Analysis of Geometric and Material Nonlinearity in the Column Bending Test

Abstract

The column bending test (CBT) is an experimental method to measure the moment–curvature behavior and failure curvature of high-strain composites (HSCs), designed to apply a relatively constant bending moment through a sample up to very high curvatures. In this paper, we first calculate the errors involved in the simplified geometric analysis used to model the CBT by considering two different effects: variations in the bending moment through the sample and nonlinearities in the material response of the fibers. The first effect, modeled using Euler’s elastica, results in a set of design guidelines for the test geometry (i.e., length of the grips and the specimens) in order to achieve moderate errors in moment and curvature predictions. The nonlinearity in the fiber behavior (tension stiffening and compression softening) does not have a strong effect on the curvature but produces significant variations in the bending stiffness of HSCs as well as the maximum strain observed in the fibers due to the shift in the neutral axis. This indicates that accounting for the nonlinear behavior of fibers is necessary in order to accurately predict the failure properties of HSCs under bending.