On the Choice of the Characteristic Length in the NMMD Model for the Simulation of Brittle Fractures

The recently proposed nonlocal macro–meso-scale consistent damage (NMMD) model has been applied successfully to various static and dynamic fracture problems. The characteristic length in the NMMD model, although proven to be necessary for the mesh insensitivity of a strain-softening regime, remains to be estimated indirectly with considerable arbitrariness. Such an issue also exists in other nonlocal models, e.g., peridynamics and phase field models. To overcome this obstacle, a series of dog-bone specimens composed of polymethyl-methacrylate (PMMA) material with and without circular defects are investigated in this paper. It is found that the NMMD model with the appropriate influence radius can correctly capture the experimentally observed size effect of the defect, which challenges the conventional local criteria without involving the characteristic length. In addition to being directly measurable and identifiable in experiments, based on the two-scale mechanism of the NMMD model, the characteristic length is also theoretically calibrated to be related to the ratio of the fracture toughness to the tensile strength of the material. Comparisons with the predictions of other modified nonlocalized criteria involving some characteristic length demonstrate the superior ability of the NMMD model to simulate brittle crack initiation and propagation from a non-singular boundary. The revalidation of short bending beams demonstrates that theoretical calibration is also suitable for problems of mixed-mode fractures with stress singularity. Although limited to brittle materials like PMMA, the current work could be generalized to the analysis of quasi-brittle or even ductile fractures in the future.