Dynamics of planar elasto-plastic Timoshenko-type beams at finite strains

Abstract

In this paper, we develop a finite strain multiplicative elasto-plastic dynamic formulation for planar Timoshenko-type beams. The multiplicative decomposition of the deformation gradient as well as the logarithmic strain measure are used. The exponential map is applied for the integration of the plastic rate. The plane-stress condition is enforced in an approximative manner by slightly modifying the right Cauchy deformation tensor based on some meaningful assumptions regarding the shear and the plastic deformation. In an attempt to deliver a stable time integration scheme in the context of finite strain elasto-plastic dynamics, we make use of the energy–momentum method recently developed by the authors for geometrically exact Timoshenko-type elastic beams. The enhanced strain method is employed to avoid locking phenomena. An enhanced strain velocity field is introduced and integrated to generate the enhanced strain itself. A range of challenging examples of large beam deformations are presented demonstrating the stability and robustness of the present formulation.