Abstract
A linear model of the microstructured continuum based on Mindlin theory is adopted which can be represented in the framework of the internal variable theory. Fully coupled systems of equations for macro-motion and microstructure evolution are represented in the form of conservation laws. A modification of wave propagation algorithm is used for numerical calculations. Results of direct numerical simulations of wave propagation in periodic medium are compared with similar results for the continuous media with the modelled microstructure. It is shown that the proper choice of material constants should be made to match the results obtained by both approaches
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Solitary Wave
- Direct Numerical Simulation
- Internal Variable
- Elastic Wave Propagation
- Dissipation Inequality
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Maugin, G.A.: Nonlinear Waves in Elastic Crystals, Oxford University Press (1999).
Sun, C.T., Achenbach, J.D., Herrmann, G.: Continuum theory for a laminated medium. J. Appl. Mech. 35 467–475 (1968).
Nemat-Nasser, S., Hori, M.: Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Amsterdam (1993).
Mindlin, R.D.: Microstructure in linear elasticity. Arch. Rat. Mech. Anal 16 51-78 (1964).
Eringen, A.C., Suhubi, E.S.: Nonlinear theory of micro-elastic solids II. Int. J. Eng. Sci. 2 189-203 (1964).
Maugin, G.A.: On the thermomechanics of continuous media with diffusion and/or weak nonlocality. Arch. Appl. Mech. 75 723-738 (2006).
Ván, P., Berezovski, A., Engelbrecht, J.: Internal variables and dynamic degrees of freedom. J. Non-Equilib. Thermodyn. 33 235-254 (2008).
Nowacki, W.: Thermoelasticity. Pergamon/PWN, Oxford/Warszawa (1962).
Maugin, G.A.: Internal variables and dissipative structures. J. Non-Equilib. Thermodyn. 15 173-192 (1990).
Engelbrecht, J., Berezovski, A., Pastrone, F., Braun, M.: Waves in microstructured materials and dispersion. Phil. Mag. 85 4127-4141 (2005).
Engelbrecht, J., Cermelli, P., Pastrone, F.: Wave hierarchy in microstructured solids. In: Maugin, G.A. (ed.) Geometry, Continua and Microstructure, pp. 99-111. Hermann Publ., Paris (1999).
Effective Computational Methods for Wave Propagation. Kampanis, N. A., Dougalis, V.A., Ekaterinaris, J.A. (eds.), Chapman & Hall/CRC, Boca Raton (2008).
LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press (2002).
Berezovski, A., Engelbrecht, J., Maugin, G.A.: Numerical Simulation of Waves and Fronts in Inhomogeneous Solids. World Scientific, Singapore (2008).
Lakes, R.S.: Experimental method for study of Cosserat elastic solids and other generalized continua. In: Mühlhaus, H.-B. (ed.) Continuum Models for Materials with Microstructure, pp.1-22. Wiley, New York (1995).
Berezovski, A., Berezovski, M. and Engelbrecht, J.: Numerical simulation of nonlinear elastic wave propagation in piecewise homogeneous media. Mater. Sci. Engng. A 418 364-369 (2006).
Janno, J., Engelbrecht J.: An inverse solitary wave problem related to microstructural materials. Inverse Problems. 21 2019-2034 (2005).
Engelbrecht, J. Berezovski, A., Salupere, A.: Nonlinear deformation waves in solids and dispersion. Wave Motion. 44 493-500 (2007).
Pastrone, F., Cermelli, P. and Porubov, A.: Nonlinear waves in 1-D solids with microstructure. Mater. Phys. Mech. 7 9-16 (2004).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this paper
Cite this paper
Engelbrecht, J., Berezovski, A., Berezovski, M. (2010). Deformation Waves in Microstructured Materials: Theory and Numerics. In: Wu, TT., Ma, CC. (eds) IUTAM Symposium on Recent Advances of Acoustic Waves in Solids. IUTAM Bookseries, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9893-1_2
Download citation
DOI: https://doi.org/10.1007/978-90-481-9893-1_2
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9892-4
Online ISBN: 978-90-481-9893-1
eBook Packages: EngineeringEngineering (R0)