Mesoscale Poroelasticity of Heterogeneous Media

Monfared, Siavash; Laubie, Hadrien; Radjaï, Farhang; Pellenq, Roland J.‐M.; Ulm, Franz‐Josef

doi:10.1061/(asce)nm.2153-5477.0000136

Cited by 7 publications

(11 citation statements)

References 31 publications

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“…All what it takes to implement the LEM approach is to choose appropriate expressions for the interaction potential representative of the solid's behavior. This has been illustrated by Laubie et al (2017b ) for elastic isotropic and transversely isotropic solids; and by Monfared et al (2017) for linear poroelastic systems. The focus of the next sections is to extend the PMF approach to fracture problems.…”

Section: Pmf-fracture Approach For Lemmentioning

confidence: 71%

“…This PMF approach to LEM was recently proposed for elastic systems ( Laubie et al, 2017a;2017b ), showing that the elasticity in the PMF context is but an evaluation of the energy content of the system around the equilibrium state defined by the lattice structure, for which most non-harmonic potentials degenerate to harmonic potentials commensurable to the original truss-beam type formulation used in classical LEM approaches. On the other hand, the PMF approach puts the LEM on the same footing as molecular approaches thus permitting to employ the canon of statistical physics, such as thermodynamic ensemble definitions, to extend the LEM approach as a tool of solid mechanics to poromechanics ( Monfared et al, 2017 ). By considering the PMF-approach for fracture modeling of homogeneous and heterogeneous systems, the purpose of this paper is to extend our earlier developments from a reversible solid behavior to irreversible solid behavior.…”

Section: Introductionmentioning

confidence: 99%

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A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

Laubie

Radjaï

Pellenq

et al. 2017

Journal of the Mechanics and Physics of Solids

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Fracture of heterogeneous materials has emerged as a critical issue in many engineering applications, ranging from subsurface energy to biomedical applications, and requires a rational framework that allows linking local fracture processes with global fracture descriptors such as the energy release rate, fracture energy and fracture toughness. This is achieved here by means of a local and a global potential-of-mean-force (PMF) inspired Lattice Element Method (LEM) approach. In the local approach, fracture-strength criteria derived from the effective interaction potentials between mass points are shown to exhibit a scaling commensurable with the energy dissipation of fracture processes. In the global PMF-approach, fracture is considered as a sequence of equilibrium states associated with minimum potential energy states analogous to Griffith's approach. It is found that this global approach has much in common with a Grand Canonical Monte Carlo (GCMC) approach, in which mass points are randomly removed following a maximum dissipa-tion criterion until the energy release rate reaches the fracture energy. The duality of the two approaches is illustrated through the application of the PMF-inspired LEM for fracture propagation in a homogeneous linear elastic solid using different means of evaluating the energy release rate. Finally, by application of the method to a textbook example of fracture propagation in a heterogeneous material, it is shown that the proposed PMF-inspired LEM approach captures some well-known toughening mechanisms related to fracture energy contrast, elasticity contrast and crack deflection in the considered two-phase layered composite material.

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Section: Pmf-fracture Approach For Lemmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

Laubie

Radjaï

Pellenq

et al. 2017

Journal of the Mechanics and Physics of Solids

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“…The lattice element method (LEM) [3,25,54] is employed here to investigate both the elastic and the poroelastic behavior of highly heterogeneous real materials, utilizing the framework of effective interaction potentials [35] and ensemble-based definitions for Biot coefficients [40]. This is achieved by importing CT scans directly into LEM and discretizing the volume into a number of mass points.…”

Section: Lattice Element Methods and Effective Interaction Potentialsmentioning

confidence: 99%

“…Then, the validation structure set is utilized as independent means for validation. With the elastic energy contents calibrated, Biot poroelastic coefficients are simulated using ensemble-based definitions for highly heterogeneous media [40]. Lastly, analyses of stress transmissions through larger sub-volumes extracted from the scans highlight the distinct underlying microtextural features and load-bearing phases in each case.…”

Section: Introductionmentioning

confidence: 99%

A methodology to calibrate and to validate effective solid potentials of heterogeneous porous media from computed tomography scans and laboratory-measured nanoindentation data

et al. 2018

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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.

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“…While the preceding approaches allowed removing some of the earlier limitations of the central-force model, a search of the relevant literature was not conclusive in finding a rational framework that clearly defines the different elements of the method, from the local interactions that link the lattice's mass points to the macroscopic properties of the assembly of links, which is, in short, the focus of this paper. Such a framework is needed though not only for elastic (i.e., reversible) phenomena, but also for extending the method to poroelasticity (Monfared et al 2016) or dissipative phenomena, related to plastic deformation, fracture, and so on, for which the method is frequently applied (e.g., Affes et al…”

mentioning

confidence: 99%

Effective Potentials and Elastic Properties in the Lattice-Element Method: Isotropy and Transverse Isotropy

Laubie

Monfared

Radjaï

et al. 2017

J. Nanomech. Micromech.

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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.with the current understanding of the link between texture (here lattice) and the deformation behavior of materials (Greaves et al. 2011). In order to overcome this limitation, several authors suggested the addition of beam-type interactions between mass points in 2D (e.g., Garboczi 1996, 1997;Bolander and Saito 1998) and 3D with or without rotational degrees of freedom (Zhao et al. 2011), with up to 178 interactions for each node in the (random lattice) system (Lilliu et al. 1999;Lilliu and van Mier 2003). While the preceding approaches allowed removing some of the earlier limitations of the central-force model, a search of the relevant literature was not conclusive in finding a rational framework that clearly defines the different elements of the method, from the local interactions that link the lattice's mass points to the macroscopic properties of the assembly of links, which is, in short, the focus of this paper. Such a framework is needed though not only for elastic (i.e., reversible) phenomena, but also for extending the method to poroelasticity (Monfared et al. 2016) or dissipative phenomena, related to plastic deformation, fracture, and so on, for which the method is frequently applied (e.g., Affes et al.

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Mesoscale Poroelasticity of Heterogeneous Media

Abstract: 7Poromechanics of heterogeneous media is reformulated in a discrete framework using Lattice

Cited by 7 publications

References 31 publications

A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

A methodology to calibrate and to validate effective solid potentials of heterogeneous porous media from computed tomography scans and laboratory-measured nanoindentation data

Effective Potentials and Elastic Properties in the Lattice-Element Method: Isotropy and Transverse Isotropy

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