FEMxDEM multi-scale modelling with second gradient regularization

The multi-scale FEMxDEM approach is an innovative numerical method for geotechnical problems,
using at the same time the Finite Element Method (FEM) at the engineering macro-scale and the
Discrete Element Method (DEM) at the scale of the microstructure of the material. The link between
scales is made via computational homogenization. In this way, the continuum numerical constitutive
law and the corresponding tangent matrix are obtained directly from the discrete response of the
microstructure [1,2,3].
In the proposed paper, a variety of operators, rather than the tangent consistent for the Newton-
Raphson method, is tested in a challenging attempt to improve the poor convergence performance.
The independence of the DEM computations between the different elements is exploited to develop a
parallelized code using an OpenMP paradigm. At the macro level, a second gradient constitutive
relation is implemented in order to enrich the first gradient Cauchy relation bringing meshindependency
to the model. The second gradient regularization, together with the speedup provided
by the parallelization allows by first time to the FEMxDEM model to be applied to real scale
problems with the desired mesh refinement.
Some results are given exhibiting the above findings with emphasis on aspects related to strain
localisation.