Inelastic Effects of Microcracking: A New Continuum Damage Model

Microcracking is an important mechanism of damage accumulation in stressed solids. Two contributions to deformation can be distinguished: modification of the bulk effective elastic behaviour as cracks are introduced; and accumulation of an inelastic offset for each crack on formation. Equivalent medium approximations consider the former. In this study we have developed a new formulation to model the latter. The change in strain energy at the instant of formation of each individual microcrack is used to calculate the incremental inelastic strain increase during monotonic loading. This leads to integral equations describing the damage state, in which stress and strain are functions of damage. The macroscopic behaviour is path dependent. We obtain an explicit form of the stress-strain relation as a function of both intrinsic and extrinsic variables (damage and loading history) in order to test the model using experimental data for uniaxial tests on rock samples. Quantitative damage estimation is made through monitoring acoustic emissions emitted as microcracks form, which are related to crack dimensions through an independently determined scaling relation. The new model successfully reproduces the experimental stress-strain behaviour through failure, and also allows secondary effects, such as residual strain or hysteresis to be modelled, which is not possible with the equivalent elastic medium approach. The results suggest that (a) the incremental damage approach is needed to fully model behaviour in compression; (b) inelastic effects arising from cracking must be considered as well as modifications to the sample stiffness; and (c) acoustic emission parameters can be used in quantitative modelling of inelastic behaviour of cracked solids.