Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Capriz, G. (1989), Continua with Microstructure, Springer Tracts Nat. Phil., v. 34, Springer, Berlin, New York.
Chen, P.J. (1973), Growth and decay of waves in solids, in Flugge’s Handbuch der Physic, vol. Via/3, Springer, Berlin.
Cosserat E. and F. (1909), Th éorie des corpes d éformables, Hermann, Paris.
Coulson, C.A. and Jeffrey, A. (1977), Waves, Longman Math. Texts, Essex, UK.
Engelbrecht, J. (1983), Nonlinear Wave Processes of Deformation in Solids, Pitman, London.
Engelbrecht, J. (1993) , Qualitative Aspects of Nonlinear Wave Motion: Complexity and Simplicity, Appl. Mech. Rev., 46, no 12, part 1, 509-518.
Engelbrecht, J. (1993) , Complexity and simplicity, Proc. Estonian Acad. Sci. Phys. Math, 421, 107-118.
Engelbrecht, J. (1997), Nonlinear Wave Dynamics, Complexity and Simplicity, Kluwer, Dordrecht, The Netherlands.
Engelbrecht, J. and Braun, M., (1998), Nonlinear waves in nonlocal media, Appl. Mech. Rev., 51, No. 8, 475-488.
Engelbrecht, J. and Pastrone, F. (2003), Waves in microstructured solids with nonlinearities in microscale, Proc. Estonian Acad. Sci. Phys. Math, 52/1, 12-20.
Engelbrecht, J., Berezovski, A., Pastrone, F. and Braun, M. (2004), Waves in microstructured materials and dispersion, Phil. Mag, 85, Nos 33-35, 4127-4141.
Engelbrecht, J., Cermelli, P. and Pastrone, F. (1999), Wave hierarchy in microstructured solids, in Geome-try, Continua and Microstructure (G. Maugin ed.) Hermann, Paris.
Ericksen, J.L. (1972), Wave propagation in thin elastic shells, Arch Rat. Mech. Anal., 43, 167-178.
Eringen, A.C. (1966), Linear theory of micropolar elasticity, J. Math. Mech., 15, 909-923.
Eringen, A.C. (2000), Microcontinuum Field Theories. I - Foundations, Springer, Berlin, New York.
Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer, Berlin, New York.
Forest, S. and Sievert, R. (2003), Elastoviscoplastic constitutive framework for generalized continua, Acta Mech., 160, 71-111.
Hayes, M.A., (1963), Wave propagation and uniqueness in prestressed elastic solids. Proc. Roy. Soc. Lond., A274, 500-506.
Hayes, M.A. and Rivlin, R.S. (1972), Propagation of sinusoidal small-amplitude waves in a deformed viscoelastic solid - II, J. Acoust. Soc. Amer., 51, 1652-1663.
Jeffrey, A. (1976), Quasilinear Hyperbolic Systems and Waves, Pitman, London.
Jeffrey, A. (1980), Lectures on nonlinear wave propagation, in Wave Propagation (Corso CIME, Bres-sanone), Liguori, Bologna, 7-97.
Kunin, I.A. (1983), Elastic Media with Microstructure, 2 Vol., Springer, Berlin.
Love, A.E.H. (1944), A Treatise on the Mathematical Theory of Elasticity (4th ed.), Dover, New York.
Marsden, J.E. and Hugues, T. (1983), Mathematical Foundations of Elasticity, Prentice Hall, Englewood Cliffs, NJ.
Maugin, G.A. (1980), Acta Mech., 35, pp.1-70.
Maugin, G.A. (1993), Material Inhomogeneities in Elasticity, Chapman & Hall, London.
Maugin, G.A. (1999), Nonlinear Waves in Elastic Crystals, Oxford Univ. Press, Oxford, UK.
Maugin, G.A. (2004a), Introduction a la mecanique des milieux continus generalises et ses applications, Proc. Colloque National MECAMAT 2004 (Aussois, Janvier 2004), eds. P. Babin, R. Dendievel, S. Forest, J.F. Ganghoffer, A. Zeghadi, and M.H. Zoberman, pp. 47-54, Association M écamat, Paris [also on CD-Rom].
Maugin, G.A. (2004b), Generalized continuum mechanics: Three paths, ICTAM’04, Warsaw (15-21 Aug.2004), Proc. CD-Rom ISBN83-89697-01-1, Eds. W. Gutkowski and T.A. Kowaleski, FSM3L 11347, 2 pages.
Mindlin, R.D. (1964). Microstructure in linear elasticity, Arch. Rat. Mech. Anal., 1, 51-78.
Pastrone, F. (2003), Waves in solids with vectorial microstructure, Proc. Estonian Acad. Sci. Phys. Math, 52/1, 21-29.
Pastrone, F. (2005), Wave propagation in microstructured solids, Math. Mech. Solids, 10, 349-357.
Pastrone, F., Cermelli, P. and Porubov, A.V. (2004), Nonlinear waves in 1-D solids with microstructure, Mater. Phys. Mech., 9-16.
Porubov, A.V. (2003), Amplification of Nonlinear Strain Waves in Solids, World Scientific, Singapore.
Porubov, A.V., Pastrone, F. (2004), Nonlinear bell-shaped and kink-shaped strain waves in microstructured solids, Intl. J. Nonlinear Mech., 39, 1289-1299.
Taniuti, T. and Nishihara, K. (1983), Nonlinear Waves, Pitman, London (in Japanese, 1977).
Thomas, T.J. (1961), Plastic Flow and Fracture in Solids, Academic, New York.
Toupin, A. (1962), Elastic materials with coupled-stresses, Arch. Rat. Mech. Anal., 11, 385-414.
Toupin, A. (1964), Theories of elasticity with coupled-stress, Arch. Rat. Mech. Anal., 17, 85-112.
Truesdell, C.A. and Noll, W. (1965), The nonlinear field theories of mechanics, in Flugge’s Handbuch der Physik, vol. III/3, Springer, Berlin, 1-602.
Truesdell, C.A. and Toupin, R. (1960), The classical field theories, in Flugge’s Handbuch der Physik, vol. III/1, Springer, Berlin, 226-793.
Truesdell, C.A. and Wang, C.C. (1973), Introduction to Rational Elasticity, Noordhoff, Leyden.
Witham, G.B. (1974), Linear and Nonlinear Waves, Wiley, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Pastrone, F. (2006). Nonlinearity and Complexity in Elastic Wave Motion. In: Delsanto, P.P. (eds) Universality of Nonclassical Nonlinearity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35851-2_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-35851-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33860-6
Online ISBN: 978-0-387-35851-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)