Localization Issues in Force-Based Frame Elements

This paper summarizes the results of an investigation on objective modeling and prediction of deformation localization in nonlinear force-based frame elements. Emphasis is placed on the behavior of reinforced concrete structures where localization is most likely to occur. The discussion begins with a brief review of the force-based element formulation. Next, plastic hinge behavior is classified into three categories: hardening plastic hinges, perfectly plastic hinges, and softening plastic hinges. The three types of inelastic behavior pose an increasing challenge to objective postpeak modeling. The physical and numerical characteristics of localized failure are outlined. Two regularization techniques for maintaining postpeak objectivity are proposed: (1) a constant fracture energy criterion, which provides objective response on the element force-displacement level; and (2) geometric scaling, which provides objective response on the local moment-curvature level in plastic hinge regions. The discussion concludes with three applications to different reinforced concrete structures: a frame, a bridge pier, and an overreinforced concrete beam. In all three cases, the proposed regularization technique successfully yields objective model predictions.