Nonlinear Fracture Mechanics—Diffuse Crack Model

The real fracture process zone (FPZ) in all materials has not only a finite length, but also a finite width, which is particularly important for quasibrittle materials. The width matters, especially in presence of crack parallel stresses. It means that, instead of a scalar stress-displacement relation, fracture needs to be described by a realistic tensorial softening damage constitutive model, for which the microplane model is a particularly effective choice. The easiest way to do that is to use the crack band model, which by now dominates in concrete and aircraft composites in industry. First the need for such a model is established by analyzing bifurcation and stability of equilibrium load-displacement response of a structure, and by demonstrating the necessity of a localization limiter, which represents the effective width of the FPZ dictated by material heterogeneity. For the cases where fracture is known to localize, as is typical for reinforced concrete, simple rules for scaling the postpeak response to preserve the correct energy dissipation are derived, and implementation in FE analysis is outlined. The nonlocal integral and gradient approaches are discussed as alternative models having some advantages and disadvantages. Finally, discrete computational lattice and particle models, with LDPM as a particularly effective choice, are described.