Homogenization and two‐scale simulations of granular materials for different microstructural constraints

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A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media (2014, methodology): “Periodic boundary is applied to both directions of the RVE, which proves to be an optimal choice in generating most realistic stiffness for the macroscopic behaviour of granular media [43] and meanwhile satisfying a priori the Hill–Mandel-type condition [10].”
A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning (2018, methodology): “Among the admissible boundary conditions fulﬁlling the Hill-Mandel micro-heterogeneity condition, we adopt the periodic boundary conditions [Miehe et al., 2010], where the motion of a particle on the boundary of the RVE is characterized by, assuming rigid particles, where X c is the initial…”