The nye cells and figures for athermic hemitropic, isotropic and ultraisotropic micropolar elastic solids

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Abstract

The paper deals with a method of the Nye figures construction for micropolar elastic solids. The method of tensors of the 4th and 3rd ranks representations by means of blocks of two-dimensional matrices and relationships between their elements is widely known in crystallography. Such approach makes it possible to simply determine the number of independent constitutive constants for micropolar elastic solids and guarantee the absence of relationships between them. In frameworks of the present study, the two-dimensional Nye figures for an ultraisotropic micropolar elastic solid were figured out based on the corresponding figures for hemitropic and isotropic micropolar elastic solids. It is shown that the constitutive tensors of ultraisotropic material characterized by only 4 independent constitutive constants: shear modulus of elasticity, Poisson’s ratio, characteristic nano/microlength and another dimensionless constant.

About the authors

E. Yu. Krylova

Saratov State University

Author for correspondence.
Email: kat.krylova@bk.ru
Russian Federation, Saratov

E. V. Murashkin

Ishlinsky Institute for Problems in Mechanics RAS

Email: murashkin@ipmnet.ru
Russian Federation, Moscow, 119526

Yu. N. Radaev

Ishlinsky Institute for Problems in Mechanics RAS

Email: radayev@ipmnet.ru
Russian Federation, Moscow, 119526

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