A finite element formulation for a direct approach to elastoplasticity in special Cosserat rods. (14th January 2021) - , Smriti; Kumar, Ajeet; Steinmann, Paul
Abstract: A finite element (FE) formulation is presented for a direct approach to model elastoplastic deformation in slender bodies using the special Cosserat rod theory. The direct theory has additional plastic strain and hardening variables, which are functions of just the rod's arc‐length, to account for plastic deformation of the rod. Furthermore, the theory assumes the existence of an effective yield function in terms of stress resultants, that is, force and moment in the cross‐section and cross‐section averaged hardening parameters. Accordingly, one does not have to resort to the three‐dimensional theory of elastoplasticity during any step of the finite element formulation. A return map algorithm is presented in order to update the plastic variables, stress resultants and also to obtain the consistent elastoplastic moduli of the rod. The presented FE formulation is used to study snap‐through buckling in a semicircular arch subjected to an in‐plane transverse load at its midsection. The effect of various elastoplastic parameters as well as pretwisting of the arch on its load–displacement curve are presented.