A Micromechanical Damage Model For Rocks And Concretes Based On The Deformation And Growth Of Elliptic Microcracks

The micromechanical damage models based on the deformation and growth of microdefects can realistically describe the development of damage, and received extensive attention in past decades. Rocks and concretes contain numerous microcracks, and the deformation and growth of microcracks play important roles in their constitutive behavior and should be included in the description of the deformation such kinds of materials. Microcracks open under tensile stress, and close under compressive stress, the research of the deformation and growth of microcracks as well as their effect should, therefore, take into account the influence of different states of stress. The microcracks in materials can generally be assumed to be elliptic, which can describe more exactly the properties of a microcracks system. In this dissertation, the influence of the deformation, growth, frictional sliding, and kinked growth of microcracks embedded in an infinite isotropic elastic matrix subjected to different stress states on the compliance on the materials are investigated, and then a unified three dimensional micromechanical damage model for the solids with randomly distributed microcracks is formulated with the Taylor's scheme.Based on the analysis of the deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, the energy release rate of the elliptic crack and a mixed fracture criterion are obtained by making use of an energy balance approach. Considering the kinked growth of the crack, an analytical approach for the determination of the initial kink location and kink direction of the elliptic crack are suggested. The results corresponding to penny shaped crack and penetrated line crack can be obtained from the proposed model as the special cases of its two limits. The comparison with the results from finite element analysis also verifies the proposed approach.The deformation and growth of an elliptic microcrack under far-field tensile-shear stress are considered, and the corresponding additional compliance tensor is derived. The description for the response of the material with randomly oriented elliptic microcracks under triaxial tensile stress is obtained by making use of the Taylor's scheme and an appropriate probability density function, and the effective moduli are deduced.The frictional sliding and kinked growth of an elliptic microcrack embedded in a representative volume element under triaxial compressive stress are investigated. The additional compliance tensor induced by a single closed elliptic microcrack is derived. A simplified method to calculate the kinked deformation of the closed elliptic microcrack is suggested. The description for the response of a microcracks solid under triaxial compressive stress is obtained with the Taylor's scheme, and the anisotropic property of the microcracks material is analyzed.A unified micromechanical damage model is constructed with the combination of the obtained triaxially tensile stress model and triaxially compressive stress model. Associated with commercially available finite element code ABAQUS, a user subroutine UMAT for the materials with randomly orientedly elliptic microcracks is developed and embedded in ABAQUS. The triaxial compression of sandstone and the uniaxial tension of a concrete is simulated and compared with the experimental results.The effect of the interaction between the elliptic microcracks on the elastic properties of the microcracked materials is considered. The effective elastic moduli of the material with random orientation of elliptic microcracks are obtained, and the comparison with those obtained with energy equivalent principle based on self-consistent scheme shows completely identical.