Multi-field continuum theory for medium with microscopic rotations

@article{Vasiliev2005MultifieldCT,
  title={Multi-field continuum theory for medium with microscopic rotations},
  author={Aleksey A. Vasiliev and Sergey V. Dmitriev and Andrey E. Miroshnichenko},
  journal={International Journal of Solids and Structures},
  year={2005},
  volume={42},
  pages={6245-6260}
}
We derive the multi-field, micropolar-type continuum theory for the two-dimensional model of crystal having finite-size particles. Continuum theories are usually valid for waves with wavelength much larger than the size of primitive cell of crystal. By comparison of the dispersion relations, it is demonstrated that in contrast to the single-field continuum theory constructed in our previous paper the multi-field generalization is valid not only for long but also for short waves. We show that… Expand

Figures from this paper

Multifield model for Cosserat media
We construct a two-field higher-order gradient micropolar model for Cosserat media on the basis of a square lattice of elements with rotational degrees of freedom. This model includes equations ofExpand
Multifield modeling of Cosserat lattice dynamics
A two-field and a version of a four-field micropolar modes of a medium with a microstructure are constructed. A structural model of the Cosserat lattice taking into account both translational andExpand
Multi-field approach in mechanics of structural solids
We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids byExpand
Auxetic Behavior of Crystals from Rotational Degrees of Freedom
We review the results obtained for the 2D microscopic model of crystal having finite size particles proposed by Ishibashi and Iwata and later generalized in order to take into account deformabilityExpand
Non-linear plane waves in materials having hexagonal internal structure
Abstract Three different continuum limits for modeling non-linear plane waves in two-dimensional hexagonal lattice are obtained. New coupled non-linear continuum equations are obtained to study theExpand
Rotational Waves in Microstructured Materials
A brief review of theoretical representations and experimental data on rotational motions of elements of a continuous medium is given. Description of wave rotational motions is impossible in theExpand
Acoustic identification of nanocrystalline media
Two-dimensional (2D) models of nanocrystalline media with close proximity (a hexagonal lattice) and with non-dense packing (a square lattice) are considered in this paper. It is supposed thatExpand
MULTI-FIELD MODELLING OF SHORT WAVELENGTH DEFORMATIONS FOR COSSERAT SOLIDS
Summary We propose the method and derive the hierarchical system of multi-field models, which describe the elastic properties of Cosserat lattice with an increasing accuracy. We show that theExpand
Double dispersion equation for nonlinear waves in a graphene-type hexagonal lattice
Abstract It is shown that plane longitudinal nonlinear strain waves in a 2D graphene-type hexagonal lattice are described by a nonlinear double dispersion equation previously developed for theExpand
Two-dimensional nonlinear shear waves in materials having hexagonal lattice structure
An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. PossibleExpand
...
1
2
3
...

References

SHOWING 1-10 OF 54 REFERENCES
Dispersion and wave propagation in discrete and continuous models for granular materials
Abstract A generalised continuum model for granular media is derived by direct homogenisation of the discrete equations of motion. In contrast to previous works on this topic, continuum concepts suchExpand
Elastic properties of a two-dimensional model of crystals containing particles with rotational degrees of freedom
We consider a discrete two-dimensional model of a crystal with particles having rotational degrees of freedom. We derive the equations of motion and analyze its continuum analog obtained in theExpand
Micro-mechanical modelling of granular material. Part 1: Derivation of a second-gradient micro-polar constitutive theory
SummaryThis contribution is one in a series of two papers. In the current paper a constitutive law is developed that includes the micro-structural effects by particle displacement as well as particleExpand
NON-CLASSICAL MATERIAL CONTINUA
A model of material continuum is considered non-classical if it violates or at least does not fully respect one or more assumptions on which the classical continuum mechanics is based. The paper isExpand
Molecular and lattice dynamical study on modulated structures in quartz
It is shown that atomistic simulations using the Tsuneyuki potential for silica (SiO 2 ) correctly reproduce the major experimentally observed properties of the incommensurate (INC) phases in quartz,Expand
Asymptotic analysis of heterogeneous Cosserat media
Abstract The present work deals with the development of homogenization procedures for periodic heterogeneous linear elastic Cosserat media. It is resorted to asymptotic methods classically used inExpand
Domain wall solutions for EHM model of crystal:: structures with period multiple of four
Abstract For a one-dimensional discrete model of a crystal the form of a moving domain wall in the structure with period multiple of four was derived in the constant amplitude approximation. TheExpand
Origin of the incommensurate phase of quartz : II. Interpretation of inelastic neutron scattering data
The results of an inelastic neutron scattering investigation of the low-frequency modes of p quartz, described in the preceding paper (I), are interpreted using two different approaches: I) aExpand
Near-surface lattice instability in 2D fiber and half-space
We study the vibrational stability of model 2D solids with surfaces when large strains are present. For a fiber under compression, the phonon analysis correctly predicts the behavior of the bucklingExpand
A critical comparison of nonlocal and gradient-enhanced softening continua
Continuous models of material degradation may cease to produced meaningful results in the presence of high strain gradients. These gradients may occur for instance in the propagation of waves withExpand
...
1
2
3
4
5
...