Development and implementation of a new computational strategy for the prediction of elastoplastic buckling

Abstract

This study proposes an innovative computational strategy to predict the initiation of elastoplastic buckling in shell structures. This strategy is developed in connection with ABAQUS/Standard Finite Element (FE) code. Toward this objective, two constitutive frameworks are implemented as User MATerial subroutines (UMATs) into this FE code; namely, the incremental flow theory of plasticity and the total deformation theory. These frameworks are formulated under the plane-stress condition, which is particularly suitable for modeling sheet structures and which enhances computational efficiency. Elastoplastic buckling is detected by the Hill loss of uniqueness criterion, which establishes that buckling occurs when the global stiffness matrix, derived from the finite element computations, becomes singular. To determine this matrix and investigate its singularity, a Python script is developed and combined to the ABAQUS computations. The reliability and accuracy of this computational strategy are assessed through various representative numerical examples. The effect of some geometric and material parameters on the onset of elastoplastic buckling in both thin and thick plates, as well as cruciform columns, is investigated and compared to reference results from the literature. The findings of the present contribution can serve as useful reference guidelines for ABAQUS/Standard users, offering valuable insights for predicting the occurrence of elastoplastic buckling, even in metallic structures characterized by complex mechanical behavior and geometric configurations.