A novel constitutive model for the mechanical properties of silica aerogels

Most studies on the mechanical properties of silica aerogels neglected the influence of structural randomness and dead-ends of nano-porous materials, whereas both of them have a considerable effect on the mechanical properties of silica aerogels. In this study, we propose a cubic frame model with random orientation as the representative volume element of a silica aerogel to investigate the dead-ends' effect on its mechanical properties. To characterize the structural randomness in open-cell porous materials, a new constitutive model is established by a statistical average of the mechanical response of the random structure. This constitutive model reveals the inherent isotropy of open-cell porous materials. It also indicates that the widely used Gibson-Ashby model may overestimate the Young's modulus and shear modulus for open-cell porous materials. Then the mass ratio of dead-ends and effective skeleton is derived using the available experimental results. It shows that the mass ratio of dead-ends increases with the decreasing density of silica aerogels because of the additional space resulting from the slimmer effective skeleton, which results in the abnormal exponent of the Young's modulus-density power-law relation. We suggest the mass ratio of the effective skeleton to be an intuitive and practical index to reflect the connectivity in silica aerogels. Besides, the dead-ends can significantly enhance the compressive strength of silica aerogels, especially for low-density silica aerogels. We hope this work can provide a new idea to consider the structural randomness in porous materials and give guidance on the mechanical reinforcement of aerogels.