Extended cubic fracture model for porous materials and the dependence of the fracture toughness on the pore size

The 3D-model published in the recent paper “A geometric model for the fracture toughness of porous materials” by Jelitto/Schneider (2018) is extended for the case of closed porosity with low density, like in polymer foams. At constant porosity, this model predicts the fracture toughness to be independent of the pore size. On the other hand, the well-known model of Ashby and Gibson yields a slight dependence on the pore size, which is discussed in detail. After investigating the mathematical derivation, it seems that their normalization of the fracture toughness needs to be reconsidered, resulting in a removal of the scale-dependence.