Multifield model for cosserat media

Journal of Mechanics of Materials and Structures

Volumn 3, Issue 7, 2008, Pages 1365-1382

  Vasiliev, Aleksey A ^a   Miroshnichenko, Andrey E ^b   Ruzzene, Massimo ^c  

^a TVER STATE UNIVERSITY   (Russian Federation)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c Georgia Institute of Technology   (United States)

Author keywords

Cosserat media; Generalized continuum models; Microstructure; Multifield models; Short wave solution; Wave propagation

Indexed keywords

EID: 70350378120     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2008.3.1365     Document Type: Article

References (32)

1. E. C. Aifantis, "Update on a class of gradient theories", Mech. Mater. 35 (2003), 259-280.
2. A. Askar, Lattice dynamical foundations of continuum theories, World Scientific, Singapore, 1986.
3. H. Askes, A. S. J. Suiker, and L. J. Sluys, "A classification of higher-order strain-gradient models - linear analysis", Arch. Appl. Mech. 72 (2002), 171-188.
4. Z. P. Bažant and M. Jirásek, "Nonlocal integral formulation of plasticity and damage: survey of progress", J. Eng. Mech. 128:11 (2002), 1119-1149.
5. M. Born and K. Huang, Dynamical theory of crystal lattices, Clarendon Press, Oxford, 1954.
6. S. Casolo, "Modelling in-plane micro-structure of masonry walls by rigid elements", Int. J. Solids Struct. 41 (2004), 3626-3641.
7. E. Cosserat and F. Cosserat, Théorie des Corps Déformables, Hermann A. et Fils, Paris, 1909.
8. A. C. Eringen, Microcontinuum Field Theories: Foundations and Solids, Springer-Verlag, New York, 1999.
9. S. Flach and C. R. Willis, "Discrete breathers", Phys. Rep. 295 (1998), 181-264.
10. N. A. Fleck and J. W. Hutchinson, "Strain gradient plasticity", Adv. Appl. Mech. 33 (1997), 295-361.
11. N. A. Fleck and J. W. Hutchinson, "A reformulation of strain gradient plasticity", J. Mech. Phys. Solids 49 (2001), 2245-2271.
12. J. N. Grima, V. Zammit, R. Gatt, A. Alderson, and K. E. Evans, "Auxetic behaviour from rotating semi-rigid units", Phys. Status Solidi (b) 244:3 (2007), 866-882.
13. R. Lakes, "Deformation mechanisms in negative Poisson's ratio materials: structural aspects", J. Mater. Sci. 26 (1991), 2287-2292.
14. L. Limat, "Percolation and Cosserat elasticity: Exact results on deterministic fractal", Phys. Rev. B 37 (1988), 672-675.
15. V. A. Lomakin, Statistical problems of the mechanics of deformable solids, Nauka, Moscow, 1970. (in Russian).
16. G. A. Maugin, Nonlinear waves in elastic crystals, Oxford Mathematical Monographs, OUP, 1999.
17. H.-B. Mühlhaus and F. Oka, "Dispersion and wave propagation in discrete and continuous models for granular materials", Int. J. Solids Struct. 33 (1996), 2841-2858.
18. A. K. Noor, "Continuum modelling for repetitive lattice structures", Appl. Mech. Rev. 41:7 (1988), 285-296.
19. E. Pasternak and H.-B. Mühlhaus, "Cosserat and non-local continuum models for problems of wave propagation in fractured materials", pp. 741-746 in Structural failure and plasticity - IMPLAST2000, edited by X. L. Zhao and R. H. Grzebieta, Pergamon, Amsterdam, 2000.
20. I. S. Pavlov, A. I. Potapov, and G. A. Maugin, "A 2D granular medium with rotating particles", Int. J. Solids Struct. 43 (2006), 6194-6207.
21. R. H. J. Peerlings, M. G. D. Geers, R. de Borst, and W. A. M. Brekelmans, "A critical comparison of nonlocal and gradient enhanced softening continua", Int. J. Solids Struct. 38 (2001), 7723-7746.
22. J. Pouget, A. Askar, and G. A. Maugin, "Lattice model for elastic ferroelectric crystals: continuum approximation", Phys. Rev. B 33 (1986), 6320-6325.
23. C. L. Randow, G. L. Gray, and F. Costanzo, "A direct continuum model of micro- and nano-scale thin films", Int. J. Solids Struct. 43 (2006), 1253-1275.
24. D. Rogula, "Non-classical material continua", pp. 339-353 in Theoretical and applied mechanics, IUTAM, edited by F. I. Niordson and N. Olhoff, Elsevier Science Publishers B.V., North Holland, 1985.
25. A. J. Sievers and S. Takeno, "Intrinsic localized modes in anharmonic crystals", Phys. Rev. Lett. 61 (1988), 970-973.
26. A. Spadoni and M. Ruzzene, "Numerical and experimental analysis of static compliance of chiral truss-core airfoils", J. Mech. Mater. Struct. 2:5 (2007), 965-981.
27. A. S. J. Suiker and R. de Borst, "Enhanced continua and discrete lattices for modelling granular assemblies", Philos. Trans. Royal Soc. A 363 (2005), 2543-2580.
28. A. S. J. Suiker, A. V. Metrikine, and R. de Borst, "Comparison of wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models", Int. J. Solids Struct. 38 (2001), 1563-1583.
29. N. Triantafyllidis and S. Bardenhagen, "On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models", J. Elasticity 33:3 (1993), 259-293.
30. A. A. Vasiliev and A. E. Miroshnichenko, "Multi-field modelling of Cosserat solids", J. Mech. Behav. Mater. 16:6 (2005), 379-392.
31. A. A. Vasiliev, S. V. Dmitriev, Y. Ishibashi, and T. Shigenari, "Elastic properties of a two-dimensional model of crystals containing particles with rotational degrees of freedom", Phys. Rev. B 65 (2002), 094101.
32. A. A. Vasiliev, S. V. Dmitriev, and A. E. Miroshnichenko, "Multi-field continuum theory for medium with microscopic rotations", Int. J. Solids Struct. 42:24-25 (2005), 6245-6260.