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Journal articles on the topic 'Micropolar theory'

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Published: 4 June 2021
Last updated: 17 June 2025

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1

Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "On the theory of linear micropolar hemitropic media." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 4(46) (December 30, 2020): 16–24. http://dx.doi.org/10.37972/chgpu.2020.89.81.031.

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В статье рассматриваются вопросы применения относительных тензоров при моделирвоании гемитропных микрополярных сред. Вводится определяющая форма микрополярного упругого потенциала. С помощью принципа виртуальной работы получаются определяющие уравнения для силовых и моментных характеристик микрополярного континуума в терминах относительных тензоров. Приводятся уравнения движения микрополярного континуума в терминах относительных тензоров. Выводится финальная форма динамических уравнений для перемещений и микровращений в случае полуизотропной (гемитропной) симметрии. The paper deals with the application of relative tensors to modeling hemitropic micropolar media. The latter is of crucial importance for biomechanics, mechanics of growing solids and mechanics of metamaterials. The constitutive form of the micropolar elastic potential is discussed. The basic equations of micropolar continuum are derived due to the principle of virtual displacements. Differential equations of the micropolar continuum are given in terms of relative tensors. The final form of dynamic equations for displacements and microrotations in the case of semi-isotropic (hemitropic) micropolar continuum is derived and discussed.
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2

Xue, Bing Bing, Hong Yu Xu, Zhu Mu Fu, and Qing Yong Sun. "Effect of Thermal Relaxation on Propagation of Longitudinal Displacement Wave." Advanced Materials Research 146-147 (October 2010): 314–17. http://dx.doi.org/10.4028/www.scientific.net/amr.146-147.314.

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The micropolar elasticity theory takes into consideration the granular character of the medium, describes deformations by a microrotation and a microdisplacement. A model can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. And if some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. Employing the model of micropolar generalized magneto-thermo-elasticity, reflection and refraction of longitudinal displacement wave at interface of two welded micropolar elastic media are studied. The amplitude ratios of reflected and refracted micropolar magneto-thermoelastic longitudinal displacement waves, longitudinal microrotational waves and the coupled transverse and microrotational waves are studied for incident longitudinal displacement wave. The numerical results show that the effects of thermal relaxation times are very significant on the amplitude ratios.
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Hassanpour, Soroosh, and Glenn R. Heppler. "Micropolar elasticity theory: a survey of linear isotropic equations, representative notations, and experimental investigations." Mathematics and Mechanics of Solids 22, no. 2 (2016): 224–42. http://dx.doi.org/10.1177/1081286515581183.

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This paper is devoted to a review of the linear isotropic theory of micropolar elasticity and its development with a focus on the notation used to represent the micropolar elastic moduli and the experimental efforts taken to measure them. Notation, not only the selected symbols but also the approaches used for denoting the material elastic constants involved in the model, can play an important role in the micropolar elasticity theory especially in the context of investigating its relationship with the couple-stress and classical elasticity theories. Two categories of notation, one with coupled classical and micropolar elastic moduli and one with decoupled classical and micropolar elastic moduli, are examined and the consequences of each are addressed. The misleading nature of the former category is also discussed. Experimental investigations on the micropolar elasticity and material constants are also reviewed where one can note the questionable nature and limitations of the experimental results reported on the micropolar elasticity theory.
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4

Chen, James. "Micropolar Theory of Flexoelectricity." Journal of Advanced Mathematics and Applications 1, no. 2 (2012): 269–74. http://dx.doi.org/10.1166/jama.2012.1021.

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5

Etse, G., M. Nieto, and P. Steinmann. "A micropolar microplane theory." International Journal of Engineering Science 41, no. 13-14 (2003): 1631–48. http://dx.doi.org/10.1016/s0020-7225(03)00031-4.

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6

Dehbani, Hossein, Mohsen Jabbari, Ahmad Reza Khorshidvand та Mehrdad Javadi. "Two-dimensional analytical solution of micropolar magneto-thermoelasticity FGM hollow cylinder under asymmetric load (r, θ)". Physica Scripta 96, № 12 (2021): 125720. http://dx.doi.org/10.1088/1402-4896/ac3313.

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Abstract This paper presents a two-dimensional analytical solution (r, θ) to study micropolar magneto-thermoelasticity for a hollow cylinder, made of FGMs, under steady-state conditions. The physical properties of materials are in the form of a power function and undergo changes in the direction of the radius. To solve the heat transfer equation and Navier equations, the complex Fourier series and the power-law functions are used. By solving the equations using the general thermal and mechanical asymmetric boundary conditions on the inner and outer surface of the cylinder, radial displacement, circumferential displacement, force stresses, coupling stresses, and micro-rotation are obtained. Numerical examples of Aluminum-epoxy composite are presented for the three theories of classical, micropolar, and micropolar magneto thermoelasticity. Results indicated that the inner and outer surface of the cylinder subject to asymmetric harmonic temperature and mechanical distribution show that the values of the micropolar magnet theory are less than those of the classical theory and more than the values of the micropolar theory. Where harmonic radial stresses are applied to the inner surface of the cylinder, the values of the classical theories correspond to those of the micropolar theory. The presence of a magnetic field makes differences between the values of the micropolar magnet theory and the values of the two classical and micropolar theories. The study was validated by examining an example of homogenous materials under ambient conditions.
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7

Dang, Song Yang, Hong Yu Xu, Qing Yong Sun, and Bin Liang. "Propagation Characteristics of Coupled Wave through Micropolar Fluid Interlayer in Micropolar Elastic Solid." Advanced Materials Research 721 (July 2013): 729–32. http://dx.doi.org/10.4028/www.scientific.net/amr.721.729.

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Based on micropolar fluid theory and micropolar solid elasticity theory, reflection and transmission characteristics of longitudinal displacement wave and two coupled waves were studied when incident coupled wave propagated through micropolar fluid interlayer in micropolar elastic solid. Using numerical example, the rules of the reflection waves and refraction waves amplitudes varied with incident angle are also discussed. Results show that there exist extremum values of reflection and transmission coefficient for coupled wave. There are two peaks and one zero value of transmission coefficient for longitudinal displacement wave.
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8

Xue, Bing Bing, Hong Yu Xu, Zhu Mu Fu, and Qing Yong Sun. "Reflection and Refraction of Longitudinal Displacement Wave at Interface between Two Micropolar Elastic Solid." Advanced Materials Research 139-141 (October 2010): 214–17. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.214.

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Using the model of generalized micropolar magneto-thermo-elasticity, reflection and refraction of longitudinal displacement wave at interface of two welded micropolar elastic media are studied. The model can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. And if some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. Using continuous conditions at the interface, the amplitude ratios of reflected and refracted micropolar magneto-thermoelastic longitudinal displacement waves, longitudinal microrotational waves and the coupled transverse and microrotational waves are studied for incident longitudinal displacement wave. The numerical results show that the effect of magnetic field is very significant on the amplitude ratios.
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9

Galeş, C. "A Mixture Theory for Micropolar Thermoelastic Solids." Mathematical Problems in Engineering 2007 (2007): 1–21. http://dx.doi.org/10.1155/2007/90672.

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We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established.
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10

Sun, Qing Yong, Hong Yu Xu, and Bin Liang. "Propagation Characteristics of Longitudinal Displacement Wave in Micropolar Fluid with Micropolar Elastic Plate." Materials Science Forum 694 (July 2011): 923–27. http://dx.doi.org/10.4028/www.scientific.net/msf.694.923.

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Based on micropolar fluid theory and micropolar solid elasticity theory, reflection and transmission characteristics of three kinds of micropolar elastic waves, which are longitudinal displacement wave and two coupled waves, were studied when incident longitudinal displacement wave propagated in micropolar fluid with micropolar elastic plate. Using numerical example, the variations of various amplitudes are also shown against the angle of incidence and the variation characteristics of various amplitudes are discussed. Results show that there exist maximum values of reflection and transmission coefficient for coupled wave, however, there exist minimum values of reflection coefficient for longitudinal displacement wave, and transmission coefficient decreases with the incident angle and the transmission coefficient are smaller for bigger incident angle.
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11

Hassanpour, Soroosh, and G. R. Heppler. "Theory of micropolar gyroelastic continua." Acta Mechanica 227, no. 5 (2016): 1469–91. http://dx.doi.org/10.1007/s00707-016-1573-x.

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12

Sofiadis, G., and I. Sarris. "Reynolds number effect of the turbulent micropolar channel flow." Physics of Fluids 34, no. 7 (2022): 075126. http://dx.doi.org/10.1063/5.0098453.

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The turbulent regime of non-Newtonian flows presents a particular interest as flow behavior is directly affected by the internal microstructure type of the fluid. Differences in the dispersed phase of a particle laden flow can either lead to drag reduction and turbulence attenuation or to drag and turbulence enhancement in polymer flows and dense suspensions, respectively. A general concept of non-Newtonian fluid flow may be considered in a continuous manner through the micropolar theory, recognizing the limitations that bound this theory. In recent articles [Sofiadis and Sarris, “Microrotation viscosity effect on turbulent micropolar fluid channel flow,” Phys. Fluids 33, 095126 (2021); Sofiadis and Sarris, “Turbulence intensity modulation by micropolar fluids,” Fluids 6, 195 (2021)], the micropolar viscosity effect of the turbulent channel flow under constant Reynolds number and its turbulent modulation were investigated. The present study focuses on the investigation of the turbulent micropolar regime as the Reynolds number increases in a channel flow. Findings support that the micropolar stress, which was found to assist turbulence enhancement in the present model, attenuates as Re increases. Effects on the friction behavior of the flow, as Reynolds number increases, become more important for cases of higher micropolar viscosity, where a reverse drag behavior is observed as compared to lower micropolar viscosity ones. Finally, turbulence intensification for these cases declines close to the wall in contrast to lower micropolar viscosity flows, which manage to sustain high turbulence and increase drag in the near-wall region along with Re.
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13

Abreu, Rafael, and Stephanie Durand. "Understanding Micropolar Theory in the Earth Sciences I: The Eigenfrequency $$\omega _r$$." Pure and Applied Geophysics 179, no. 3 (2021): 915–32. http://dx.doi.org/10.1007/s00024-021-02932-7.

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AbstractEven though micropolar theories are widely applied for engineering applications such as the design of metamaterials, applications in the study of the Earth’s interior still remain limited and in particular in seismology. This is due to the lack of understanding of the required elastic material parameters present in the theory as well as the eigenfrequency $$\omega _r$$ ω r which is not observed in seismic data. By showing that the general dynamic equations of the Timoshenko’s beam is a particular case of the micropolar theory we are able to connect micropolar elastic parameters to physically measurable quantities. We then present an alternative micropolar model that, based on the same physical basis as the original model, circumvents the problem of the original eigenfrequency $$\omega _r$$ ω r laking in seismological data. We finally validate our model with a seismic experiment and show it is relevant to explain observed seismic dispersion curves.
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14

Singh, S. S., and R. Lianngenga. "Plane Waves in Micropolar thermoelastic Materials with Voids." Science & Technology Journal 4, no. 2 (2016): 141–51. http://dx.doi.org/10.22232/stj.2016.04.02.09.

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The problem of plane waves in micropolar thermoelastic materials with voids has been investigated. Using the linear theory of micropolar thermoelastic materials with voids developed by Passarella [27], we come to know that there exist six waves, which are three coupled dilatational waves, two coupled shear waves and micropolar dilatational wave, in the materials. The phase velocities and their attenuation coefficients of the three coupled and micropolar dilatational and two coupled shear waves are obtained numerically and analytically.
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15

Xu, Hong Yu, Bing Bing Xue, and Zhu Mu Fu. "Frequency Equations of Magneto-Thermoviscoelastic Surface Wave." Advanced Materials Research 97-101 (March 2010): 479–83. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.479.

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The model of the generalized linear micropolar magneto-thermoviscoelastic theory is presented in this paper. It can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. If some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. The magneto-thermo- viscoelastic waves at an interface between two micropolar viscoelastic solid mediums are discussed with the model. Using continuous conditions, the general frequency equations are obtained. Also as a validation, if one media is replaced by vacuum, we have deduced the frequency equation of Rayleigh wave. And if the problem is reduced to elastic case, it coincides with the results of Ewing et al.
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16

ASADI, H., K. JAVAHERDEH, and S. RAMEZANI. "FINITE ELEMENT SIMULATION OF MICROPOLAR FLUID FLOW IN THE LID-DRIVEN SQUARE CAVITY." International Journal of Applied Mechanics 05, no. 04 (2013): 1350045. http://dx.doi.org/10.1142/s1758825113500452.

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The micropolar fluid theory augments the laws of classical continuum mechanics by incorporating the effects of fluid molecules on the continuum. So, the micropolar theory has been able to explain many phenomena at micro and nano scales. In this paper, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, analytical solution of the Poiseuille flow of micropolar fluid in a microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow in a lid-driven square cavity is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.
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17

Dang, Song Yang, Hong Yu Xu, Qing Yong Sun, and Bin Liang. "Reflection and Transmission of Longitudinal Displacement Wave through Micropolar Fluid Interlayer in Micropolar Solid." Applied Mechanics and Materials 438-439 (October 2013): 408–12. http://dx.doi.org/10.4028/www.scientific.net/amm.438-439.408.

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Based on micropolar fluid theory and micropolar solid elasticity theory, reflection and transmission characteristics of longitudinal displacement wave and two coupled waves are studied when incident longitudinal displacement plane wave propagates through micropolar fluid interlayer in micropolar solid. Theoretical and numerical analytical results reveal that in general the amplitude ratios of various reflected and transmitted waves are functions of the incidence angle, the frequency of the incident wave and the material properties of the medium. At normal incidence, the reflection and transmission of only longitudinal waves take place and no coupled transverse wave is found to reflect or transmit. At grazing incidence, no reflection or transmission phenomena take place and the same wave propagates along the interface. The change rules of the amplitudes varied with incident angle are also discussed.
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18

Kucaba-Piętal, A. "Squeeze flow modeling with the use of micropolar fluid theory." Bulletin of the Polish Academy of Sciences Technical Sciences 65, no. 6 (2017): 927–33. http://dx.doi.org/10.1515/bpasts-2017-0100.

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AbstractThe aim of this paper is to study the applicability of micropolar fluid theory to modeling and to calculating tribological squeeze flow characteristics depending on the geometrical dimension of the flow field. Based on analytical solutions in the lubrication regime of squeeze flow between parallel plates, calculations of the load capacity and time required to squeeze the film are performed and compared – as a function of the distance between the plates – for both fluid models: the micropolar model and the Newtonian model. In particular, maximum distance between the plates for which the micropolar effects of the fluid become significant will be established. Values of rheological constants of the fluids, both those experimentally determined and predicted by means of using equilibrium molecular dynamics, have been used in the calculations. The same analysis was performed as a function of dimensionless microstructural parameters.
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19

Radayev, Yuri N. "Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 20, no. 4 (2020): 468–77. http://dx.doi.org/10.18500/1816-9791-2020-20-4-468-477.

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The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out. A notion of proportionality of the vortex parts of the displacements and microrotations to a single vector, which satisfies the screw equation, is employed. Finally the problem of finding the vortex parts of the displacements and micro-rotations fields is reduced to solution of four uncoupled screw differential equations. Corresponding representation formulae are given. Obtained results can be applied to problems of the linear micropolar elasticity concerning harmonic waves propagation along cylindrical waveguides.
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20

Izadi, Razie, Meral Tuna, Patrizia Trovalusci, and Esmaeal Ghavanloo. "Torsional Characteristics of Carbon Nanotubes: Micropolar Elasticity Models and Molecular Dynamics Simulation." Nanomaterials 11, no. 2 (2021): 453. http://dx.doi.org/10.3390/nano11020453.

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Efficient application of carbon nanotubes (CNTs) in nano-devices and nano-materials requires comprehensive understanding of their mechanical properties. As observations suggest size dependent behaviour, non-classical theories preserving the memory of body’s internal structure via additional material parameters offer great potential when a continuum modelling is to be preferred. In the present study, micropolar theory of elasticity is adopted due to its peculiar character allowing for incorporation of scale effects through additional kinematic descriptors and work-conjugated stress measures. An optimisation approach is presented to provide unified material parameters for two specific class of single-walled carbon nanotubes (e.g., armchair and zigzag) by minimizing the difference between the apparent shear modulus obtained from molecular dynamics (MD) simulation and micropolar beam model considering both solid and tubular cross-sections. The results clearly reveal that micropolar theory is more suitable compared to internally constraint couple stress theory, due to the essentiality of having skew-symmetric stress and strain measures, as well as to the classical local theory (Cauchy of Grade 1), which cannot accounts for scale effects. To the best of authors’ knowledge, this is the first time that unified material parameters of CNTs are derived through a combined MD-micropolar continuum theory.
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21

Ambartsumian, S. A., and M. V. Belubekyan. "On micropolar theory of shallow shells." Mechanics - Proceedings of National Academy of Sciences of Armenia 63, no. 3 (2010): 23–32. http://dx.doi.org/10.33018/63.3.4.

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22

IDO, Yasushi, and Takahiko TANAHASHI. "Micropolar Theory for Viscoelastic Magnetic Fluids." JSME international journal. Ser. 2, Fluids engineering, heat transfer, power, combustion, thermophysical properties 34, no. 2 (1991): 122–28. http://dx.doi.org/10.1299/jsmeb1988.34.2_122.

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23

Eringen, A. Cemal. "Micropolar mixture theory of porous media." Journal of Applied Physics 94, no. 6 (2003): 4184–90. http://dx.doi.org/10.1063/1.1598640.

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24

Kumar, Rajneesh, Aseem Miglani, and Rekha Rani. "Eigenvalue formulation to micropolar porous thermoelastic circular plate using dual phase lag model." Multidiscipline Modeling in Materials and Structures 13, no. 2 (2017): 347–62. http://dx.doi.org/10.1108/mmms-08-2016-0038.

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Purpose The purpose of this paper is to study the axisymmetric problem in a micropolar porous thermoelastic circular plate with dual phase lag model by employing eigenvalue approach subjected to thermomechanical sources. Design/methodology/approach The Laplace and Hankel transforms are employed to obtain the expressions for displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain. A numerical inversion technique has been carried out to obtain the resulting quantities in the physical domain. Effect of porosity and phase lag on the resulting quantities has been presented graphically. The results obtained for Lord Shulman theory (L-S, 1967) and coupled theory of thermoelasticity are presented as the particular cases. Findings The variation of temperature distribution is similar for micropolar thermoelastic with dual (MTD) phase lag model and coupled theory of thermoelasticity. The variation is also similar for tangential couple stress for MTD and L-S theory but opposite to couple theory. The behavior of volume fraction field and tangential couple stress for L-S theory and coupled theory are observed opposite. The values of all the resulting quantities are close to each other away from the sources. The variation in tangential stress, tangential couple stress and temperature distribution is more uniform. Originality/value The results are original and new because the authors presented an eigenvalue approach for two dimensional problem of micropolar porous thermoelastic circular plate with dual phase lag model. A comparison of porosity, L-S theory and coupled theory of micropolar thermoelasticity is made. Such problem has applications in material science, industries and earthquake problems.
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Zozulya, V. V. "Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models." Curved and Layered Structures 4, no. 1 (2017): 104–18. http://dx.doi.org/10.1515/cls-2017-0008.

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AbstractNew models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.
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Радаев, Юрий Николаевич, Евгений Валерьевич Мурашкин, and Тимофей Константинович Нестеров. "Pseudotensor formalism for neuber’s micropolar elasticity theory." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 4(50) (December 30, 2021): 73–81. http://dx.doi.org/10.37972/chgpu.2021.50.4.006.

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В настоящей работе рассматривается теория микрополярной упругости Нейбера в псевдотензорной формулировке. Приводятся минимально необходимые для понимания статьи сведения из алгебры и анализа псевдотензоров. Уравнения динамики микрополярного континуума представлены (наряду с абсолютной тензорной формой) в терминах псевдотензоров (относительных тензоров). Проведено сравнение динамических уравнений микрополярной теории упругости в псевдотензорной форме с абсолютной тензорной формой, предложенной Нейбером. То же самое сопоставление выполнено и для определяющих уравнений. Устранены недочеты в уравнениях динамики Нейбера и приведена их окончательная псевдотензорная форма. The paper deals with Neuber’s theory of micropolar elasticity in a pseudotensor formulation. The minimum notes and requisite equations from algebra and analysis of pseudotensors are given. The micropolar dynamic equations are presented in terms of pseudotensors (relative tensors). The pseudotensor form of dynamic equations is compared with the absolute tensor form of the Neuber dynamic equations. The refinements of Neuber’s dynamic equations are discussed.
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27

Benariba, Aboubakeur, Ahmed Bouzidane, Marc Thomas, and Raynald Guilbault. "Numerical analysis of a rigid rotor mounted on four-pad hydrostatic squeeze film damper lubricated with micropolar lubricant." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 232, no. 5 (2017): 513–24. http://dx.doi.org/10.1177/1350650117721119.

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The present work deals with a numerical resolution of the modified Reynolds equation using micropolar lubrication theory to study the effects of coupling number and the characteristic length of the micropolar lubricant on the performance characteristics of hydrostatic squeeze film damper, which consists of four hydrostatic pads fed through four capillary restrictors. According to the results, the bearing operating with micropolar lubricant shows an increase in the value of pressure inside the recess. These results suggest that the influence of micropolar effect on the bearing performance is predominantly affected by the pressure ratio. Therefore, the bearing operator must judiciously choose an appropriate value of the pressure ratio in order to get an overall enhanced bearing performance.
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28

Stamenkovic, Zivojin, Milos Kocic, Jasmina Bogdanovic-Jovanovic, and Jelena Petrovic. "Nano and micropolar MHD fluid flow and heat transfer in inclined channel." Thermal Science, no. 00 (2023): 170. http://dx.doi.org/10.2298/tsci230515170k.

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Magnetohydrodynamic (MHD) fluid flows attract a lot of attention in the extrusion of polymers, in the theory of nanofluids, as well as in the consideration of biological fluids. The considered problem in the paper is the flow and heat transfer of nano and micropolar fluid in inclined channel. Fluid flow is steady, while nano and micropolar fluids are incompressible, immiscible, and electrically conductive. The upper and lower channel plates are electrically insulated and maintained at constant and different temperatures. External applied magnetic field is perpendicular to the fluid flow and considered problem is in induction-less approximation. The equations of the considered problem are reduced to ordinary differential equations, which are analytically solved in closed form. The influence of characteristics parameters of nano and micropolar fluids on velocity, micro-rotation and temperature fields are graphically shown and discussed. The general conclusions given through the analysis of graphs can be used for better understanding of the flow and heat transfer of nano and micropolar fluid, which have a great practical application. Fluids with nanoparticles innovated the modern era, due to their comprehensive applications in nanotechnology and manufacturing processes, while the theory of micropolar fluids explains the flow of biological fluids and various types of liquid metals and crystals.
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29

Bazdid-Vahdati, Majid, Mohammad Faraji Oskouie, Reza Ansari, and Hessam Rouhi. "Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity." Mathematics and Mechanics of Solids 24, no. 6 (2018): 1893–907. http://dx.doi.org/10.1177/1081286518808839.

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In this paper, within the framework of two-dimensional (2D) elasticity, a novel finite element formulation is proposed based on the micropolar theory (MPT) and the micromorphic theory (MMT). First, general formulations are developed for the micromorphic and micropolar continua in the context of 2D elasticity. Then, they are presented in a matrix form which is useful from the computational viewpoint. In the next step, using the matricized MPT and MMT formulations, a linear finite element approach including the effects of micro-deformation and micro-rotation degrees of freedom (DOFs) of material particles is developed, and a quadratic size-dependent element is proposed accordingly. Two test problems are solved to reveal the efficiency of the developed formulation. The influence of the length scale parameter on the bending of micromorphic and micropolar plates is illustrated in the given examples. Furthermore, comparisons are made between the results obtained from classical elasticity theory and those calculated based upon MPT and MMT.
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30

Nobili, Andrea. "On the Generalization of the Timoshenko Beam Model Based on the Micropolar Linear Theory: Static Case." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/914357.

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Three generalizations of the Timoshenko beam model according to the linear theory of micropolar elasticity or its special cases, that is, the couple stress theory or the modified couple stress theory, recently developed in the literature, are investigated and compared. The analysis is carried out in a variational setting, making use of Hamilton’s principle. It is shown that both the Timoshenko and the (possibly modified) couple stress models are based on a microstructural kinematics which is governed by kinosthenic (ignorable) terms in the Lagrangian. Despite their difference, all models bring in a beam-plane theory only one microstructural material parameter. Besides, the micropolar model formally reduces to the couple stress model upon introducing the proper constraint on the microstructure kinematics, although the material parameter is generally different. Line loading on the microstructure results in a nonconservative force potential. Finally, the Hamiltonian form of the micropolar beam model is derived and the canonical equations are presented along with their general solution. The latter exhibits a general oscillatory pattern for the microstructure rotation and stress, whose behavior matches the numerical findings.
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31

Chetti, Boualem. "Analysis of a circular journal bearing lubricated with micropolar fluids including EHD effects." Industrial Lubrication and Tribology 66, no. 2 (2014): 168–73. http://dx.doi.org/10.1108/ilt-12-2011-0114.

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Purpose – The performance of finite circular journal bearing lubricated with micropolar fluids taking into account the elastic deformation of the bearing liner is presented. The paper aims to discuss these issues. Design/methodology/approach – The modified Reynolds equation is obtained using the micropolar lubrication theory. The solution of the modified Reynolds equation is determined using finite difference technique. The static characteristics in terms of load-carrying capacity, attitude angle, side leakage and friction coefficient for micropolar and Newtonian fluids are determined for various values of eccentricity ratio and different values of elastic coefficient. Findings – Compared with Newtonian fluids, the micropolar fluids produce an increase in the load-carrying capacity and a reduction in the attitude angle, the friction factor and side leakage for both the rigid and deformable bearings. Originality/value – It is concluded that the influence of elastic deformation on the bearing characteristics lubricated with micropolar fluids is significantly apparent compared with bearing lubricated with Newtonian fluids.
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32

ASADI, H., K. JAVAHERDEH, and S. RAMEZANI. "MICROPOLAR FLUID MODEL FOR BLOOD FLOW THROUGH A STENOSED ARTERY." International Journal of Applied Mechanics 05, no. 04 (2013): 1350043. http://dx.doi.org/10.1142/s1758825113500439.

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Various experimental observations have demonstrated that the classical fluid theory is incapable of explaining many phenomena at micro and nano scales. On the other hand, micropolar fluid dynamics can naturally pick up the physical phenomena at these scales owing to its additional degrees of freedom caused by incorporating the effects of fluid molecules on the continuum. Therefore, one of the aims of this paper is to investigate the applicability of the theory of micropolar fluids to modeling and calculating flows in circular microchannels depending on the geometrical dimension of the flow field. Hence, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, the analytical and exact solution of the micropolar Hagen–Poiseuille flow in a circular microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is also shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow such as blood flow in a stenosed artery, having multiple kinds of stenoses, is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.
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33

Anya, Augustine Igwebuike, and Aftab Khan. "Reflection and Propagation of Magneto-Thermoelastic Plane Waves at Free Surfaces of a Rotating Micropolar Fibre-Reinforced Medium under G-L Theory." International Journal of Acoustics and Vibration 25, no. 2 (2020): 190–99. http://dx.doi.org/10.20855/ijav.2020.25.21575.

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This article is concerned with the investigation of reflection of waves at the free surface of a rotating micropolar fibre-reinforced thermoelastic medium, in the presence of a magnetic field using Green and Lindsay theory. It is observed that when a P-wave is incident on the free surface of rotating micropolar fibre-reinforced thermoelastic medium in the presence of a magnetic field, four waves are reflected; quasi-longitudinal displacement (qLD), quasi-transverse displacement (qTD), quasi-transverse micro-rotational (qTM) and quasi-thermal waves. The normal modes method, also called the harmonic solution approach, is used simultaneously with Snell's laws and Maxwell's equation, governing electromagnetic fields, in the determination of a solution for the micropolar fibre-reinforced modelled problem. Amplitude ratios or reflection coefficients, which correspond to reflected waves in vertical and horizontal components, are presented analytically. Moreover, the reflection coefficients are presented using numerically simulated results in graphical form for a particular chosen material. We observe that the micropolar fibre-reinforced, rotation, and magneto-thermoelastic field parameters, have varied degree of effects on the propagation and reflection of waves in the medium. The study should be helpful in understanding the behaviour of propagation and reflection of rotating micropolar fibre-reinforced magneto-thermoelastic machination fields and on future works about behaviour of seismic waves.
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34

Murashkin, E. V., and Yu N. Radaev. "Coupled Thermoelasticity of Hemitropic Media. Pseudotensor Formulation." Известия Российской академии наук. Механика твердого тела, no. 3 (May 1, 2023): 163–76. http://dx.doi.org/10.31857/s0572329922600876.

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The present paper deals with the problem of deriving the constitutive equations for the micropolar thermoelastic continuum GN-I in terms of the standard pseudotensor formalism. In most cases, the pseudotensor approach is justified in modeling hemitropic micropolar solids, the thermomechanical properties of which are sensitive to mirror reflections of three-dimensional space. The requisite equations and notions from the theory of pseudotensors are revisited. General thermodynamic approaches are used, entropy and energy balance equations are discussed. The weights of the main thermomechanical pseudotensors are established. In a linear approximation, the constitutive equations of the hemitropic micropolar thermoelastic continuum (GN-I) of the first type are derived. A coupled system of differential equations of heat conduction and dynamic equations of the micropolar thermoelastic continuum GN-I is obtained.
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35

Neff, Patrizio, and Krzysztof Chełmiński. "Infinitesimal elastic–plastic Cosserat micropolar theory. Modelling and global existence in the rate-independent case." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, no. 5 (2005): 1017–39. http://dx.doi.org/10.1017/s030821050000425x.

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In this article we investigate the regularizing properties of generalized continua of Cosserat micropolar type in the elasto-plastic case. We propose an extension of classical infinitesimal elasto-plasticity to include consistently non-dissipative micropolar effects. It is shown that the new model is thermodynamically admissible and allows for a unique, global-in-time solution of the corresponding rate-independent initial–boundary-value problem. The method of choice is the Yosida approximation and a passage to the limit.
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36

Neff, Patrizio, and Krzysztof Chełmiński. "Infinitesimal elastic–plastic Cosserat micropolar theory. Modelling and global existence in the rate-independent case." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, no. 5 (2005): 1017–39. http://dx.doi.org/10.1017/s0308210505000533.

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In this article we investigate the regularizing properties of generalized continua of Cosserat micropolar type in the elasto-plastic case. We propose an extension of classical infinitesimal elasto-plasticity to include consistently non-dissipative micropolar effects. It is shown that the new model is thermodynamically admissible and allows for a unique, global-in-time solution of the corresponding rate-independent initial–boundary-value problem. The method of choice is the Yosida approximation and a passage to the limit.
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37

Hayrapetyan, G. S., and S. H. Sargsyan. "Theory of micropolar orthotropic elastic thin plates." Mechanics - Proceedings of National Academy of Sciences of Armenia 65, no. 3 (2012): 22–33. http://dx.doi.org/10.33018/65.3.3.

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38

Nikabadze, Michael. "Some Variants of Micropolar Shell Theory Equations." Applied Mathematics and Mathematical Physics 1, no. 1 (2015): 101–18. http://dx.doi.org/10.18262/ammp.2015.0101-07.

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39

Nikabadze, M. U. "Compatibility conditions in the linear micropolar theory." Moscow University Mechanics Bulletin 65, no. 5 (2010): 110–13. http://dx.doi.org/10.3103/s0027133010050031.

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40

Sargsyan, Samvel H. "General theory of micropolar elastic thin shells." Physical Mesomechanics 15, no. 1-2 (2012): 69–79. http://dx.doi.org/10.1134/s1029959912010079.

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41

Murashkin, Eugenii Valeryevich, and Yuri Nikolaevich Radayev. "On a micropolar theory of growing solids." Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 24, no. 3 (2020): 424–44. http://dx.doi.org/10.14498/vsgtu1792.

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Обсуждается принцип вывода граничных условий в краевых задачах механики растущих микрополярных тел. Приводится вывод уравнений динамики микрополярного континуума в терминах относительных тензоров для тел постоянного состава. Указана определяющая квадратичная форма упругого потенцила (абсолютного скаляра) для линейного гемитропного микрополярного тела. Выведены определяющие соотношения для симметричных и антисимметричных частей тензоров силовых и моментных напряжений. Получены конечные формы уравнений динамики гемитропного микрополярного континуума в терминах скоростей перемещений и микровращений. Полученные динамические уравнения для тел постоянного состава остаются справедливыми и в теориях растущих тел. Предложена процедура преобразования уравнений равновесия для получения граничных условий на поверхности наращивания в терминах относительных тензоров в форме дифференциальных ограничений. Полученные условия справедливы для весьма широкого круга материалов и метаматериалов. При выводе определяющих соотношений на поверхности наращивания активно используется аппарат алгебры рациональных относительных инвариантов. Получены полные системы совместных относительных инвариантов для тензоров силовых, моментных напряжений и единичного вектора нормали, в том числе системы инвариантов, не выдерживающие зеркальных отражений.
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42

Chen, J., C. Liang, and J. D. Lee. "Theory and simulation of micropolar fluid dynamics." Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems 224, no. 1-2 (2010): 31–39. http://dx.doi.org/10.1177/1740349911400132.

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43

Erbay, H. A. "An asymptotic theory of thin micropolar plates." International Journal of Engineering Science 38, no. 13 (2000): 1497–516. http://dx.doi.org/10.1016/s0020-7225(99)00118-4.

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44

Roy Chowdhury, Shubhankar, Md Masiur Rahaman, Debasish Roy, and Narayan Sundaram. "A micropolar peridynamic theory in linear elasticity." International Journal of Solids and Structures 59 (May 2015): 171–82. http://dx.doi.org/10.1016/j.ijsolstr.2015.01.018.

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45

Atoyan,, A. A., and S. H. Sargsyan,. "Dynamic Theory of Micropolar Elastic Thin Plates." Journal of the Mechanical Behavior of Materials 18, no. 2 (2007): 81–88. http://dx.doi.org/10.1515/jmbm.2007.18.2.81.

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46

Aouadi, Moncef. "The coupled theory of micropolar thermoelastic diffusion." Acta Mechanica 208, no. 3-4 (2009): 181–203. http://dx.doi.org/10.1007/s00707-008-0137-0.

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47

Altenbach, H., and V. A. Eremeyev. "On the linear theory of micropolar plates." ZAMM 89, no. 4 (2009): 242–56. http://dx.doi.org/10.1002/zamm.200800207.

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48

Sargsyan, S. O. "The theory of micropolar thin elastic shells." Journal of Applied Mathematics and Mechanics 76, no. 2 (2012): 235–49. http://dx.doi.org/10.1016/j.jappmathmech.2012.05.015.

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49

Marin, Marin. "On the Nonlinear Theory of Micropolar Bodies with Voids." Journal of Applied Mathematics 2007 (2007): 1–11. http://dx.doi.org/10.1155/2007/15745.

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50

Sekar, Sangeetha, Sujatha Elamparithi, Sivakami Lakshmi Nathan, and Lakshmi Priya Saravanathan. "Effect of MHD with Micropolar Fluid Between Conical Rough Bearings." International Journal of Heat and Technology 40, no. 5 (2022): 1210–16. http://dx.doi.org/10.18280/ijht.400512.

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MHD effect using micropolar fluid between rough conical bearings is analyzed in this paper. The Reynolds equation is derived in the form of magnetic field using the Eringen principle with Christensen theory. The stochastic modified Reynolds equation for two types of one-dimensional structure, the radial roughness pattern and azimuthal roughness patterns is derived for micropolar fluid. In terms of dimensionless pressure, load carrying capacity and time, the numerical results are presented. The importance of roughness, MHD and micropolar fluid is greater than that of the classical Newtonian case. From the analysis, the impact of micropolar fluid and electrically conducting fluid increases the load carrying capacity further decreases the time relative to the Newtonian instance. On the whole, the squeezing film characteristics of conical bearings is improved for higher values of coupling number and Hartmann number.
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