Stress transmission and failure in disordered porous media
Hadrien Laubie, Farhang Radjai, Roland Pellenq, Franz-Josef Ulm
By means of extensive lattice-element simulations, we investigate stress transmission and its relation with failure properties in increasingly disordered porous systems. We observe a non-Gaussian broadening of stress probability density functions under tensile loading with increasing porosity and disorder, revealing a gradual transition from a state governed by single-pore stress concentration to a state controlled by multipore interactions and metric disorder. This effect is captured by the excess kurtosis of stress distributions and shown to be nicely correlated with the second moment of local porosity fluctuations, which appears thus as a (dis)order parameter for the system. By generating statistical ensembles of porous textures with varying porosity and disorder, we derive a general expression for the fracture stress as a decreasing function of porosity and disorder. Focusing on critical sites where the local stress is above the global fracture threshold, we also analyze the transition to failure in terms of a coarse-graining length. These findings provide a general framework which can also be more generally applied to multiphase and structural heterogeneous materials.
A methodology to calibrate and to validate effective solid potentials of heterogeneous porous media from computed tomography scans and laboratory-measured nanoindentation data
Siavash Monfared, Hadrien Laubie, Farhang Radjai, Mija Hubler, Roland Pellenq, Franz-Josef Ulm
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 .
Mesoscale poroelasticity of heterogeneous media
Siavash Monfared, Hadrien Laubie, Farhang Radjai, Roland Pellenq, Franz-Josef Ulm
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 μVT and NPTensembles 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.
Disorder-induced stiffness degradation of highly disordered porous materials
Hadrien Laubie, Siavash Monfared, Farhang Radjaï, Roland Pellenq, Franz-Josef Ulm
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, φsa, 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.
Discrete Poroelasticity of Heterogeneous Media
Siavash Monfared, Hadrien Laubie, Farhang Radjai, Roland Pellenq, F-J Ulm
A discrete framework to reformulate poroelasticity of heterogeneous media is proposed using lattice element method (LEM). In congruence with μVT and NPT ensembles of statistical mechanics, discrete expressions for Biot poroelastic coefficients are derived. 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. Furthermore, this formulation accounts for the presence of interfaces as well as local microtextural and elastic variations. The theory is validated against continuum based expressions of Biot poroelastic coefficients for porous media with isotropic and tranversely isotropic elastic solid behavior.