Implicit Gradient Delocalization Method for Force-Based Frame Element

Abstract

In this study, a novel force-based frame element with delocalization is developed to address localization issues induced by material strain softening. A regularization procedure for section deformations is introduced on the basis of the concept of deformation gradient dependency. The internal length scale of the gradient-based regularization model is discussed and related to the plastic hinge length of the structural members. The weak form of the governing equation is derived, and a subscale numerical strategy is utilized within each element to implement the proposed model in the frame element. In addition, an adaptive scheme is developed for the RC members to determine the real-time gradient coefficient. Finally, two numerical examples are utilized and the results show that the proposed model can achieve an objective response for and excellent prediction of the nonlinear behavior of RC members.