Nonlocality of continuum approximation of microcracked materials

A continuum with nonlocal damage has recently been shown to be an effective approach for the analysis of strain-softening structures. The basic idea is that only the damage, normally caused by microcracking, is nonlocal, being a function of the averaged strain, while the strain and stress are local continuum properties. Physical justification by micromechanics, however, has been rather limited. In a recent study, it was suggested that the physical source of nonlocality of damage is the fact that the formation and growth of a microcrack depends on the strain energy stored in a nonzero volume of the material surrounding the microcrack, whose release drives the growth of the microcrack. This argument was developed only for a rather idealized, easily tractable case - a uniaxial stress field, a quasiperiodic array of small cracks arranged on a cubic lattice, and neglect of crack interactions. The present presentation shows an improved version of this arguments, as well as another argument that is based on interactions among microcracks.