Nonlinear mechanics of fragmented beams

This paper presents an analytical model for the nonlinear analysis of fragmented beams — beams which are assembled from separate fragments (blocks) without any binding material or connector. The structural integrity in these structures is provided by the shapes of the fragments and the axial compression applied at the boundaries. However, this compression also introduces a destabilizing mechanism in the form of P-Delta effect, which may lead to a loss of the global stability. In addition, the absence of binding allows the fragments to move and rotate independently, which causes detachments between them. In this paper, this coupled nonlinear behavior is thoroughly studied by applying geometrically nonlinear kinematic relations at the fragments and nonlinear traction laws at the interfaces between them. In order to capture the localization of stresses in the partially separated fragments, the high-order beam theory is implemented. The obtained nonlinear governing equations are solved numerically and the results are compared with ones obtained by finite element simulations. It is demonstrated that the progressive detachment between the fragments yields a localization of stresses at the contact areas. These detachments and stress localizations impair the bending stiffness of the beam, and together with the axial compression, present a destructive coupled mechanism. This mechanism controls the strength and stability of the fragmented beam. Finally, a parametric study on the effects of the axial compression and boundary conditions on the strength and energy absorption capacity of the beams is presented.