Analytical and Computational Aspects of Surface Energy-Induced Strain in Models of Porous Materials
Edward Garboczi, J E. Taylor, A P. Roberts
It has long been observed that porous materials undergoing a change in specific surface energy also undergo a volumetric strain in the direction to minimize the change in total surface energy. In the case of an increase in specific surface energy, this phenomenon has often been called Gibbs-Bangham shrinkage. This effect has not been studied as a function of microstructure, and as such forms an interesting mechanical problem. Extensive computations for isotropic porous materials (geometrically and elastically isotropic solid phase and geometrically isotropic pore phase) are reported here that indicate that the amount of induced strain depends primarily on the Young's modulus of the solid backbone, the surface energy change, and on the microstructure only via the porosity and the surface area per unit solid volume. This result is for the volumetric strain averaged over the entire object, pores and solid. What remains, after these parameters are factored out, is a simple linear function of the solid Poisson's ratio that is the same, within numerical uncertainty, for all porous models studied. This result is conjectured to be true for all such porous materials.To attempt to explain this apparently universal behavior, one can rigorously prove what appears to be a new result for solid objects (including the solid backbone in porous materials), that their average strain, induced as a result of a change in specific surface energy, depends only on the surface area per unit volume and the bulk modulus. The dependence on these quantities is the samefor any solid object, no matter what its shape. In porous materials, the average strain of the pore phase, however, does have a more complicated dependence on porosity. But when the pore space is averaged together with the solid phase, this extra dependence on porosity cancels out, giving the possibly universal result we have found for porous models.
Royal Society of London
Gibbs-Bangham, porosity, porous material, shrinkage, surface area, surface energy