The studies of the elastic properties of materials with many cracks utilizing theories of composites such as the self-consistent scheme or differential scheme have been confined to the case when the cracks nei- ther grow nor shorten during loading. The…
The studies of the elastic properties of materials with many cracks utilizing theories of composites such as the self-consistent scheme or differential scheme have been confined to the case when the cracks nei- ther grow nor shorten during loading. The present paper, extending the recent ;tudies of Prat and Bafant adapts the theory of stiffness of composites to the case of incremental deformations during which the cracks can grow or shorten. Several families of cracks of different sizes, densities and orientations, characterized by the crack density tensor, are considered. The equality of the energy release rate to the fracture energy of the material is enforced only globally for all the cracks in each family. The theory yields a macroscopic stress-strain relation that appears to give qualitatively good predictions for the response of concrete in basic types of tests. Calculation results are not yet available but are planned for presentation at the conference.