On strain localization under bending

The aim of the present contribution is to assess the localization properties of nonlocal damage models under bending. To permit a partially analytical treatment and to display the fundamental properties of various formulations, the idealized case of uniform bending is considered. This means that the beam has a constant cross section and is subjected to a uniformly distributed bending moment and zero normal force. The beam is assumed to be very long, and boundary effects that might be introduced by the supports at the end sections are eliminated by imposing periodic boundary conditions on the fluctuating part of the response, which is superimposed on the solution that corresponds to uniform curvature. The average curvature serves as a loading parameter that is monotonically increased.