FEMxDEM double scale approach with second gradient regularization applied to granular materials modeling

The multi-scale FEMxDEM approach is an innovative numerical method for geotechnical
problems involving granular materials. The Finite Element Method (FEM) and
the Discrete Element Method (DEM) are simultaneously applied to solve, respectively,
the structural problem at the macro-scale and the material microstructure at the microscale.
The advantage of using such a double scale configuration is that it allows to study
an engineering problem without the need of standard constitutive laws, thus capturing
the essence of the material properties. The link between scales is obtained via numerical
homogenization, so that, the continuum numerical constitutive law and the corresponding
tangent matrix are obtained directly from the discrete response of the microstructure.
Typically, the FEMxDEM approach presents some drawbacks; the convergence velocity
and robustness of the method are not as efficient as in classical FEM models.
Furthermore, the computational cost of the microscale integration and the typical meshdependency
at the macro-scale, make the multi-scale FEMxDEM approach questionable
for practical uses. The aim of this work is to focus on these theoretical and numerical
issues with the objective of making the multiscale FEMxDEM approach robust and
applicable to real-scale configurations. A variety of operators is proposed in order to
improve the convergence and robustness of the method in a quasi-Newton framework.
The independence of the Gauss point integrations and the element intensive characteristics
of the code are exploited by the use of parallelization 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 mesh-independency to the model.
The aforementioned improvements make the FEMxDEM approach competitive with
classical FEM models in terms of computational cost thus allowing to perform robust
and mesh-independent multi-scale FEMxDEM simulations, from the laboratory scale
(e.g. biaxial test) to the engineering-scale problem, (e.g. gallery excavation).