Extended micropolar approach within the framework of 3M theories and variations thereof

Abstract As part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides most general framework for a with translational (internal) rotational degrees freedom (DOF), whilst DOFs continua are subjected to more constraints. More recently, an “extended” theory has been presented by one authors: Eringen’s theories were children solid mechanics based indestructible material particle. Extended was formulated both ways systems as well in spatial description, which is useful when describing fluid matter. latter opens possibility model situations point that microscale consists no longer same elementary units during physical process. difference culminates equation microinertia tensor, kinematic identity. Rather it contains new field, independent production term and, consequently, establishes constitutive quantity. This makes possible describe processes structural change, difficult if not impossible be captured within particle model. paper compares various points out their communalities differences.