A Review on the Modeling of the Elastic Modulus and Yield Stress of Polymers and Polymer Nanocomposites: Effect of Temperature, Loading Rate and Porosity

Abstract

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.

Development of bio-based membranes for building envelope applications from poly(lactic acid) and cellulose microfibers

“…8, the addition of untreated and modified CMFs to PLA remarkably reduced the Eˊ values of PLA-based biocomposites. The results might be attributed to the fibers' agglomeration and formation of voids between the polymer matrix and fibers, thereby diminishing the mechanical properties of materials (Kuan et al 2021;Alasfar et al 2022). The neat PLA exhibited the Tg at 69.6 °C, which is somewhat higher than the obtained Tg value from DSC (67.9 °C).…”

“…The incorporation of modified CMFs to PLA can regulate humidity by facilitating the transmission of water vapor from the interior atmosphere of building to the outside. Therefore, the developed membrane with enhanced permeability properties could prevent the mold growth, moisture build-up, and dampening of building envelopes which would otherwise lead to economic damage and impair the building's indoor air quality (Eder and Carus 2013;Alasfar et al 2022).…”

Electric Conductivity Study of Porous Polyvinyl Alcohol/Graphene/Clay Aerogels: Effect of Compression

“…At rupture stress σ R , (around 30–35%) the phenomenon of densification occurs in the compressed sample, where the space between lamellae and faces is reduced, producing a sharp increase in the stress experienced. On the other hand, it can be observed how the compression behavior of the PVOH/GN/clay aerogels is a typical behavior similar to that of a polymer nanocomposite . It can be contrasted how initially a stage of linear behavior can be seen corresponding to the elastic deformation of the PVOH/GN/clay lamellae.…”

“…On the other hand, it can be observed how the compression behavior of the PVOH/GN/clay aerogels is a typical behavior similar to that of a polymer nanocomposite. 30 It can be contrasted how initially a stage of linear behavior can be seen corresponding to the elastic deformation of the PVOH/GN/clay lamellae. When moving to zone II, the connections between the GN/clay sheets undergo brittle fracture and a gradual increase in stress is observed.…”

Tactile Sensing Using Magnetic Foam

“…Instead of using a continuous matrix, like the usual silicone rubber of MRE, a porous foam is used as the host matrix. Porosity in materials is known to reduce the effective Young’s modulus [ 9 , 10 ]; the composite is then softer. Polymeric foams, such as polyurethane, are highly compressible thanks to their Poisson’s ratio, which can be as low as 0.1 [ 11 ].…”