A 2D/3D implicit gradient-enhanced nonlocal meso-scale damage model for deformation and fracturing of brittle materials

An implicit gradient-enhanced nonlocal meso‑scale damage model is developed to investigate deformation and fracturing of brittle materials. In the model, an implicit gradient integration scheme is adopted to deal with mesh dependency and strain localization. The mechanical parameters are assigned randomly using a Weibull statistical distribution to reflect the material heterogeneity at the meso‑scale. A linear elastic damage constitutive law with residual strength is used to describe the stress-strain relationship at the mesoscale and the Mohr-Coulomb criterion as well as the tensile stress criterion are used to evaluate the damage of the elements in tension or shear. The local equivalent strain is replaced by a nonlocal description employing the non-local implicit gradient model. Benchmark tests are conducted to document the potential of the model in simulating crack initiation and propagation processes in brittle materials. The benchmark tests also demonstrate that the proposed non-local damage model can effectively achieve strain localization and eliminate mesh dependency to some extent.