Plastic failure of nonlocal beams

This paper questions the mode of collapse of some simple softening nonlocal structural systems comprising the classical cantilever beam. Nanobeams can be concerned by such an elementary model. The homogeneous cantilever beam loaded by a concentrated force at its extremity is first considered as a structural paradigm. A nonlocal plasticity model is developed in order to control the localization process induced by microcracking phenomena. An implicit gradient plasticity model equivalent to a nonlocal integral plasticity model is used in this paper. It is shown that the regularized problem is well posed. Closed-form solutions of the elastoplastic deflection are finally derived. The length of the plastic zone grows during the softening process until an asymptotic limited value, which depends on the characteristic length of the material. Scale effects are clearly obtained for these static bending tests. Other structural cases are also presented, including the simply supported beam under uniform transverse loading. It is concluded that the mode of collapse is firmly a nonlocal phenomenon.