In this study, an algorithm is proposed for deriving a sixth-order approximation of the potential for force and couple stresses in a hemitropic micropolar elastic body, which incorporates corrections up to the sixth algebraic order—beyond the fundamental quadratic approximation through the systematic application of algebraic invariant theory. For this aim, a complete enumeration of irreducible invariants for a system of two asymmetric second-rank tensors is represented in the form of invariant traces. An initial set of 86 invariant traces, with a maximum degree of six, is discussed.

A scheme for deriving sixth-order invariants is proposed, organized for convenience into eight subgroups. Ultimately, the hemitropic micropolar potential is defined via 1034 independent mechanical moduli. Constitutive equations for force and couple stresses are derived, incorporating corrections of the second, third, fourth, and fifth algebraic orders.

Mikhail N. Mikhin, Cand. Sci. (Phys. & Math.), Associate Professor, Head of the Department of Mathematics and Natural Sciences e-mail: mmikhin@inbox.ru;https://orcid.org/0009-00072081-3462; AuthorID: 493518

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