Many-Field Theory for Crystals Containing Particles with Rotational Degrees of Freedom

Vasiliev, Aleksey A.; Miroshnichenko, Andrey A.; Shigenari, Takeshi; Kagawa, Yutaka; Ishibashi, Yoshihiro

doi:10.1080/00150190390204204

Cited by 2 publications

(4 citation statements)

References 34 publications

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“…The equations (8), (18) and the coefficients for dispersion relations (11), (19) of the two-field model for the case of two-layer square lattice when the layers are parallel to the jc-axis will be obtained in the next section. The equations (8), (18) and the coefficients for dispersion relations (11), (19) of the two-field model for the case of two-layer square lattice when the layers are parallel to the jc-axis will be obtained in the next section.…”

Section: «ίι -4)k N+ (K 2 X+ K 2 Y -A)k D N -K 2 Y K S C 22 =2k D Nmentioning

confidence: 99%

“…Additionally, it contains a new system (19) corresponding to the two-field model for the case when the layers are parallel to the x-axis. Additionally, it contains a new system (19) corresponding to the two-field model for the case when the layers are parallel to the x-axis.…”

Section: Four-field Modelmentioning

confidence: 99%

“…3. Four surfaces for micro-rotational waves of the four-field model corresponding to (11), (12), (16), (19) are plotted inside the domains G 0 , G1, G 2 , G 3 , respectively. 2.…”

Section: Four-field Modelmentioning

confidence: 99%

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Multi-field Modelling of Cosserat solids

Vasiliev¹,

Miroshnichenko²

2005

Journal of the Mechanical Behavior of Materials

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We constructed multi-field generalisations of the Cosserat continuum model on the basis of the square lattice model that takes into account rotational degree of freedom of microstructural elements. This approach allows us to model not only long but also short wavelength fields of displacements and rotations. The accuracy of the wave solutions is examined. The dispersion relations of plane harmonic waves for multi-field Cosserat continuum models are obtained and compared with those of the basic model. Key words:Cosserat solid, Cosserat continuum model, short wavelength solutions INTRODUCTIONContinuum models are effectively used for modelling of solids composed of a large number of microstructural elements and have a wide range of applications from nano-materials to space constructions.They are useful for prediction of physical-mechanical characteristics, obtaining of analytical solutions, constructing of efficient algorithms for numerical simulations, etc. But such models should be corrected in order to describe some essential microstructural effects. The development of more precise models is often based on analysis and rejection of some assumptions of the classical theories. Different classifications of the generalised models are given, for example, in /1, 2/.Several types of generalised models are constructed by taking into account more degrees of freedom of structural elements than in classical models, e.g. /3-8/. In Cosserat and micropolar models not only space displacements but also independent rotations of the elements are taken into consideration and field of 379 Brought to you by | Western University Authenticated Download Date | 6/8/15 11:04 AM Vol. 16, No. 6, 2005 Multi-field Modelling of Cosserat Solidsrotations in addition to the field of displacements is introduced. Structural models are useful for development and applications of field theories. The discrete models of materials with beam-microstructure and grid frameworks, corresponding micropolar models and methods for their obtaining are presented, for example, in /9-12/. The complex-valued Cosserat continuum model was constructed for vibrating grid frameworks in /5/.The variants of lattice models and corresponding Cosserat continuum models were obtained in /13, 14/. Via analysis of the dispersion curves, it has been demonstrated that the Cosserat continuum model gives accurate results for deformation fields with wavelengths larger than approximately six times micro-structural cell distance but produces unrealistic results for short wavelengths. In the present article, we construct generalisations of the Cosserat continuum model applicable not only for long but also for short wavelengths oscillating fields. As a rule, single cell of periodicity and one corresponding vector field of generalised displacements are used for obtaining of continuum models. Rejection of this not self-evident assumption leads to a new class of models. We construct TV-field models on the basis of macrocell /15/, which is consist of Ν simple cells. By using of Ν vector fields...

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Section: «ίι -4)k N+ (K 2 X+ K 2 Y -A)k D N -K 2 Y K S C 22 =2k D Nmentioning

confidence: 99%

Section: Four-field Modelmentioning

confidence: 99%

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Multi-field Modelling of Cosserat solids

Vasiliev¹,

Miroshnichenko²

2005

Journal of the Mechanical Behavior of Materials

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“…Reciprocal rotation of tetrahedrons plays an important role in the α-β-phase transition via the incommensurate phase and formation of acoustic properties in quartz in the vicinity of this transition [17][18][19][20]. In the course of analyzing the results obtained on quartz [25][26][27][28][29][30][31][32][33][34] an assumption was made concerning the existence of a relationship between the major effects and the rotational degrees of freedom [35,36].…”

Section: Introductionmentioning

confidence: 99%

Long-period states of a crystal finite-size-particle system

Потекаев

Samsonov

2009

Russ Phys J

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A one-dimensional model is proposed, which ensures description of origination and main properties of longperiod and incommensurate phases of crystal having complex structure and consists of comparatively rigid "atomic clusters". In the case where reciprocal rotations of theses clusters are considerably large, not only translational but also rotational degrees of freedom have to be taken into account for the clusters. It is consideration of the rotational degrees of freedom which might provide for formation of long-period states and development of a number of physical effects, such as a variety of soliton solutions (of domain walls) and their non-trivial dynamics.

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Many-Field Theory for Crystals Containing Particles with Rotational Degrees of Freedom

Cited by 2 publications

References 34 publications

Multi-field Modelling of Cosserat solids

Multi-field Modelling of Cosserat solids

Long-period states of a crystal finite-size-particle system

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