Stochastic Modeling of Plane Strain Compression Tests With Micropolar Hypoplasticity Based on Screened Poisson Averaging of μCT Data
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X-ray microtomography (μCT) scans reveal the inherent heterogeneity of granular solids at small scales. To account for this heterogeneity in numerical simulations rooted in continuum mechanics, the μCT data must first be related to macroscopic quantities. This is typically achieved by voxel-based averaging, where the voxel grid size corresponds to the size of a representative volume element. Here we introduce a novel method for relating μCT data to macroscopic quantities, which exploits the averaging property of the screened Poisson equation. We introduce this method as screened Poisson averaging, which produces continuous distributions of the macroscopic quantity controlled by a single length parameter – the averaging length. Using screened Poisson averaging, we obtain the void ratio distribution for a μCT scan of a sample of dense Hostun sand [1]. This distribution is then used to compute the auto covariance function of the underlying spatial process, resulting in a physically motivated procedure for determining the parameters of a spatial random field for the void ratio. Based on multiple realizations of such spatial random fields, Monte Carlo simulations of plane strain compression tests are conducted, where micropolar hypoplasticity [2] is used for obtaining results insensitive to the finite element discretization. The implications of accounting for heterogeneous initial conditions obtained by means of the proposed methods are highlighted along with the effect of the averaging length. [1] Andò E, Hall SA, Viggiani G, Desrues J, Bésuelle P. “Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach”. Acta Geotech. 2012;7(1):1-13 [2] Maier, T. (2004). “Comparison of non-local and polar modelling of softening in hypoplasticity”. In: Int. J. Numer. Anal. Methods Geomech. 2004;28(3):251-268
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