Strain rate tensors and constitutive equations of inelastic micropolar materials

Nonlinear micropolar continuum model allows to describe complex micro-structured media, for example, polycrystals, foams, cellular solids, lattices, masonries, particle assemblies, magnetic rheological fluids, liquid crystals, etc., for which the rotational degrees of freedom of material particles are important. The constitutive equations of the hyperelastic nonlinear micropolar continuum can be expressed using the strain energy density depending on two strain measures. In the case of inelastic behavior the constitutive equations of the micropolar continuum have more complicated structure, the stress and couple stress tensors as well as other quantities depend on the history of strain measures. In what follows we discuss the constitutive equations of the nonlinear micropolar continuum using strain rates.