Free Access
Issue
ESAIM: M2AN
Volume 41, Number 6, November-December 2007
Page(s) 1061 - 1087
DOI https://doi.org/10.1051/m2an:2007050
Published online 15 December 2007
  1. G. Allaire, Shape Optimization by the Homogenization Method. Springer-Verlag, New York (2002). [Google Scholar]
  2. G. Allaire and S. Gutiérrez, Optimal design in small amplitude homogenization. R.I. 576, École Polytechnique, C.M.A UMR-CNRS 7641 (2002). [Google Scholar]
  3. M.J. Arts, A Mathematical Model of the Dynamics of the Left Ventricle. Ph.D. thesis, University of Limburg, The Netherlands (1978). [Google Scholar]
  4. A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis for periodic Structures. North-Holland (1978). [Google Scholar]
  5. M. Briane, Homogénéisation de materiaux fibrés et multi-couches. Ph.D. thesis, Université Paris 6, France (1990). [Google Scholar]
  6. M. Briane, Three models of non periodic fibrous materials obtained by homogenization. RAIRO Modél. Math. Anal. Numér. 27 (1993) 759–775. [MathSciNet] [Google Scholar]
  7. M. Briane, Homogenization of a nonperiodic material. J. Math. Pures Appl. 73 (1994) 47–66. [MathSciNet] [Google Scholar]
  8. D. Caillerie, A. Mourad and A. Raoult, Towards a fibre-based constitutive law for the myocardium. ESAIM: Proc. 12 (2002) 25–30. [CrossRef] [EDP Sciences] [Google Scholar]
  9. D. Caillerie, A. Mourad and A. Raoult, Cell-to-muscle homogenization. Application to a constitutive law for the myocardium. ESAIM: M2AN 37 (2003) 681–698. [Google Scholar]
  10. R.S. Chadwick, Mechanics of the left ventricle. Biophys J. 39 (1982) 279–288. [CrossRef] [PubMed] [Google Scholar]
  11. T.S. Feit, Diastolic pressure-volume relations and distribution of pressure and fiber extension across the wall of a model of left ventricle. Biophys. J. 28 (1979) 143–166. [CrossRef] [PubMed] [Google Scholar]
  12. G. Francfort and F. Murat, Homogenization and optimal bounds in linear elasticity. Arch. Rational Mech. Anal. 94 (1986) 307–334. [CrossRef] [MathSciNet] [Google Scholar]
  13. P. Gérard, Microlocal defect measures. Comm. Partial Diff. Equations 16 (1991) 1761–1794. [Google Scholar]
  14. G.A. Holzapfel, Nonlinear solid mechanics. A continuum approach for engineering. John Wiley and Sons, Ltd., Chichester (2000). [Google Scholar]
  15. F. Murat and L. Tartar, H-convergence, in Topics in the Mathematical Modelling of Composite Materials, A.V. Cherkaev and R.V. Kohn Eds., Progress in Nonlinear Differential Equations and their Applications, Birkaüser, Boston (1998) 21–43. [Google Scholar]
  16. R.W. Ogden, Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue, in Biomechanics of Soft Tissue in Cardiovascular Systems, G.A. Holzapfel and R.W. Ogden Eds., CISM Courses and Lectures Series 441, Springer, Wien (2003) 65–108. [Google Scholar]
  17. C.S. Peskin, Fiber architecture of the left ventricular wall: an asymptotic analysis. Commun. Pure Appl. Math. 42 (1989) 79–113. [CrossRef] [Google Scholar]
  18. S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellitiche. Ann. Sc. Norm. Sup. Pisa 22 (1968) 571–597. [Google Scholar]
  19. A.J.M. Spencer, Constitutive theory for strongly anisotropic solids, in Continuum Theory of the Mechanics of Fiber-Reinforced Composites, A.J.M. Spencer Ed., CISM Courses and Lectures Notes 282, International Center for Mechanical Sciences, Springer, Wien (1984) 1–32. [Google Scholar]
  20. D.D. Streeter, Gross morphology and fiber geometry of the heart, in Handbook of physiology. The cardiovascular system, R.M. Berne and N. Sperelakis Eds., Vol. 1, Williams and Wilkins, Baltimore (1979) 61–112. [Google Scholar]
  21. L. Tartar, H-measures and Small Amplitude Homogenization, in Random Media and Composites, R.V. Kohn and G.W. Milton Eds., SIAM, Philadelphia (1989) 89–99. [Google Scholar]
  22. L. Tartar, H-measures, a New approach for studying homogenization, oscillations and concentration effects in partial differential equations. Proc. R. Soc. Edin. 115-A (1990) 193–230. [Google Scholar]
  23. L. Tartar, An Introduction to the Homogenization Method in Optimal Design. Springer Lecture Notes Math. 1740 (2000) 47–156. [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