A traditional physics approach has been used to develop a thermodynamic formalism that generalizes continuum mechanics (elasticity theory) by including a hierarchy of cracks, namely, microcracks that join up to form macroscopic cracks. Fracture processes are then derived by minimizing thermodynamic energies that are functionals of crack densities and of strains (or stresses) that vary on successively smaller scales (from macroscopic-crack down to microcrack scales). Crack densities can be treated in the formalism as state variables. A numerical application in which the crack density was postulated to be uniform leads to several specific predictions. Under fixed-grip conditions, the material may be in a metastable state with cracks at a density below that needed for percolation. Fracture is effected only at infinite elongation; the fracture stress, however, remains finite. In solids containing pores, the fracture stress is found to be an increasing function of the pore size.

• Received 13 December 1991

DOI:https://doi.org/10.1103/PhysRevB.45.10331