Porous polymer-based nanocomposites have been used for various applications due to their advantages, including multi-functionalities, easy and known manufacturability, and low cost. Understanding of their mechanical properties has become essential to expand the nanocomposites’ applications and efficiency, including service-life, resistance to different loads, and reliability. In this review paper, the focus is on the modeling of the mechanical properties of porous polymer-based nanocomposites, including the effects of loading rates, operational temperatures, and the material’s porosity. First, modeling of the elastic modulus and yield stress for glassy polymers and polymer reinforced by nanofillers are addressed. Then, modeling of porosity effects on these properties for polymers are reviewed, especially via the use of the well-known power-law approach linking porosity to elastic modulus and/or stress. Studies related to extending the mechanical modeling to account for porosity effects on the elastic modulus and yield stress of polymers and polymer-nanocomposites are discussed. Finally, a brief review of the implementation of this modeling into 3D computational methods to predict the large elastic-viscoplastic deformation response of glassy polymers is presented. In addition to the modeling part, the experimental techniques to measure the elastic modulus and the yield stress are discussed, and applications of polymers and polymer composites as membranes for water treatment and scaffolds for bone tissue engineering are addressed. Some modeling results and validation from different studies are presented as well.

The mechanical properties of polymeric membranes are very important in water treatment applications. In this study, polysulfone (PSF) membranes with different loadings of cellulose nanofibers (CNFs) were prepared via the phase inversion method. CNF was characterized through transmission electron microscopy (TEM) and scanning electron microscopy (SEM). The pore morphology, mechanical properties, membrane performance and hydrophilicity of pure PSF membranes and PSF/CNF membranes were investigated. The changes in membrane pore structure with the addition of different CNF contents were observed using SEM images. It was shown that the calculated membrane pore sizes correlate with the membrane water fluxes. The pure water flux (PWF) of fabricated membranes increased with the addition of CNFs into the PSF matrix. It was shown that the optimal CNF loading of 0.3 wt.% CNF improved both the elastic modulus and yield stress of the PSF/CNF membranes by 34% and 32%, respectively (corresponds to values of 234.5 MPa and 5.03 MPa, respectively). This result indicates a strong interfacial interaction between the PSF matrix and the reinforced nanofibers. The calculated compaction factor (CF) showed that the membrane resistance to compaction could be improved with CNF reinforcement. Compared to pure PSF membrane, the hydrophilicity was significantly enhanced with the incorporation of 0.1 wt.%, 0.2 wt.% and 0.3 wt.% CNF, as shown by the water contact angle (WCA) results. It can be concluded that CNFs are homogeneously dispersed within the PSF matrix at CNF loading less than 0.5 wt.%.

The mechanical properties of polymeric membranes are critical factors for a successful and durable application in water treatment technologies. Fabricating membranes with optimal mechanical properties require delicate balancing between material, additives, processing conditions, porosity, and many other variables. Several variables to be optimized demands detailed experimental and computational investigations. The design of experiments (DOEs) technique using a validated framework with a computational model for the prediction of the elastic behavior can lower the number of conducted experiments for optimal membrane fabrication conditions. In this study, optimization of the elastic modulus of polymeric membranes is performed using DOE with computational modeling and validated with experiments. The optimum storage modulus of polymeric nano‐filled membranes is determined at an operating temperature of 35°C. DOE is employed with a three‐factor–three‐level problem. The Taguchi DOE is utilized to obtain the experiments scheme, followed by the prediction of the storage modulus and fabrication of the polymeric nano‐filled membrane with the optimum modulus. Predicted results demonstrate that the modulus of polyether sulfone (PES) reinforced with 0.3 wt.% halloysite nanotubes (HNTs) is the optimum combination. The fabricated PES/0.3 wt.% HNT membrane is in good agreement with the predicted modulus with a percentage error of 3%.