Calibration of non-local damage models from full-field measurements: Application to discrete element fields

Continuous damage models are increasingly used in numerical simulations to design structures, but their local formulations are sensitive to mesh size and present localization of strains in an infinitely thin region. To overcome these problems non-local damage models and related regularization methods, have been developed introducing a characteristic/internal length, thus avoiding pathological mesh dependence. Those methods make the damage evolution depends on the mechanical quantities at the current material point (local) and its neighborhood (non-local).

Existing approaches to calibrate the internal length use global quantities in the calibration process, although local data is now becoming accessible (e.g., using digital image correlation). In this study, we investigate the use of full-field displacement measurements an propose a new methodology for calibrating a non-local damage model based on local field measurements and we apply it to calibrate the Eikonal Non-local Gradient (ENL-G) approach from the measured strain and damage field. After detailing the calibration procedure, we then apply it on a simple ideal case. We illustrate, and analyze the robustness of the calibration procedure with respect to the choice of evolution law and measurement noise of the proposed calibration method. To confront the procedure to a more realistic case, we employed a 2D beam-particle model. This discrete model is first identified with respect to the size and shape effect based on one of the comprehensive experimental data sets available in the literature, including four shapes with three sizes each. Then, it is used to generate a “reference” evolution of the damage and strain fields in beams of different sizes subjected to uniaxial tension.

The parameters of the discrete model used have been calibrated to represent the scale and size effects, giving a very good representation of the experiments. We also illustrate the evolution of non-local interactions in the Eikonal approach using Green functions. Finally, the application of the calibration procedure shows that it is possible to determine the internal length of the non-local problem studied as well as the damage evolution law and its parameters. The outcomes of this study contribute to shed light on a new methodology to identify non-local damage models based on full-field measurements, and call for experimental size effect campaign with displacement field.