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

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.

Murashkin Evgenii Valeryevich, Cand. Sci. (Phys.-Math.), MD, Senior Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Russia.