Modelling & Simulation


Cascade micromechanics model for the effective diffusivity and permeability of microcracked materials

Jithender J. Timothy, Structural Mechanics/Ruhr University Bochum, Bochum, Germany
Günther Meschke, Structural Mechanics/Ruhr University Bochum, Bochum, Germany

Heterogeneous materials, such as ceramics, polymers, biological, geological or cement-based materials are often characterized by a distributed network of microcracks, which either exists a priori, e.g. caused by the production process, or which is later induced by the loading process. Molecular transport and fluid flow in such materials is strongly influenced by the density and the topology (geometry, distribution, connectivity) of microcracks. The overall transport characteristics of such microcracked, heterogeneous materials can be quantified in terms of an effective diffusivity and permeability, respectively.

Using the mean-field homogenization method as a general framework, microcracks are modeled as inclusions in a porous matrix material and the corresponding microscopic gradient localization tensors – induced by the microcracks – are computed using the Eshelby matrix-inclusion technique. Using localization tensors, we present a novel recursive cascade micromechanics model [1,2], which accounts for the tortuous (fractal) character of complex porous and microcracked microstructures, to derive the effective permeability and diffusivity tensors for an isotropic and an anisotropic distribution of microcracks. For comparison, existing homogenization schemes, such as the dilute, Mori-Tanaka and the self-consistent scheme, and their range of applicability, are also investigated. The predictive capability of the cascade model and the existing models is demonstrated by means of comparison with numerical experiments on the mesoscale.

It is demonstrated that the cascade scheme is able to correctly predict the effective permeability and diffusivity for the full range of microcrack densities, including the prediction of the percolation threshold (i.e. the critical microcrack density, where the network starts to connect) with remarkable accuracy for all investigated scenarios, including unstructured as well as highly structured microcrack topologies, different intrinsic transport properties and aspect ratios of the microcracks.

[1] Timothy, J. J. & Meschke, G., A micromechanics model for molecular diffusion in materials with complex pore structure. Int. J. Num. Anal. Meth. Geomech., 40(5), 686—712, 2016.
[2] Timothy, J. J. & Meschke, G., A cascade continuum micromechanics model for the effective elastic properties of porous materials. Int. J. Sol. Struct., 83, 1-12, 2016.

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