This article is cited in 21 papers

On the relationship of micropolar constitutive parameters of thermodynamic state potentials

E. V. Murashkin

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

Abstract: The paper is devoted to some problems concerning modeling semi-isotropic elastic media. Several quadratic energy forms of a thermodynamic state potential are introduced in terms of pseudotensors. These energy forms are assumed to be absolute invariants with respect to arbitrary transformations of the three-dimensional Euclidean space (including mirror reflections). As a result of applying special coordinate representations of semi-isotropic (semi-isotropic) pseudotensors of the fourth rank, it is possible to determine 9 covariantly constant constitutive pseudoscalars characterizing a semi-isotropic elastic medium. The Neuber's, conventional, first and second base natural energy forms are compared and equations are derived for constitutive scalars and pseudoscalars, including the conventional semi-isotropic pseudoscalars: shear modulus, Poisson's ratio, characteristic microlength (a pseudoscalar of negative weight, sensitive to reflections of three-dimensional space), and six dimensionless pseudoscalars.

Keywords: pseudotensor, quadratic energy form, thermodynamic state potential, constitutive pseudotensor, characteristic microlength, chiral medium, micropolar semi-isotropic continuum.

Received: 20.03.2023
Revised: 06.06.2023
Accepted: 01.05.2023

DOI: 10.37972/chgpu.2023.55.1.012