EAP - Proceedings of the Estonian Academy of Sciences

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proceedings
of the estonian academy of sciences

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Hierarchical structures in complex solids with microscales; pp. 79–86

PDF | doi: 10.3176/proc.2010.2.04

Author

Franco Pastrone

Abstract

In nonclassical mechanics it is natural to deal with the problem of the propagation of nonlinear waves in solids with different internal structural scales (Engelbrecht, J., Pastrone, F., Braun, M., and Berezovski, A. Hierarchy of waves in nonclassical materials. In Universality of Nonclassical Nonlinearity (Delsanto, P. P., ed.). Springer, 2007, 29–48). The choice of suitable microstrain functions of the microdisplacements, of their time derivatives as strain velocities, allows us to obtain the field equations via a variational principle (see Pastrone, F., Cermelli, P., and Porubov, A. V. Nonlinear waves in 1-D solids with microsctructure. Mater. Phys. Mech., 2004, 7, 9–16; Casasso, A. and Pastrone, F. Wave propagation in solids with vectorial microstructures. Wave Motion, doi: 10.1016/j.wavemoti.2009.12.006; Porubov, A. V., Pastrone, F., and Maugin, G. A. Selection of two-dimensional nonlinear strain waves in micro-structured media. C. R. Acad. Sci. Paris}, 2004, Ser. I 337, 513–518) in three different cases: one-dimensional solids with two different microscales, two-dimensional solids with microstructures, and plane granular media. In all cases the hierarchical structure of equations due to the scales in materials is evident.

References

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