@article {239, title = {Disorder-induced stiffness degradation of highly disordered porous materials}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {106}, year = {2017}, month = {Sep-2017}, chapter = {207-228}, abstract = {

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.

Fig. 1. Two-dimensional porous media: (a) ordered system, (b) type 1 disorder (pores{\textellipsis}

Fig. 2. Two-point probability functions and associated microstructures of four systems{\textellipsis}

Fig. 3. Probability Density Function (PDF) of the local porosity (φa) and associated{\textellipsis}

Fig. 4. (a) Degrees of freedom of a link element between points i and j, (b) D3Q18 unit{\textellipsis}

Fig. 5. Dimensionless effective Young{\textquoteright}s modulus: Eeff(φ)/Es as function of the porosity{\textellipsis}

Fig. 6. Dimensionless effective Young{\textquoteright}s modulus: Eeff(φ)/Es as function of the porosity

Fig. 7. Ordered system under uniaxial strain, (a) schematic stress map, the darker the{\textellipsis}

Fig. 8. Dimensionless effective Young{\textquoteright}s modulus: Eeff(φ)/Es as function of the porosity

Fig. 9. Probability Density Function (PDF) of the normalized stress (σxx/〈σxx〉) in the{\textellipsis}

Fig. 10. Dimensionless disordered Young{\textquoteright}s modulus: F(φsa)=Eeff(φ,sa)/Eordered(φ) as{\textellipsis}

Fig. 11. Two-phase periodic porous solid

Fig. 12. Dimensionless disordered Young{\textquoteright}s modulus: FMT(φsa)=Eeff(φ,sa)/EMT(φ) as{\textellipsis}

Fig. 13. Integration path for the lower bound differential scheme

Fig. 14. Dimensionless effective Young{\textquoteright}s modulus: Eeff(φ)/Es as function of porosity the

Fig. 15. Dimensionless disordered Young{\textquoteright}s modulus: FMT(φsa)=Eeff(φ,sa)/EMT(φ) as{\textellipsis}

Fig. B.16. (a) Porosity as a function of the number of pores

Fig. D.17. High porosity limit geometry

Fig. E.18. Calculation of the local porosity in a square observation window

}, doi = {10.1016/j.jmps.2017.05.008}, author = {Hadrien Laubie and Monfared, Siavash and Farhang Radja{\"\i} and Roland Jean-Marc Pellenq and Franz-Josef Ulm} }