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Advances in Mechanics of Microstructured Media and Structures pp 297–341Cite as

Acoustic Approximation of the Governing Equations of Liquid Crystals Under Weak Thermomechanical and Electrostatic Perturbations

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 87))

Abstract

A simplified mathematical model of thermomechanical behavior of a liquid crystal in nematic phase under weak mechanical and thermal perturbations as a micropolar viscoelastic medium with rotating particles is constructed. This model is based on the assumption that potential energy of elastic deformation depends on four parameters—the change in volume, angle of relative rotation of particles, first invariant of curvature measure and entropy. The heat conduction process is described taking into account the anisotropy of a material due to the difference in coefficients of thermal conductivity along the axis of orientation of particles and in the transverse direction. Influence of electric field on the layer of a liquid crystal is modeled by means of the equations of electrostatics for an inhomogeneous anisotropic medium. In the plane formulation, the parallel computational algorithm is worked out on the basis of splitting method with respect to spatial variables, Godunov’s gap decay method, Ivanov’s method of constructing finite-difference schemes with controlled dissipation properties and method of straight lines for finding electric field. The algorithm is implemented using the CUDA technology for computer systems with graphics accelerators. Results of computations of wave motions demonstrating the efficiency of proposed method and algorithm are represented. It is shown that the effect of orientational thermoelasticity of a liquid crystal in the form of re-orientation of particles in an inhomogeneous temperature field can only be evident in the presence of tangential stresses at the boundary. The modes of resonance excitation in a liquid crystal at the eigenfrequency of rotational motion of particles are analyzed numerically.

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Acknowledgements

This work was supported by the Complex Fundamental Research Program no. II.2P “Integration and Development” of Siberian Branch of the Russian Academy of Sciences (project no. 0356-2016-0728).

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Authors and Affiliations

  1. Siberian Branch of the Russian Academy of Sciences, Institute of Computational Modeling, Akademgorodok 50/44, Krasnoyarsk, 660036, Russia

    Vladimir Sadovskii & Oxana Sadovskaya

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  1. Vladimir Sadovskii
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  2. Oxana Sadovskaya
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Correspondence to Vladimir Sadovskii .

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Editors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma “La Sapienza”, Rome, Italy

    Francesco dell'Isola

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  3. Department of Micromechanics of Materials, Institute of Problems in Mechanical Engineering, Saint Petersburg, Russia

    Alexey Porubov

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Sadovskii, V., Sadovskaya, O. (2018). Acoustic Approximation of the Governing Equations of Liquid Crystals Under Weak Thermomechanical and Electrostatic Perturbations. In: dell'Isola, F., Eremeyev, V., Porubov, A. (eds) Advances in Mechanics of Microstructured Media and Structures. Advanced Structured Materials, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-319-73694-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-73694-5_17

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