Sequentially Linear Saw-Tooth Softening Model

A model is proposed that replaces a nonlinear softening curve by a sequentially linear saw-tooth curve. A linear analysis is performed, the most critical element is traced, the stiffness and strength of that element are reduced according to the saw-tooth curve, and the process is repeated. The sequence of scaled critical steps provides the global loaddisplacement response. This procedure is both simple and stable as the secant stiffness of the saw-teeth is always positive. nonlinear crack models into sequentially linear saw-tooth models. The approach captures the snaps automatically and may help engineers to find practical solutions in case of complex structural cracking. A mesh regularization procedure is also provided, in order to achieve the mesh objectivity for the proposed approach. The regularization procedure is similar to the one commonly used in the smeared crack framework but, in addition, both the initial tensile strength and the ultimate strain are rescaled. In this way, the dissipated fracture energy is invariant with respect not only to the mesh size, but also to the number of saw-teeth adopted to discretize the softening branch. Furthermore, the algorithm to be used to study non-proportional loading conditions has been fully implemented, and results from a practical case are shown.