Length scale of nonlocal gradient regularisation inferred from DEM virtual experiments

Nonlocal gradient continua are a reliable way to regularise numerical models of boundary value problems affected by strain localisation. However, the determination of the additional parameters of such formulations, including those controlling the length scale of potential shear bands, is not straightforward, in that it is affected by the interplay among stress–strain relations and shear band morphology. To address this challenge, this study proposes a parameter determination strategy for a nonlocal gradient strain-softening Mohr–Coulomb model based on discrete-element (DEM) virtual biaxial tests on a dense granular material. The strategy involves the initial calibration of the conventional model parameters based on stress–strain relations and shear band inclination, followed by subsequent calibration of the strain-softening parameters and length scale parameter, l. It is shown that a unique combination of these parameters exists that ensures an effective replication of both stress–strain relations and shear band morphology. Finally, shear band scale effects are analysed by varying the sample size W to l ratio. The simulated mechanical response and shear band patterns align well with DEM data obtained by changing the ratio of W to mean particle size d₅₀. These results indicate a direct relation between l and d₅₀.