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The study of the deformation in inhomogeneous materials is essential for the understanding and interpretation of geological processes. Whether it is to to provide the dynamics of the inhomogeneities them self, or to extract effective material properties for large scale simulations.
While the behavior of single particles is well understood the effects of interaction and flow partitioning in denser packed suspensions with realist numbers of heterogeneities are largely unknown in terms of quantitative analysis. In this study we consider such particle suspensions and investigate the end-member case of rigid inclusions in an isotropic viscous matrix, driven in the Stokes-flow limit. The number of heterogeneities exceeds 1000.
Two computational approaches are considered. One is the direct solution of the problem by the finite element method and the other is by Stokesian dynamics, where the hydrodynamical interaction between the particles are resolved without a direct calculation of the flow in the matrix. Due to the simplifications that underly the Stokesian dynamics approach it could potentially serve as a tool to investigate large particle systems such as are common in nature. We will compare the two different approaches and provide an analysis of the results obtained for effective material properties and mechanically induced diffusion of the the inclusions.
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