Towards a Hierarchical Continuum-Discrete Multiscale Methodology for the Thermomechanical Simulation of Dense Granular Media
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In this work, a continuum-discrete hierarchical multiscale approach for the numerical simulation of thermomechanical behaviour of densely packed granular materials is proposed. The Discrete Element Method (DEM) is used to accurately reproduce the microstructural response of the granular material. On the other hand, an Eulerian continuum approach is employed to solve the macroscale problem. These two methods are hierarchically coupled through the homogenization of the discrete behaviour in Representative Volume Elements (RVEs). This homogenization process consists of obtaining from a microscale solution the tensors needed for the continuum method (i.e. tangent operator, stress and thermal conductivity tensors) for a given macroscale state. The overall multiscale methodology avoids the use of specific phenomenological rheologies and provides a general framework for an accurate description of varied granular materials. A robust protocol is proposed for generating RVEs with a targeted granular assembly configuration. The optimum number of particles for the RVEs is defined via a convergence analysis of relevant homogenized variables. Several multiscale case studies are presented to validate the proposed methodology.
