On quadratic corrections of constitutive equations for a hemitropic micropolar elastic solid

In the present paper, cubic approximations of energy forms for the potentials of force and couple stresses in hemitropic micropolar elastic solids are proposed and discussed. H/E/A-representations for these potentials were introduced in earlier studies. However, the A-form allows us to obtain a cubic approximation for the stress potential in the form of a polynomial combination of invariants, comprising integer powers of individual and joint base rational algebraic invariants and pseudoinvariants. Some of these pseudoinvariants have “pseudo-tensor pre-images” that are sensitive to mirror reflections and inversions of three-dimensional space.
Within the framework of this study, a complete irreducible set of individual and joint linear, quadratic, and cubic integer rational algebraic invariants is obtained for a set consisting of the symmetric and antisymmetric parts of the asymmetric strain tensor and the wryness tensor. A cubic energy form for a hemitropic micropolar solid is determined, and a complete set of 37 constitutive moduli is specified. Additionally, constitutive equations for force and couple stresses in arbitrary curvilinear coordinates are derived, including quadratic corrections.