The asymptotic expansion load decomposition elastoplastic beam model

Summary A new higher-order elastoplastic beam model is derived and implemented in this paper. The reduced kinematic approximation is based on a higher-order elastic beam model using the asymptotic expansion method. This model introduces new degrees of freedom associated to arbitrary loads as well as eigenstrains applied to the beam. In order to capture the effect of plasticity on the structure, the present elastoplastic model considers the plastic strain as an eigenstrain imposed on the structure, and new degrees of freedom are added on the fly into the kinematics during the incremental-iterative process. The radial return algorithm of J₂ plastic flow is used. Because of the constant evolution of beam kinematics, the Newton-Raphson algorithm for satisfying the global equilibrium is modified. An application to a cantilever beam loaded at its free extremity is presented and compared to a three-dimensional reference solution. The beam model shows satisfying results even at a local scale and for a significantly reduced computation time.