Constitutive Modeling of the Densification Behavior in Open-Porous Cellular Solids

The macroscopic mechanical behavior of open-porous cellular materials is dictated by the geometric and material properties of their microscopic cell walls. The overall compressive response of such materials is divided into three regimes, namely, the linear elastic, plateau and densification. In this paper, a constitutive model is presented, which captures not only the linear elastic regime and the subsequent pore-collapse, but is also shown to be capable of capturing the hardening upon the densification of the network. Here, the network is considered to be made up of idealized square-shaped cells, whose cell walls undergo bending and buckling under compression. Depending on the choice of damage criterion, viz. elastic buckling or irreversible bending, the cell walls collapse. These collapsed cells are then assumed to behave as nonlinear springs, acting as a foundation to the elastic network of active open cells. To this end, the network is decomposed into an active network and a collapsed one. The compressive strain at the onset of densification is then shown to be quantified by the point of intersection of the two network stress-strain curves. A parameter sensitivity analysis is presented to demonstrate the range of different material characteristics that the model is capable of capturing. The proposed constitutive model is further validated against two different types of nanoporous materials and shows good agreement

The effect of pore sizes on the elastic behaviour of open-porous cellular materials

The influence of the pore structure characteristics in open-porous cellular materials on their macroscopic elastic behaviour is investigated by considering three important microstructural features viz. the relative density, the pore-size distribution, and the pore-wall thickness. To this end, a microstructure-informed modelling approach is presented, where all elements of the three-dimensional (3-d) pore structure can be controlled effectively. The results show that while density does dictate the mechanical properties of open-porous solids, the effects of the pore-wall thickness and the pore-size distribution are not negligible and must be considered while developing such materials, in particular those that exhibit a poly-disperse nature and require load-bearing capabilities under finite strains

Physics-informed constitutive modelling of hydrated biopolymer aerogel networks

Hydration induces significant structural rearrangements in biopolymer aerogels, resulting in a completely different mechanical behaviour compared to the one in the dry state. A network decomposition concept was earlier introduced to account for these changes, wherein the material network was decomposed into an open-porous aerogel one and a hydrogel-like one. Recent experimental evidences have supported this idea of the formation of a hydrogel-like network. Using these observations as a basis, in this paper, we present a micromechanical model describing the effect of hydration on the structural and mechanical properties of aerogels. The aerogel network is modelled based on the mechanics of their pore-walls, while the hydrogel-like network is modelled based on the statistical mechanics of their polymer chains by means of the Arruda–Boyce eight-chain model. The influence of diverse structural and material parameters on the mechanical behaviour is investigated. The effect of different degrees of wetting, from a pure aerogel to a pure hydrogel-like state, is captured by the model. The results are shown to be in good agreement with available experimental data

Effect of diffusive and ballistic aggregation on properties of gels

Effect of diffusive and ballistic aggregation on structural and fractal properties of gels was demonstrated in the poster

Impact of pearl-necklace-like skeleton on pore sizes and mechanical properties of porous materials: A theoretical view

The structural and mechanical properties of open-porous cellular materials are often described in terms of simple beam-based models. A common assumption in these models is that the pore walls have a constant cross section, which may be in agreement for a vast majority of such materials. However, for many of those materials that are characterized by a pearl-necklace-like network, this assumption seems too idealized. Aerogels are perfect examples of such materials. In this paper, we investigate the effect of such pore walls having a string of pearls-like morphology on the properties of such open-porous materials. First, the pore size is mathematically modeled. Three scenarios are described, where the pore sizes are calculated for cells in 2D, 3D, and 3D with overlapping particles. The dependency of the skeletal features on the resulting pore size is investigated. In the second part, pore walls with 3D overlapping spheres are modeled and subjected to axial stretching, bending, and buckling. The effect of the particle sizes and the amount of overlap between the particles on the mechanical features is simulated and illustrated. The results are also compared with models that assume a constant cross section of pore-walls. It can be observed that neglecting the corrugations arising from the pearl-necklace-like morphology in open-porous cellular materials can result in serious miscalculations of their mechanical behavior. The goal of this paper is not to quantify the bulk mechanical properties of the materials by accounting for the pearl-necklace-like morphology but rather to demonstrate the significant deviations that may arise when not accounted for

Mechanical characterization of cellulose aerogels

Due to dwindling fossil resources, biobased cellulose aerogels, whose three-dimensionally structured networks are characterized by nanoscale fibrils, have been of particular interest in recent years. They can be produced by bringing the polymer chains into solution and subsequent regeneration processes and offer the low density and thermal conductivity typical of aerogels. Their bulk properties depend on their nano and microstructure, which is influenced by their manufacturing process [1]. For practical applications of cellulose aerogels, insights into their elastic and inelastic mechanical properties are desired. To the best of our knowledge, the reports in the literature merely describe the stress-strain curves under monotonic uniaxial compressive loading [2] without exploring the inelastic features. This work aims at extending the state of the art knowhow on mechanical characterization of cellulose aerogels within this context. For this purpose, cellulose aerogels having different cellulose concentrations synthesized using ZnCl2 as solvent, salt hydrate routine [3] were subjected to an intensive mechanical characterization. This included quasi static compression and tensile tests, which for the first time allow a detailed characterization of their strain dependent elastic as well as inelastic properties. Furthermore, the results will be illustrated in the context of computational design of their microstructure with already established approaches [4] to better investigate structure property relations in the future. REFERENCES [1] Rege A, Schestakow M, Karadagli I, Ratke L, Itskov M, Micro mechanical modelling of cellulose aerogels from molten salt hydrates, Soft Matter. 12(34),7079-88, 2016. [2] Buchtova N, Pradille C, Bouvard JL, Budtova T, Mechanical properties of cellulose aerogels and cryogels, Soft Matter, 15, 7901-8, 2019. [3] Schestakow M, Karadagli I, Ratke L, Cellulose aerogels prepared from an aqueous zinc chloride salt hydrate melt, Carbohydrate Polymers, 137, 642-9, 2016. [4] Aney S, Rege A, The effect of pore sizes on the elastic behaviour of open porous cellular materials, Mathematics and Mechanics of Solids, 0(0), 2022

Insights into the Micromechanics of Organic Aerogels Based on Experimental and Modeling Results

While the characteristics of the macroscopic mechanical behavior of organic aerogels are well known, the mechanisms responsible for the substructural evolution of their networks under mechanical deformation are not fully understood. Herein, organic aerogels from the aqueous sol−gel polymerization of resorcinol with formaldehyde are first prepared. Specifically, the resorcinol to water (R:W) molar ratio is varied for obtaining diverse highly open‐cellular porous structures with mean pore sizes ranging between 30 and 50 nm. The corresponding network structures are then characterized and exhibit different morphological and mechanical properties. Furthermore, a micromechanical constitutive model based on the pore‐wall kinematics is proposed. While the arrays of particles forming the pore walls are moderately connected, the pore walls are considered to behave as solid beams under mechanical deformation. Moreover, the damage mechanisms in the pore walls that result in the network collapse are defined. All model parameters are shown to be physically derived, and their sensitivity to the macroscopic network behavior is analyzed. The model predictions are shown to be in good agreement with the experimental stress−strain data of the different aerogels

Geometric and finite element modeling of biopolymer aerogels to characterize their microstructural and mechanical properties

Biopolymer aerogels belong to a class of highly open-porous cellular materials. Their macroscopic mechanical properties (such as elasticity or thermal conductivity) depend on microstructural features (namely pore size distribution (PSD), fiber diameter and solid fraction), which can be tailored by different synthesis and drying routes. The design of modern aerogel materials requires a better perception into the microstructure and its influence on the mechanical properties. To predict the material properties using simulation, it is significant to construct a geometric model which is sufficiently precise to represent the microstructure of real materials. A tessellation approach based on Voronoi diagrams is a powerful tool to model such cellular-like materials. In this contribution, the diversified cellular morphology of aerogels is described computationally using a Voronoi tessellation-based approach [1]. Accordingly, Voronoi tessellations are generated to create periodic representative volume elements (RVEs) resembling the microstructural properties of the cellular network. Stress-strain curves resulting from finite element simulations of these RVEs and experiments of the aerogels under compression are compared. This work is an extension of our previous Voronoi tessellation-based on the 2-d description of biopolymer aerogels [2]

On the origin of power-scaling exponents in silica aerogels

The macroscopic properties of open-porous cellular materials hinge upon the microscopic skeletal architecture and features of the material. Typically, bulk material properties, viz. the elastic modulus, strength of the material, thermal conductivity, and acoustic velocity, of such porous materials are expressed in terms of power-scaling laws against their density. In particular, the relation between the elastic modulus and the density has been intensively investigated. While the Gibson and Ashby model predicts an exponent of 2 for ideally connected foam-like open-cellular solids, the exponent is found to lie between 3 and 4 for silica aerogels. In this paper, we investigate the origins of this scaling exponent. Particularly, the effect of the pearl-necklace-like skeletal features of the pore walls and that of the random spatial arrangement is extensively computationally studied. It is shown that the latter is the driving factor in dictating the scaling exponent and the rest of the features play a negligible or no role in quantifying the scaling exponent

Predictive modeling and simulation of silica aerogels by using aggregation algorithms

Silica aerogels are highly porous solids with very low densities and thermal conductivities. Their high porosity results in a fractal morphology which has a strong influence on their mechanical properties. The geometric structure of silica aerogels can be described by diffusion-limited cluster-cluster aggregation (DLCA) models. In this work, the DLCA method is implemented to model silica aerogel networks and investigate the influence of different input parameters, as for example, varying particle sizes on their fractal properties. The resulting model networks are characterized for their fractal properties and compared with the small angle X-ray scattering (SAXS) results of silica aerogels. Furthermore, their mechanical properties are simulated using the finite element method. There, the effect of varying densities on their mechanical properties is examined. In addition, an artificial neural network (ANN) is trained based on the input parameters of the DLCA algorithm to predict the fractal properties of the silica aerogel model. By inverting the ANN it is possible to identify the necessary inputs to generate desired fractal morphologies with specific mechanical properties