We discuss the multiscale modeling of a granular material trapped between continuum elastic domains. The amorphous granular region, usually termed “gouge,” is under high confinement pressure, to represent the loading of faults at depth. We model the granularity of gouge using the discrete element method (DEM), while the elastic regions surrounding it are represented with two continuum domains modeled with the finite element method (FEM). We resort to a concurrent coupling of the discrete and continuum domains for a proper transmission of waves between the discrete and continuum domains. The confinement pressure results in the appearance of a new kind of ghost forces, which we address via two different overlapping coupling strategies. The first one is a generalization to granular materials of the bridging method, which was originally introduced to couple continuum domains to regular atomic lattices. This method imposes a strong formulation for the Lagrange constraints at the coupling interface. The second strategy considers a weak formulation. Different DEM samples sizes are tested in order to determine at which scale a convergence of the elastic properties is reached. This scale sets the minimal mesh element size in the DEM/FEM interface necessary to avoid undesirable effects due to an elastic properties mismatch. Then, the two DEM/FEM strategies are compared for a system initially at equilibrium. While the performance of both strategies is adequate, we show that the strong coupling is the most stable one as it generates the least spurious numerical noise. Finally, as a practical example for the strong coupling approach, we analyze the propagation of pressure and shear waves through the FEM/DEM interface and discuss dispersion as function of the incoming wave frequency.
<p><span dir="ltr" role="presentation">The behavior of seismic faults depends on the response of the discrete microconstituents trapped in </span><span dir="ltr" role="presentation">the region between continuum masses, which is usually termed &#8220;gouge&#8221;. The gouge is a particle region </span><span dir="ltr" role="presentation">composed of amorphous grains. Conversely, the regions surrounding the gouge can be conceptualized </span><span dir="ltr" role="presentation">as continua. The study of such system dynamics (slip) requires the understanding of several scales, </span><span dir="ltr" role="presentation">from particle size to meter scale and above, to properly account for loading conditions.</span> <span dir="ltr" role="presentation">Our final </span><span dir="ltr" role="presentation">objective in this study is to assess to what extent we can understand friction by leveraging an analogy </span><span dir="ltr" role="presentation">to fracture. Dynamic friction between sliding surfaces resembles a dynamic mode-II crack, but this </span><span dir="ltr" role="presentation">equivalence is brought into question when granularity at the interface is considered. Based on the </span><span dir="ltr" role="presentation">theory of linear-elastic fracture mechanics (LEFM), a stress concentration should be observed at the </span><span dir="ltr" role="presentation">rupture front if indeed friction can be modeled with the toolkit of LEFM.</span></p> <p><span dir="ltr" role="presentation">Simulating this system numerically remains a challenge, as, in order to capture proper physics, both </span><span dir="ltr" role="presentation">the continuum and discrete aspects of the system must be harmoniously incorporated and coupled into </span><span dir="ltr" role="presentation">a single model. An energy-based coupling strategy between the Finite Element Method (FEM), used </span><span dir="ltr" role="presentation">to resolve the continuum portions, and the Discrete Element Method (DEM), to model the granularity </span><span dir="ltr" role="presentation">of the interface, is used [2]. In this exploratory study, we begin by modeling a medium with strong </span><span dir="ltr" role="presentation">inter-granular cohesion [1]. <span id="divtagdefaultwrapper" dir="ltr">The use of the coupling ensures a large enough effective domain to control nicely the crack propagation.&#160; The linear-elastic properties of both DEM and FEM portions are therefore matched to avoid wave reflections. </span></span><span dir="ltr" role="presentation"> Both mode-I and mode-II cracks are considered.</span></p>
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