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

A plastic-damage-contact constitutive model for concrete with smoothed evolution functions

A new 3D finite element concrete model is described. The model brings together two recently developed sub-models for simulating cracking and crack contact behaviour, both of which use smoothed evolution functions, with a triaxial plasticity model component. A number of examples are presented that validate the model using a range of plain and reinforced concrete test data. These examples demonstrate that the model is numerically robust, has good equilibrium convergence performance and is objective with respect to mesh grading and increment size. The examples also illustrate the model’s ability to predict peak loads, failure modes and post-peak responses