Multiscale modeling of thermo-mechanical responses of granular materials: A hierarchical continuum–discrete coupling approach

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A hierarchical multiscale coupling of the finite element method (FEM) and the discrete element method (DEM) is proposed to model coupled thermo-mechanical behavior of granular materials. The DEM is employed to model the thermo-mechanical responses of a representative volume element (RVE, a granular assembly) embedded at a Gauss (quadrature) point of the FEM. The material responses derived from each Gauss point feed two superimposed FEMs to find global solutions subject to two concurrent boundary value problems (BVPs), i.e., heat conduction and mechanical deformation. The two concurrent FEMs exchange information on temperature change and fabric variation at their commonly shared Gauss points. The proposed approach is benchmarked by two examples of transient and steady-state thermal conduction where analytical solutions are available. It is further applied to investigating the thermo-mechanical responses of confined granular columns under cyclic thermal loads with emphasis placed on the effect of boundary condition and inherent anisotropy of a granular column. The proposed approach offers a novel multiscale pathway to model thermo-mechanical responses of granular media based on sound physics.