The Asymptotic Expansion Load Decomposition elastoplastic beam model

Abstract

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 incrementaliterative 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.

A new higher-order elastoplastic beam model for reinforced concrete

“…This paper is based on the elastoplastic beam model developed in [1] called the Asymptotic Expansion Load Decomposition (AELD) beam model. This higher-order elastoplastic beam model does not need any a priori knowledge on the solution of the problem to extend its kinematics.…”

“…The displacement modes are computed by using the asymptotic expansion method. This model was first introduced for elastic beams loaded by external forces in [39] and extended to the case of elastic beams loaded by eigenstrains in [40] before its adaptation to elastoplasticity [1]. This higher-order elastoplastic beam model was presented with 2 -plasticity.…”

“…In order to preserve local accuracy of the element and to get a better description of macroscopic forces, the approach adopted in the present paper is to use a higher-order elastoplastic beam model. First developed for elasticity in [39], it has been extended to eigenstrains [40] before being adapted to the case of elastoplasticity [1]. The kinematics is enriched thanks to a systematic method with displacement modes computed on the 2D cross-section of the structure.…”

“…These modes bring local accuracy and can easily describe higher-order shear effects as well as bending or torsion. When required, the kinematics may be updated on the fly according to inelastic strains which occurs in the 3D body [1].…”

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The present paper introduces a new elastoplastic beam model for reinforced concrete based on a higher-order beam model previously developed [1]. Steel and concrete are both defined as elastoplastic materials.

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