pseudotensor, fundamental orienting pseudoscalar, quadratic energy form, potential detection, detecting pseudotensor, characteristic microlength, chiral medium, micropolar hemitropic continuum

The paper is devoted to some problems concerning modeling hemitropic elastic media. Two main quadratic energy forms of a stress 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 (hemitropic) pseudotensors of the fourth rank, it is possible to determine 9 covariantly constant constitutive pseudoscalars characterizing a hemitropic elastic medium. Symmetric and antisymmetric parts of asymmetric tensors and pseudotensors of strains and stresses are discriminated. The first and second base natural energy forms are compared and equations are derived for constitutive scalars and pseudoscalars, including the conventional hemitropic pseudoscalars: shear modulus, Poisson’s ratio, characteristic microlength (a pseudoscalar of negative weight, sensitive to reflections of three-dimensional space), and six dimensionless pseudoscalars.

Murashkin Evgenii Valeryevich, Cand. Sc., PhD, MD, Senior Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Russia.

Radayev Yuri Nikolaevich, D. Sc., PhD, MSc, Professor of Continuum Mechanics, Leading Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Russia.