A dispersive continuum model of jointed media

Authors:
S. Shkoller, A. Maewal and G. A. Hegemier

Journal:
Quart. Appl. Math. **52** (1994), 481-498

MSC:
Primary 73B27; Secondary 35B27, 73K12

DOI:
https://doi.org/10.1090/qam/1292199

MathSciNet review:
MR1292199

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The problem of formulating higher-order continuum models for a jointed medium is considered for propagation of waves whose wavelengths are much larger than the cell width. A multiscale asymptotic approach is used to derive exact solutions for the microstructure in this large wavelength limit. A mixed variational principle is then invoked to obtain the homogenized model. This model, which incorporates dispersive wave phenomena, yields results which agree well with the exact solution for the dispersion of harmonic waves propagating through the medium.

**[1]**J. B. Keller,*Effective behavior of heterogeneous media*, Statist. Mech. and Statist. Meth. in Theory and Appl. (U. Landman, ed.), Plenum Press, New York, 1977, p. 631**[2]**I. Babuska,*Solution of interface problems by homogenization*. I, II, SIAM J. Math. Anal.**7**, 603-634, 635-645 (1976)**[3]**A. Bensoussan, J. L. Lions, and G. Papanicolaou,*Asymptotic Analysis of Periodic Structures*, North-Holland, Amsterdam, 1978**[4]**J. M. Burgers,*On some problems of homogenization*, Quart. Appl. Math.**XXXV**, 421-434 (1978)**[5]**E. Sanchez-Palencia,*Non-homogeneous media and vibration theory*, Lecture Notes in Phys., vol. 127, Springer-Verlag, Berlin, 1980**[6]**G. A. Hegemier, et al.,*On construction of mixture theories for composite materials by the method of multi-variable asymptotic expansion*, Cont. Models of Discrete Systems, Univ. of Waterloo Press, 1980, pp. 423-441**[7]**A. Maewal,*Construction of models of dispersive elastodynamic behavior of periodic composites: A computational approach*, Comp. Meth. Appl. Mech. Engrg.**57**, 191-205 (1986)**[8]**F. Santosa and W. W. Symes,*A dispersive effective medium for wave propagation in periodic composites*, SIAM J. Appl. Math.**51**, 984-1005 (1991)**[9]**H. Murakami and G. A. Hegemier,*Development of a nonlinear continuum model for wave propagation in jointed media: Theory for single joint set*, Mech. Mat.**8**, 199-218 (1989)**[10]**J. P. Keener,*Principles of Applied Mathematics*, Addison-Wesley, New York, 1988**[11]**W. Rudin,*Real and Complex Analysis*, 3rd. ed., McGraw-Hill, New York, 1987**[12]**J. P. Aubin,*Approximation of Elliptic Boundary-Value Problems*, Wiley-Interscience, New York, 1972

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
73B27,
35B27,
73K12

Retrieve articles in all journals with MSC: 73B27, 35B27, 73K12

Additional Information

DOI:
https://doi.org/10.1090/qam/1292199

Article copyright:
© Copyright 1994
American Mathematical Society