The Asymptotic Expansion Load Decomposition elasto-plastic beam model

Grégoire Corre (1, 2) , Arthur Lebée (2) , Karam Sab (2) , Mohammed Khalil Ferradi (1) , Xavier Cespedes (1)

1 Strains
2 navier umr 8205 - Laboratoire Navier

A new higher-order elasto-plastic 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 elasto-plastic 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 2 plastic flow is used. Because of the constant evolution of the 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 3D reference solution. The beam model shows satisfying results even at a local scale and for a computation time significantly reduced.

Mots clés: Model reduction; Structural analysis; Plasticity; Asymptotic expansion; Higher-order beam model

Domaines: Mécanique des structures [physics.class-ph]

Grégoire Corre, Arthur Lebée, Karam Sab, Mohammed Khalil Ferradi, Xavier Cespedes. The Asymptotic Expansion Load Decomposition elasto-plastic beam model. International Journal for Numerical Methods in Engineering, 2018, ⟨10.1002/nme.5926⟩. ⟨hal-01830425⟩