Built on the framework of effective interaction potentials using lattice element method, a methodology to calibrate and to validate the elasticity of solid constituents in heterogeneous porous media from experimentally measured nanoindentation moduli and imported scans from advanced imaging techniques is presented. Applied to computed tomography (CT) scans of two organic-rich shales, spatial variations of effective interaction potentials prove instrumental in capturing the effective elastic behavior of highly heterogeneous materials via the first two cumulants of experimentally measured distributions of nanoindentation moduli. After calibration and validation steps while implicitly accounting for mesoscale texture effects via CT scans, Biot poroelastic coefficients are simulated. Analysis of stress percolation suggests contrasting pathways for load transmission, a reflection of microtextural differences in the studied cases. This methodology to calibrate elastic energy content of real materials from advanced imaging techniques and experimental measurements paves the way to study other phenomena such as wave propagation and fracture while providing a platform to fine-tune effective behavior of materials given advancements in additive manufacturing and machine learning algorithms .

VL - 13 UR - http://link.springer.com/10.1007/s11440-018-0687-9 IS - 6 JO - Acta Geotech. ER - TY - JOUR T1 - Disorder-induced stiffness degradation of highly disordered porous materials JF - Journal of the Mechanics and Physics of Solids Y1 - 2017 A1 - Hadrien Laubie A1 - Monfared, Siavash A1 - Farhang Radjaï A1 - Roland Jean-Marc Pellenq A1 - Franz-Josef Ulm AB -The effective mechanical behavior of multiphase solid materials is generally modeled by means of homogenization techniques that account for phase volume fractions and elastic moduli without considering the spatial distribution of the different phases. By means of extensive numerical simulations of randomly generated porous materials using the lattice element method, the role of local textural properties on the effective elastic properties of disordered porous materials is investigated and compared with different continuum micromechanics-based models. It is found that the pronounced disorder-induced stiffness degradation originates from stress concentrations around pore clusters in highly disordered porous materials. We identify a single disorder parameter, φ*sa*, which combines a measure of the spatial disorder of pores (the clustering index, *sa*) with the pore volume fraction (the porosity, φ) to scale the disorder-induced stiffness degradation. Thus, we conclude that the classical continuum micromechanics models with one spherical pore phase, due to their underlying homogeneity assumption fall short of addressing the clustering effect, unless additional texture information is introduced, e.g. in form of the shift of the percolation threshold with disorder, or other functional relations between volume fractions and spatial disorder; as illustrated herein for a differential scheme model representative of a two-phase (solid–pore) composite model material.

VL - 106 ER - TY - JOUR T1 - Effective Potentials and Elastic Properties in the Lattice-Element Method: Isotropy and Transverse Isotropy JF - Journal of Nanomechanics and Micromechanics Y1 - 2017 A1 - Hadrien Laubie A1 - Monfared, Siavash A1 - Farhang Radjaï A1 - Roland Jean-Marc Pellenq A1 - Franz-Josef Ulm AB -

Lattice approaches have emerged as a powerful tool to capture the effective mechanical behavior of heterogeneous materials using harmonic interactions inspired from beam-type stretch and rotational interactions between a discrete number of mass points. In this paper, the lattice element method (LEM) is reformulated within the conceptual framework of empirical force fields employed at the lattice scale. Within this framework, because classical harmonic formulations are but a Taylor expansion of nonharmonic potential expressions, they can be used to model both the linear and the nonlinear response of discretized material systems. Specifically, closed-form calibration procedures for such interaction potentials are derived for both the isotropic and the transverse isotropic elastic cases on cubic lattices, in the form of linear relations between effective elasticity properties and energy parameters that define the interactions. The relevance of the approach is shown by an application to the classical Griffith crack problem. In particular, it is shown that continuum-scale quantities of linear-elastic fracture mechanics, such as stress intensity factors (SIFs), are well captured by the method, which by its very discrete nature removes geometric discontinuities that provoke stress singularities in the continuum case. With its strengths and limitations thus defined, the proposed LEM is well suited for the study of multiphase materials whose microtextural information is obtained by, e.g., X-ray micro-computed tomography. (c) 2017 American Society of Civil Engineers.

VL - 7 UR - http://ascelibrary.org/doi/10.1061/%28ASCE%29NM.2153-5477.0000125 IS - 3 JO - J. Nanomech. Micromech. ER - TY - JOUR T1 - Mesoscale Poroelasticity of Heterogeneous Media JF - Journal of Nanomechanics and Micromechanics Y1 - 2017 A1 - Monfared, Siavash A1 - Hadrien Laubie A1 - Farhang Radjaï A1 - Roland Jean-Marc Pellenq A1 - Franz-Josef Ulm AB -The poromechanics of heterogeneous media is reformulated in a discrete framework using the lattice element method (LEM) that accounts for the presence of interfaces as well as local microtextural and elastic variations. The exchange of mechanical information between pore and solid(s) is captured by means of force field potentials for these domains, which eliminate the requirement of scale separability of continuum-based poromechanics approaches. In congruence with mu VT and NPT ensembles of statistical mechanics, discrete expressions for Biot poroelastic coefficients are derived. Considering harmonic-type interaction potentials for each link, analytical expressions for both isotropic and transversely isotropic effective elasticity are presented. The theory is validated against continuum-based expressions of Biot poroelastic coefficients for porous media with isotropic and transversely isotropic elastic solid behavior. (C) 2017 American Society of Civil Engineers.

VL - 7 UR - http://ascelibrary.org/doi/10.1061/%28ASCE%29NM.2153-5477.0000136 IS - 4 JO - J. Nanomech. Micromech. ER - TY - JOUR T1 - A molecular informed poroelastic model for organic-rich, naturally occurring porous geocomposites JF - Journal of the Mechanics and Physics of Solids Y1 - 2016 A1 - Monfared, Siavash A1 - Franz-Josef Ulm AB -Molecular simulation results on organic maturity (mature and immature kerogen as the two asymptotic cases) are introduced into a continuum micromechanics based model for organic-rich shales. Through a fundamental functional relationship that constrains microporous kerogen density and elasticity variable spaces and within the framework of effective media theory; the model bridges the gap between asymptotic cases of organic maturity with texture as the overriding theme, specifically a matrix/inclusion (Mori–Tanaka) texture for immature systems and a granular (self-consistent) texture for mature ones. The utility of the molecular results merged into a continuum framework is demonstrated by estimating kerogen's microporosity () from nanoindentation measurements. The effect of burial and diagenetic processes on the effective poroelasticity of these porous, naturally occurring geocomposites are captured by introduction of imperfect interfaces. Finally, the performance of the model is fully characterized by ranking the normalized contribution of uncertainty of input to the overall behavior and parameters of interest to geophysicists and geomechanicians such as degree of anisotropy and *in situ* stresses.