Nonlocal Damage Formulation for a Flexibility-Based Frame Element

Abstract

This paper presents the formulation for a novel flexibility-based one-dimensional (1D) finite element that captures material and structural softening within a reinforced concrete framed structure. Separating the total elastic and inelastic components of the strain at integration points, a secant solution strategy is introduced that is consistent with damage models in the framework of nested iterative algorithms. In this formulation and solution strategy, at every stage of loading the inelastic deformation of the element can be obtained directly without resorting to unloading processes, which is useful when the value of inelastic deformation is required according to some seismic design provisions. In addition, a nonlocal integral damage model, based on averaged strain, has been used to ensure mesh size independent objectivity of local and global responses. The efficiency and accuracy of the formulation is compared with numerical and experimental data with good correlation observed and mesh objectivity demonstrated.