The conference paper is devoted to the fluid-structure interaction (FSI) in periodic porous structures with electroactive elements (EAE), such as the piezoelectric, or flexoelectric segments controlable by external circuits. Such smart porous materials can serve for fluid pumping, or conversely to energy harvesting, in both cases the electro-mechanic energy conversion is due to the peristaltic deformation. To explore functionality of such metamaterial structures, multiscale computational tools using the homogenization of the FSI problem. Cell problems (at the microlevel) provide characteristic responses of the microstructures with respect to macroscopic strains, fluid pressure and electric potentials. The homogenized model is derived under the small deformation and linear constitutive law assumptions at the heterogeneity level, however, in the deformed configuration; this is necessary to respect the nonlinearity in the FSI and to capture ``the fluid pumping'' property. At the microlevel, a strong heterogeneity in the material parameters is introduced in terms the scale parameter of the asymptotic analysis. To respect dynamic effects of the flow in bulged pores, where the nonlinear advection term of the acceleration is non-negligible, two time scales are considered and an appropriate time scaling of the fast-slow dynamics is introduced in a proportion to the spatial scaling. In addition, propagating acoustic waves (actuated by the EAE) lead to the acoustic streaming effect also characterized by two temporal scales. The nonlinearity associated with deforming configuration is respected by deformation-dependent homogenized coefficients. To reduce the computational efficiency, the sensitivity analysis of the homogenized coefficients with respect to deformation induced by the macroscopic quantities is employed. This enables to avoid the two-scale tight coupling of the macro- and microproblems otherwise needed in nonlinear problems using the ``FE^2'' method. The paper summarizes our recent theoretical results and their potential applications in the research of multi-functional materials with potential use in civil engineering.

A clear understanding of the physical mechanisms leading to sorption-induced deformations in porous materials is essential to model the mechanical response of various materials, such as coalbed and shale formation during natural gas production and CO₂ sequestration or wood during drying. To describe the drying shrinkage of partially saturated porous materials with a wide pore size distribution, we improve a poromechanical model proposed by El Tabbal et al. (2020), based on the thermodynamic theory and which takes into consideration the capillary forces, Bangham effect, and Shuttleworth effect. One improvement lies in how we estimate strain variation during cavitation. We validate the model by applying it to experiments conducted by various authors with various pairs of adsorbate and adsorbent, during which both sorbed amounts and strains were measured. In general, this macroscopic model can predict the shape of strain isotherms during physisorption without any fitting parameters. We then discuss the impact of several uncertainties on the predicted deformations, namely the uncertainty on the cavitation pressure, the experimentally defined “dry” state, and the calculation of BET-specific surface area. We show that the impact of those various uncertainties on the predicted shape of the strain isotherm is negligible.

El Tabbal, G., P. Dangla, M. Vandamme, M. Bottoni, et S. Granet. « Modelling the Drying Shrinkage of Porous Materials by Considering Both Capillary and Adsorption Effects ». Journal of the Mechanics and Physics of Solids 142 (1 September 2020): 104016. https://doi.org/10.1016/j.jmps.2020.104016.

The process of salt crystallization within porous media is widely recognized as a substantial contributor to the deterioration of construction materials, geomaterials, and built heritage. When salts crystallize, they can exert mechanical pressure on pore surfaces, leading to material damage. However, despite its importance, the crystallization within porous networks remains poorly understood. We propose an investigation combining molecular simulations and theoretical development to quantify and clarify the origin of the crystallization pressure at the finest scale. This study should allow the identification of the parameters controlling the phenomenon and thus pave the way to mitigate or prevent salt damage.

At thermodynamic equilibrium, crystallization pressure results from the change in the solubility of a crystal as it is compressed. Direct molecular dynamics simulations to compute the solubility of salts are challenging because the time scale of dissolution and precipitation, microseconds or more, is at the limit or beyond computing capabilities. For this reason, we use a thermodynamic integration approach to overcome this issue. With this approach, we can quantify the effect of stress on NaCl solubility, and more specifically the effect of stress anisotropy which has been disregarded so far. We use these results to revisit the existing theory describing crystallization pressure and extend it to account for stress anisotropy.

Moreover, we conduct molecular simulations to determine the critical pressure threshold at which the wetting film, separating the crystal from the surface of the pore and responsible for the crystal growth, will disappear. This approach offers valuable insights into the stability and resilience of this film under varying pressure and temperature conditions.

This research endeavours to initiate a robust foundation for investigating various mechanical properties linked to the complex interaction between the solid and fluid phases within nanoporous materials with potential application in Civil Engineering.

In this study, we investigate the elastic properties of solids using the classical density functional theory (cDFT). While typically used for understanding the properties of inhomogeneous fluids, cDFT has only been used in a few studies for solid phases [1, 2]. In this contribution, we start by computing the phase diagram of a Lennard-Jones gas-liquid-FCC system to gain insights into its equilibrium behaviour. Then, we depart from the liquid-FCC system and compute a stable reference crystal solid state where the crystal is in equilibrium with external forces at a given temperature. Using this reference state, we subject the stable structure to small deformations while keeping the number of atoms constant. By minimizing the free energy of the deformed structure, we can derive the stress and deduce the elastic properties.

We compare our approach with data on real FCC materials, such as Nickel (Ni) and Iron (Fe), to assess the reliability of cDFT as an upscaling technique based on the atomistic description of a material, and providing continuum-based expressions. The ultimate goal of this study is to propose an upscaling-based poromechanical framework that integrates cDFT descriptions of both fluids and solids.

References

[1] M. Oettel, Description of hard-sphere crystals and crystal-fluid interfaces: A comparison between density functional approaches and a phase-field crystal model, Physical review E 86.2 (2012).

[2] T. Neuhaus, A. Härtel, Density functional theory of heterogeneous crystallization, Eur. Phys. J. Special Topics 223 (2014).

Aknowledgments: This work was partially financed by the Investissement d’Avenir French programme (ANR-16-IDEX-0002) under the framework of the E2S UPPA hub Newpores.