Spurious Bifurcations in Transient Analysis with Isotropic Damage

In the setting of thermomechanical transient analysis of concrete using isotropic damage, the writers noted the consistent occurrence of spurious bifurcations of the deformation field, for thermal and mechanical loading of panel specimens. The cause of the problem is discussed, noting that bifurcation occurs in a simple uniaxial problem, in tension or compression, when there is any (small) difference in material properties. With a transient analysis there are always small momentum effects, and these generate slight variations in strain. For a strain-based isotropic damage model, this results in slight variations in damage, hence stiffness, and so bifurcation is inevitable in the symmetric homogeneous problem. A simple cure to the problem is adopted and the model is tested on three point bend specimens. Apart from its known deficiencies, the local damage model is shown to be very sensitive to the choice of model parameters, mesh size and structure, and the level of numerical error. A nonlocal formulation, on the other hand, is shown to be quite robust.