Analysis of post-necking behavior in structural steels using a one-dimensional nonlocal model. (1st February 2019) - Zhu, Yazhi; Kanvinde, Amit; Pan, Zuanfeng
Highlights: A one-dimensional nonlocal model is proposed to address the necking problem. Spectral analysis of the model is presented to examine mathematical regularization. The tangent operator is derived for the proposed nonlocal formulation. The proposed model effectively characterizes the post-necking behavior. Abstract: In modeling necking in steel bars subjected to uniaxial tension using a classical one-dimensional elastoplastic continuum, numerical results exhibit strong mesh dependency without convergence upon mesh refinement. The strain localization and softening with respect to necking in structural steels is induced by hybrid material and geometric nonlinearities rather than material damage. A one-dimensional nonlocal model is proposed to address these numerical difficulties and to provide an enhanced numerical representation of necking-induced localization in structural steels for the potential implementation in fiber-based formulations. By introducing a characteristic length and a nonlocal parameter to the standard constitutive model, the enhanced nonlocal continuum provides a well-posed governing equation for the necking problem. The finite element calculations based on this one-dimensional nonlocal model give rise to objective solutions, i.e., numerical results converge under mesh refinement. In addition, the size of the necking region also exhibits mesh-independence. The characteristic length and nonlocal parameter significantly influence the post-necking response and the dimension of the necked region. Comparison of the local and global response of necking between one-dimensional analysis and 3D simulations demonstrates that the proposed model is capable of accurately characterizing the post-necking behavior. Relationships between characteristic length for the nonlocal model and the diameter of a cylindrical bar are examined. The novel contributions of the paper are: (1) providing a transparent link between the nonlocal formulation and the physics of the necking phenomenon, and (2) providing a mathematical basis for the necessity of the "over-nonlocal" formulation.