A smooth unloading-reloading approach for the nonlinear finite element analysis of quasi-brittle materials

This paper presents a new method for improving the robustness and convergence characteristics of a finite element damage model for quasi-brittle materials. In this method, a smooth unloading-reloading function (SUR) is employed to compute an approximate tangent matrix in a Newton type solution procedure. A new method is also presented for predicting a converged value of the damage parameter. The performance of the new methods are assessed using a range of idealised quasi-brittle specimens. Results show that the new SUR approaches are robust and result in considerable savings relative to solutions obtained with a secant unloading-reloading function.