Fracture in concrete due to percolating cracks and pores

The standard (Griffith) criterion for crack growth is reformulated by consideration of a crack population present in a medium containing voids (pores). The crack density is the “order parameter” in the free energy, which consists of the total crack surface energy, the relaxed stress energy and the entropy. Percolation theory (for discrete and continuous media) is used to express these energies as functions of the crack density. Minimization of the free energy yields the critical stress for fracture, taking account of the total porosity in the multi-phase material and of the microstructure of the pores. A non-linear, temperature dependent R-curve is derived from first principles. Applications are made to concrete and ceramics.