ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
cover
Proceedings of the Estonian Academy of Sciences. Physics. Mathematics
Elastic waves in heterogeneous materials as in multiscale-multifield continua; 100–107
PDF | https://doi.org/10.3176/phys.math.2007.2.05

Authors
Patrizia Trovalusci, Giuseppe Rega
Abstract

A multifield continuum to describe grossly the dynamic behaviour of composite materials (fibre reinforced, polymers, masonry-like, etc.) is proposed using a multiscale modelling based on the hypotheses of the classical molecular theory of elasticity. Referring to a one-dimensional sample, the possibility of revealing the presence of internal heterogeneities is investigated.

References

1. Trovalusci, P. and Masiani, R. Non-linear micropolar and classical continua for anisotropic discontinuous materials. Int. J. Solids Struct., 2003, 40, 1281–1297.
https://doi.org/10.1016/S0020-7683(02)00584-X
https://doi.org/10.1006/jcph.1995.1004

2. Aifantis, E. C. On the role of gradients in the localization of deformation and fracture. Int. J. Eng. Sci., 1992, 30, 1279–1299.
https://doi.org/10.1016/0020-7225(92)90141-3

3. Sluys, L. J., de Borst, R. and Mühlhaus, H.-B. Wave propagation, localization and dispersion in a gradient-dependent medium. Int. J. Solids Struct., 1993, 30, 1153–1171.
https://doi.org/10.1016/0020-7683(93)90010-5

4. Capriz, G. Continua with Microstructure. Springer-Verlag, Berlin, 1989.
https://doi.org/10.1007/978-1-4612-3584-2

5. Trovalusci, P. and Masiani, R. A multifield model for blocky materials based on multiscale description. Int. J. Solids Struct., 2005, 42, 5778–5794.
https://doi.org/10.1016/j.ijsolstr.2005.03.027

6. Sansalone, V., Trovalusci, P. and Cleri, F. Multiscale modelling of composite materials by a multifield finite element method. Int. J. Multiscale Comput. Eng., 2005, 3, 463–480.
https://doi.org/10.1615/IntJMultCompEng.v3.i4.50

7. Maugin, G. Material Inhomogeneities in Elasticity. Chapman & Hall, London, 1993.
https://doi.org/10.1007/978-1-4899-4481-8

8. Gurtin, M. E. Configurational Forces as Basic Concepts of Continuum Physics. Springer-Verlag, Berlin, 2000.

9. Needleman, A. Material rate dependence and mesh sensitivity on localization problems. Comput. Methods Appl. Mech. Eng., 1988, 67, 69–86.
https://doi.org/10.1016/0045-7825(88)90069-2

10. Pijaudier-Cabot, G. and Bažant, Z. P. Nonlocal damage theory. J. Eng. Mech., ASCE, 1987, 113, 1512–1533.
https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)

11. Gurtin, M. E. Thermodynamics and the possibility of spatial interaction in elastic materials. Arch. Rat. Mech. Anal., 1965, 19, 339–352.
https://doi.org/10.1007/BF00253483

12. Trovalusci, P. and Augusti, G. A continuum model with microstructure for materials with flaws and inclusions. J. Physique IV, 1998, Pr8, 383–390.
https://doi.org/10.1051/jp4:1998847

13. Ericksen, J. L. Special topics in elastostatics. Adv. App. Mech., 1977, 17, 189–244.
https://doi.org/10.1016/S0065-2156(08)70221-7

14. Voigt, W. Lehrbuch der Kristallphysik. Math. Wissenschaften, 1910, XXXIV, 596–616.

15. Di Carlo, A. A non-standard format for continuum mechanics. In Contemporary Research in the Mechanics and Mathematics of Materials (Batra, R. C. and Beatty, M. F., eds). CIMNE, Barcelona, 1996, 92–104.

16. Trovalusci, P. and Rega, G. A continuum model for the analysis of propagating elastic waves in microcracked materials. In Proceedings ICM9, Geneve, 2003 (CD ROM).

Back to Issue

Back issues