Effect of higher order constitutive terms on the elastic buckling of thin-walled rods

In this paper we revisit an elastic constitutive equation proposed in two previous works and extend it in order to include all higher-order terms on the deformations. Our purpose is to assess the influence of these terms on the elastic buckling of thin-walled rods. The resulting material model was incorporated into a geometrically exact rod formulation and implemented into a nonlinear finite element code. By means of simple numerical examples we show that the higher order terms may play a significant role on the values of the buckling loads and on the post-buckling behavior of thin-walled beams and columns.