A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity

Abstract

The aim of this work is to formulate a geometrically exact theory of finite deformation and finite rotation micropolar elastoplasticity to obtain a generalized nonlinear continuum framework. To this end, the classical deformation map is supplemented by an independent rotation field to yield an enhanced configuration space. Thereby, the rotational part of the formulation is consequently parameterized in terms of the rotation (pseudo) vector via the Euler-Rodrigues formula. Then, micropolar hyperelasticity and multiplicative elastoplasticity are conceptionally derived as in the classical Boltzmann continuum. The proposed theory is consequently developed in a modern geometry oriented fashion. Linearization of the kinematics retrofits the well-known structure of the micropolar geometrically linear theory.