Computational modeling of the transition from damage to fracture in intrinsically anisotropic porous media
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The initiation and propagation of discontinuities in brittle materials is of great interest to engineers, at several scales. Discontinuities can be detrimental for structures (borehole for nuclear waste disposal, cavity for storage, tunnel for transportation) but discontinuities are necessary to extract energy (hydraulic fracturing for oil, gas and geothermal resources). A number of numerical tools are available to model fracture propagation in brittle solids. However, the fundamental inception mechanisms at the micro-scale are not fully understood. Therefore, the goal of this doctoral research work is to understand the processes that govern the initiation and propagation of micro-cracks in mixed mode in crystalline and porous media, and to predict the transition from diffused micro-crack distribution to discrete macro-fracture. We first developed two constitutive laws that couple micro-mechanics and thermodynamics principles. Phenomena observed at the scale of a Representative Elementary Volume (REV), such as nonlinear behavior, induced anisotropy and unilateral effects, are captured by modeling microstructure evolution, e.g., mixed mode propagation for open cracks and secondary wing crack development for closed cracks. Dilute homogenization is used to connect the scale of the microstructure to that of the REV. The resulting nonlocal anisotropic damage model is coupled with a cohesive zone model. The transition point from continuum damage to discrete fracture is rigorous calibrated, so as to ensure energy conservation at the scale of the entire fractured domain. We further extended the framework of damage-fracture transition to simulate multiscale fracture propagation driven by fluid injection in transversely isotropic porous media. After deriving the weak formulation and discretizing the model with the extended finite element method, we investigated the influence of material and stress anisotropy on hydraulic fracture paths. Advanced numerical methods presented in this thesis shed light on the mechanical behavior of brittle materials at several scales, and provide tools to solve practical engineering problems.