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JOURNALS // Vestnik Chuvashskogo Gosudarstvennogo Pedagogicheskogo Universiteta im. I. Ya. Yakovleva. Seriya: Mekhanika Predel'nogo Sostoyaniya // Archive

Vestn. Chuvash. Gos. Ped. Univ. im.I.Ya. Yakovleva Ser.: Mekh. Pred. Sost., 2024 Issue 3(61), Pages 140–153 (Mi mps92)

Generalized nye figures for ultrahemitropic and ultraisotropic micropolar elastic solids

E. V. Murashkin

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow

Abstract: In present paper, the construction of Nye figures for micropolar solids is discussed. A general anisotropic micropolar elastic solid is reduced to a hemitropic, then to an ultrahemitropic, and finally to an ultraisotropic micropolar solid. The constitutive tensors of the fourth rank are transformed to a two-dimensional matrix form. The final Nye figures for the considered micropolar solids are obtained by combining the elementary figures for the constitutive tensors. We obtain Nye figures that graphically represent a hemitropic, ultrahemitropic, and ultraisotropic micropolar elastic solid and the couples between the components of the asymmetric constitutive tensors.

Keywords: micropolar medium, elastic potential, constitutive tensor, hemitropic micropolar solid, ultrahemitropy, ultraisotropy, Nye figure, matrix representation.

UDC: 539.374

Received: 03.10.2024
Revised: 24.12.2024
Accepted: 16.12.2024

DOI: 10.37972/chgpu.2024.61.3.010



© Steklov Math. Inst. of RAS, 2026