geoscience.net logo
+ Resolve Article
+ Follow Us
Follow on FacebookFollow on Facebook
Follow on TwitterFollow on Twitter

+ Translate
+ Subscribe to Site Feed
GeoScience Most Shared ContentMost Shared Content

Effective Willis constitutive equations for periodically stratified anisotropic elastic media


, : Effective Willis constitutive equations for periodically stratified anisotropic elastic media. Proceedings Mathematical Physical & Engineering Sciences 467(2130): 1749-1769

A method to derive homogeneous effective constitutive equations for periodically layered elastic media is proposed. The crucial and novel idea underlying the procedure is that the coefficients of the dynamic effective medium can be associated with the matrix logarithm of the propagator over a unit period. The effective homogeneous equations are shown to have the structure of a Willis material, characterized by anisotropic inertia and coupling between momentum and strain, in addition to effective elastic constants. Expressions are presented for the Willis material parameters which are formally valid at any frequency and horizontal wavenumber as long as the matrix logarithm is well defined. The general theory is exemplified for scalar SH motion. Low frequency, long wavelength expansions of the effective material parameters are also developed using a Magnus series, and explicit estimates are derived for the rate of convergence.

US$19.90

DOI: 10.1098/rspa.2010.0389


Other references

Kashfi K.; Weakley L.J.; Cook G.A., 1988: Effects of diabetes on the carnitine palmitoyltransferase of isolated hepatic mitochondrial outer membranes. Biochemical Society Transactions 16(6): 1010-1011

Aripova, N.; Vernik, R.S.; Talipov, K., 1968: Some results of study of the water regime of Walnut/fruit forest. Describes transpiration measurements in natural communities of Juglans regia, Prunus sogdiana and Crataegus turkestanica in Uzbekistan. Transpiration rates were greater on S.W. slopes than on N.E. slopes, and were less in a dense J. regia stand (1...

Anonymous, 2012: TRICARE reimbursement revisions. Final rule. This final rule provides several necessary revisions to the regulation in order for TRICARE to be consistent with Medicare. These revisions affect: Hospice periods of care; reimbursement of physician assistants and assistant-at-surgery claims; and...

Tian, J-Liang.; Sun, L.; Hu, R-Yin.; Tian, X-Bin., 2014: Cementless total hip arthroplasty with structural allograft for massive acetabular defect in hip revision. To study retrospectively 20 hip revison patients treated by cementless total hip arthroplasty with structural allograft. Twenty patients suffering from aseptic loosening of an uncemented cup complicated by a large defect underwent cementless total...

Nishiura, M.; Shichijo, T.; Ueno, I.; Yamada, Y.; Yoshida, T.; Kihara, T.; Iwamasa, M.; Iwasaki, T., 1983: The new Citrus cultivar Sweet Spring. The monoembryonic tangelo cultivar Sweet Spring (C. unshiu 'Ueda' X C. hassaku) has been described elsewhere [see PBA 52, 10757].

Graham D.; Smillie R.M., 1971: Chloroplasts and lamellae algal preparations. San Pietro, Anthony (Ed ) Methods in Enzymology Vol Xxiii Photosynthesis, Part A Xix+743p Illus Academic Press: New York, N Y , U S A ; London, England 228-242

Jiang, S.; Peng, D.; He, L., 2015: Progress in regulatory T cells and hepatocellular carcinoma. As a functionally unique subset of T cells, regulatory T cells (Treg) suppress tumor immune responses effectively through a variety of mechanisms and play an important role in tumorigenesis and tumor progression. There is growing evidence to sugge...

Magrassi, L.; Graziadei, P.P.C., 1994: Developmental potential of cells dissociated from the mature and developing olfactory organ and transplanted into the fetal brain. Society for Neuroscience Abstracts 20(1-2): 655

Rivas Martinez, Salvador, 1962: Contribution to the phytosociological study of the Spanish beech woods. The various phytosociological units that apply to Spanish beech woods are surveyed and described. A newly named association, Galio-Fagetum, and two newly named subassociations, Helleboro-Fagetum Piroletosum and Helleboro-Fagetum Epipactidetorum ar...

Shovers, J.; Bavisotto, V.S., 1967: Fermentation-derived enzyme substitute for animal rennet. Cheese made with a milk-clotting enzyme elaborated by Endothia parasitica had a completely acceptable and accelerated body and flavour development. A description is given of the enzyme's milk-clotting and curd-forming properties (which are co...