Higher order elastoplastic beam model
Résumé
Bridge decks, metallic meshes or concrete beams have long been numerically described by beam models with a simple kinematic. Those classic models can capture elementary deformations like traction or bending moment. But when it comes to wide decks or thin beams, higher order effects become non negligible. Moreover, plasticity in the structure is associated to an infinitely large number of degrees of freedom, which are not provided by the classic models. Added to the computational cost of a full volumic computation, this has motivated the development of higher order beam models. Based on the elastic beam model developed by Ferradi et al. [1], a new elastoplastic beam model is presented here. As for the model described in [1], the kinematic of the beam is extended using the asymptotic expansion method [2]. Degrees of freedom specific to the geometry of the section of the beam and specific to the loading applied on the structure are added to the kinematic. In the elastoplastic model presented here, new degrees of freedom specific to the plasticity are also introduced: at each iteration of the plasticity algorithm, the updated plastic strain field is considered as an eigenstrain loading the beam. The asymptotic expansion method yields new degrees of freedom from these new external loads. Unlike many POD-like plastic reduced models, this elastoplastic beam model does not need any a priori knowledge on the solution of the problem. This is a systematic method in which the degrees of freedom are specific to the plastic strains, these latter being updated at each iteration of the algorithm. This model shows similar results to volumic computations, with much higher time performances.