A Numerical Tool for Periodic Heterogeneous Media: Application to Interface in Al/SiC Composites

[+] Author and Article Information
D. Dumont

Faculté de Mathématiques et d’Informatique, 33, rue Saint-Leu, 80 039 Amiens, France e-mail: Serge.Dumont@u-picardie.fr

F. Lebon

Laboratoire de Mécanique et Génie Civil, Université Montpellier 2, Pl. E. Bataillon, 34 095 Montpellier Cedex 5, France e-mail: lebon@lmgc.univ-montp2.fr

A. Ould Khaoua

Departamento de Matematicas, Universidad de los Andes, Calle 19 1-11, Bogota, Columbia e-mail: ahmed@media.uniandes.edu.co

J. Appl. Mech 67(1), 214-217 (Sep 15, 1999) (4 pages) doi:10.1115/1.321169 History: Received March 15, 1999; Revised September 15, 1999
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Charton,  P., and Perrier,  V., 1996, “A Pseudo-Wavelet Scheme for the Two Dimensional Navier-Stokes Equation,” Comp. Appl. Math., 15, pp. 139–160.
Lazaar,  S., Ponenti,  P. J., Liandrat,  J., and Tchamitchian,  P., 1994, “Wavelet Algorithms for Numerical Resolution of Partial Differentiable Equations,” Comput. Methods Appl. Mech. Eng., 116, pp. 309–314.
Dumont, S., 1996, “Ondelettes, Homogénéisation Périodique et Elasticité,” Ph.D. thesis, Université Montpellier 2.
Dumont,  S., and Lebon,  F., 1996, “Wavelet-Galerkin Method for Heterogeneous Media,” Comput. Struct., 61, pp. 55–65.
Dumont,  S., and Lebon,  F., 1999, “Wavelet-Galerkin Method for Plane Elasticity,” Comp. Appl. Math., 18, pp. 127–142.
Daubechies,  I., 1992, “Orthonormal Bases of Compactly Supported Wavelets,” Commun. Pure Appl. Math., 41, pp. 909–998.
Dumont,  S., and Lebon,  F., 1996, “Representation of Plane Elastostatics Operators in Daubechies Wavelets,” Comput. Struct., 60, pp. 561–569.
Hashin,  Z., and Strickman,  S., 1963, “A Variational Approach to the Theory of the Elastic Behavior of Multiphase Materials,” J. Mech. Phys. Solids, 11, pp. 127–140.
Hill,  R., 1964, “Theory of Mechanical Properties of Fiber-Strenghened Materials,” J. Mech. Phys. Solids, 12, pp. 199–212.
Bensoussan, A., Lions, J. L., and Papanicolaou, G., 1978, Asymptotic Analysis for Periodic Structures, 1st Ed., North-Holland, Amsterdam.
Dumontet,  H., 1983, “Homogénéisation par Développement en Séries de Fourier,” C. R. Acad. Sci. Paris, 296, pp. 1625–1628.
Beylkin,  G., 1992, “On the Representation of Operators in Bases of Compactly Supported Wavelets,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 29, pp. 1716–1740.
Hackbusch, W., 1985, Multigrid Method and Applications, Springer-Verlag, New York.
Lebon,  F., 1995, “Two-Grid Method for Regularized Frictional Elastostatics Problems,” Eng. Comput., 12, pp. 657–664.
Ould Khaoua, A., 1995, “Etude Théorique et Numérique de Problèmes de Couches Minces,” Ph.D. thesis, Université Montpellier 2.
Ould Khaoua, A., Lebon, F., Licht, C., and Michaille, G., 1996, “Thin Layers in Elasticity: A Theoretical and Numerical Study,” Proceedings of the 1996 ESDA Conference, Vol. 4, ASME, New York, pp. 171–178.
Lebon,  F., Ould Khaoua,  A., and Licht,  C., 1997, “Numerical Study of Soft Adhesively Bonded Joints in Finite Elasticity,” Comp. Mech., 21, pp. 134–140.
Garboczi,  E. J., and Bentz,  D. P., 1991, “Digital Simulation of Interfacial Packing in Concrete,” J. Mater. Res., 6, pp. 196–201.
Hervé,  E., and Zaoui,  A., 1995, “Elastic Behavior of Multiply Coated Fibre-Reinforced Composites,” Int. J. Eng. Sci., 33, pp. 1419–1433.
Lagache,  M., Agbossou,  A., Pastor,  J., and Muller,  D., 1994, “Role of Interphase on the Elastic Behavior of Composite Materials: Theoretical and Experimental Analysis,” J. Compos. Mater., 28, pp. 1140–1157.


Grahic Jump Location
An example of a composite and its representative volume
Grahic Jump Location
Wavelet element matrix (j0=J, jmax=J+4)
Grahic Jump Location
Al-SiC composite with an interfacial zone (thickness η)
Grahic Jump Location
Jump of displacement for different values of α and β (M=3)
Grahic Jump Location
Homogenized coefficient for different values of α and β (M=3)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In