Higher-order damage models for the analysis of fracture in quasi-brittle materials

Higher-order continuum descriptions invariably introduce one or more additional material parameters. An experimental problem resides in the determination of these additional parameters. In the present contribution two materials are examined and the relation between the internal length scale and the observed experimental results is examined. A gradientenhanced damage model is used for concrete, while a strain-based transient gradient damage (STGD) method is used to describe the behaviour of SGFPP. In the STGD-model, the unloaded material is modelled in a strictly local way, and the nonlocal effect increases with the local strain state of the material. This method leads to a well-defined crack opening and converges to a damaged zone with a finite width which does not broaden during crack propagation. The convergence upon mesh refinement with this method is adequate. In the case of SGFPP, the experimental results obtained from the Compact-Tension tests have been used to make a local comparison with the computational results obtained with the STGDmethod. The parameters in the model are quantified and the proper modelling of the size and notch effects are investigated.