Finite Strain Plasticity Formulations for Dynamic Beams With and Without Rotational Degrees of Freedom

Abstract

In this paper, we developed a finite strain multiplicative elasto-plasto-dynamic formulation for Euler-Bernoulli and Timoshenko-type beam. The relations are formulated in an inertial frame approach. The multiplicative decomposition of the deformation gradient and the logarithmic strain measure are used. The exponential map for material evolution equations, as well as the derivative forms is given. In an attempt to deliver a stable time integration scheme for this non-linear beams in the context of finite strain elasto-dynamics, we made use of the concept of the energy-momentum method recently developed by the authors for geometrically exact Euler-Bernoulli and Timoshenko-type elastic beams. One example of finite strain elasto-plastic beam deformation is presented.