmillan, Strong Solids. Monographs on the Physics and Chemistry of Materials. Clarendon Press, Oxford, (1986). [Google Scholar]
  19. F. Leonetti and V. Nesi, Quasiconformal solutions to certain first order systems and the proof of a conjecture of G.W. Milton. J. Math. Pures. Appl. 76 (1997) 109–124. [CrossRef] [Google Scholar]
  20. Y.Y. Li and L. Nirenberg, Estimates for elliptic systems from composite material. Comm. Pure Appl. Math. LVI (2003) 892–925. [CrossRef] [Google Scholar]
  21. Y.Y. Li and M. Vogelius, Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients. Arch. Rational Mech. Anal. 153 (2000) 91–151. [CrossRef] [Google Scholar]
  22. R. Lipton, Assessment of the local stress state through macroscopic variables. Phil. Trans. R. Soc. Lond. Ser. A 361 (2003) 921–946. [CrossRef] [Google Scholar]
  23. R. Lipton, Bounds on the distribution of extreme values for the stress in composite materials. J. Mech. Phys. Solids 52 (2004) 1053–1069. [CrossRef] [Google Scholar]
  24. R. Lipton, Homogenization and design of functionally graded composites for stiffness and strength, in Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, edited by P.P. Castaneda et al., Kluwer Academic Publishers, Netherlands (2004) 169–192. [Google Scholar]
  25. R. Lipton, Homogenization and field concentrations in heterogeneous media. SIAM J. Math. Anal. 38 (2006) 1048–1059. [CrossRef] [MathSciNet] [Google Scholar]
  26. R. Lipton and M. Stuebner, Inverse homogenization and design of microstructure for point wise stress control. Quart. J. Mech. Appl. Math. 59 (2006) 139–161. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Lipton and M. Stuebner, Optimal design of composite structures for strength and stiffness : an inverse homogenization approach. Struct. Multidisc. Optim. 33 (2007) 351–362. [CrossRef] [Google Scholar]
  28. R. Lipton and M. Stuebner, A new method for design of composite structures for strength and stiffness, 12th AIAA/ISSMO Multidisciplinary Analysis & Optimization Conference. American Institute of Aeronautics and Astronautics Paper AIAA, Victoria British Columbia, Canada (2008) 5986. [Google Scholar]
  29. A.J. Markworth, K.S. Ramesh and W.P. Parks, Modelling studies applied to functionally graded materials. J. Mater. Sci. 30 (1995) 2183–2193. [CrossRef] [Google Scholar]
  30. N. Meyers, An Lp-Estimate for the gradient of solutions of second order elliptic divergence equations. Annali della Scuola Norm. Sup. Pisa 17 (1963) 189–206. [Google Scholar]
  31. G.W. Milton, Modeling the properties of composites by laminates, edited by J. Erickson, D. Kinderleher, R.V. Kohn and J.L. Lions. Homogenization and Effective Moduli of Materials and Media, IMA Volumes in Mathematics and Its Applications 1 (1986) 150–174. [Google Scholar]
  32. F. Murat and L. Tartar, Calcul des Variations et Homogénéisation, Les Méthodes de l’Homogénéisation : Théorie et Applications en Physique, edited by D. Bergman et al. Collection de la Direction des Études et Recherches d’Electricité de France 57 (1985) 319–369. [Google Scholar]
  33. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [CrossRef] [MathSciNet] [Google Scholar]
  34. R.J. Nuismer and J.M. Whitney, Uniaxial failure of composite laminates containing stress concentrations, in Fracture Mechanics of Composites, ASTM Special Technical Publication, American Society for Testing and Materials 593 (1975) 117–142. [Google Scholar]
  35. Y. Ootao, Y. Tanigawa and O. Ishimaru, Optimization of material composition of functionally graded plate for thermal stress relaxation using a genetic algorithim. J. Therm. Stress. 23 (2000) 257–271. [CrossRef] [Google Scholar]
  36. G. Papanicolaou and S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Random fields, Rigorous results in statistical mechanics and quantum field theory, Esztergom 1979. Colloq. Math. Soc. Janos Bolyai 27 (1981) 835–873. [Google Scholar]
  37. E. Sanchez-Palencia, Non Homogeneous Media and Vibration Theory. Springer, Heidelberg (1980). [Google Scholar]
  38. S. Spagnolo, Convergence in Energy for Elliptic Operators, Proceedings of the Third Symposium on Numerical Solutions of Partial Differential Equations, edited by B. Hubbard. College Park (1975); Academic Press, New York (1976) 469–498. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you