The paper deals with an application of theory of invariant to determinig cubic approximations of energy forms of potentials of force and couple stressed in hemitropic micropolar elastic solids. At this aim, the most suitable are A-representations, which allow one to easily obtain an approximation of sufficient accuracy for the stress potentials as a polynomial linear combination of rational invariants with respect to the hemitropic group of three-dimensional transformations are proposed. Within the framework of this study, a complete irreducible set of 86 individual and joint hemitropic integer rational algebraic invariants for systems of two symmetric and two antisymmetric second-rank tensors is considered. This set of invariants is then used to determine a cubic energy form of hemitropic micropolar elastic solid and specify a complete set of 37 constitutive constants. Requisite formulae are derived for obtaining constitutive equations of micropolar elasticity.

Evgenii V. Murashkin, Cand. Sci. Phys. & Math., MD, Senior Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; e-mail: evmurashkin@gmail.ru; https://orcid.org/0000-0002-3267-4742; AuthorID: 129570

Yuri N. Radayev, Dr. Sci. Phys. & Math., Prof., Leading Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; e-mail: radayev@ipmnet.ru; https://orcid.org/0000-0002-0866-2151; AuthorID: 103116