The pore-size distributions play a critical role in the determination of the properties of nanoporous cellular materials like aerogels. In this paper, we propose a micromechanical model, and by further designing artificial normal pore-size distributions, we inspect their effect on the macroscopic stress-strain curves. We show that the location of the mean pore size as well as the broadness of the distribution strongly affects the overall macroscopic behavior. Moreover, we also show that by using different damage criteria within the proposed model, the elastic, inelastic, and brittle nature of the macroscopic material can be captured. The damage criteria are based on the different modes of deformation in the pore walls, namely, elastic buckling, irreversible bending and brittle collapse under compression, and combined bending and stretching under tension. The proposed model approach serves as a reverse engineering tool to develop cellular solids with desired mechanical properties.

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.

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.

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.

Mechanical properties of open-porous materials are often described by constructing a cellular network with beams of constant cross sections as the struts of the cells. Such models have been applied to describe, for example, thermal and mechanical properties of aerogels. However, in many aerogels, the pore walls or the skeletal network is better described as a pearl-necklace, in which the particles making up the network appear as a string of pearls. In this paper, we investigate the effect of neck sizes on the mechanical properties of such pore walls. We present an analytical and a numerical solution by modeling these walls as corrugated beams and study the subsequent deviations from the classical scaling theory. Additionally, a full numerical model of such pearl-necklace-like walls with concave necks of varying sizes are simulated. The results of the numerical model are shown to be in good agreement with those resulting from the computational one.

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. Graphical Abstract

The influence of the pore structure characteristics on the macroscopic mechanical properties of open‐porous cellular materials has been computationally investigated in this contribution. While the effects of the pore‐size distribution on the macroscopic mechanical response of open‐porous cellular materials have been studied previously, the investigations regarding the effects of the pore structure characteristics are relatively scarce. The pore walls of open porous cellular materials are often modelled as beams and the pore wall structure is assumed to have a constant cross section. Although this assumption is valid for a large class of materials, insights into the influence of this assumption on the calculations of the properties of those materials that exhibit a rather pearl‐necklace‐like pore wall morphology are described in this paper. On comparing the simulation results for a corrugated pore‐wall with that having a constant cross‐section, it is observed that the maximal stresses in the pore wall may differ significantly.