Multi-cell continuum approximation for discrete medium with microscopic rotations

• Published in: Physica Status Solidi (b) Vol. 242; no. 3; pp. 528 - 537
• Main Authors: Dmitriev, S. V., Vasiliev, A. A., Yoshikawa, N., Shigenari, T., Ishibashi, Y.
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 01.03.2005; WILEY‐VCH Verlag
• Subjects: 02.70.Ns; 62.20.Dc; 63.20.-e; 64.70.Rh; 83.10.Ff
• ISSN: 0370-1972; 1521-3951
• DOI: 10.1002/pssb.200460373

We consider 1D and 2D microscopic models for crystals having finite size particles, as is the case with many dielectric crystals. Finite size particles with rotational degrees of freedom can lead to several unusual effects exhibited by such crystals, e.g., a negative Poisson's ratio, incommensurate phase, and unique properties of topological defects. Derivation of the continuum approximations for these models leads to two developments: i) micropolar media, i.e., the continuum analog to the microscopic model with particles having rotational degrees of freedom; ii) the continuum approximation based on an extended periodic cell, which will be called the multi‐cell approximation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)