Two-scale off-and online approaches to geometrically exact elastoplastic rods

Abstract This work compares two different computational approaches to geometrically exact elastoplastic rods. The first approach applies an constitutive model in terms of stress resultants, i.e. forces and moments. It requires knowledge the rod’s elasticity yield-criterion resultants. Furthermore a resultant-type hardening expression must be formulated. These are obtained by integrating measures from three-dimensional continuum mechanics over deformed cross-section, which is performed offline stage. second $$FE ^2$$ F E 2 as established homogenization. Therein, macro-scale describing rod coupled micro-scale, i.e., cross-section rod. A novelty presented determination tensor for use resultant approach. mechanical response both compared on material point level, single uniformly strained Later, also deformation finitely non-uniformly rods investigated.