On strain rate tensors and constitutive equations of inelastic micropolar materials

Following Altenbach and Eremeyev (Int J Plast 63:3–17, 2014) we introduce a new family of strain rate tensors for micropolar materials. With the help of introduced strain rates we discuss the possible forms of constitutive equations of the nonlinear inelastic micropolar continuum, that is micropolar viscous and viscoelastic fluids and solids, hypo-elastic and viscoelastoplastic materials. Considering the fact that some of strain rates are not true tensors but pseudotensors we obtain some constitutive restrictions following from the material frame indifference principle. Using the theory of tensorial invariants we present the general form of constitutive equations of some types of inelastic isotropic micropolar materials including several new constitutive equations.