Abstract
A micromechanical anisotropic damage model with a non-associated plastic flow rule is developed for describing the true triaxial behaviors of brittle rocks. We combine the Eshelby’s solution to the inclusion problem with the framework of irreversible thermodynamics. The main dissipative mechanisms of inelastic deformation due to the frictional sliding and damage by microcrack propagation are strongly coupled to each other. A Coulomb-type friction criterion is formulated in terms of the local stress applied onto the microcracks as the yielding function. The back-stress term contained in this local stress plays a critical role in describing the material’s hardening/softening behaviors. With a non-associated flow rule, a potential function is involved. Some analytical analysis of the non-associated micromechanical anisotropic damage model are conducted, which are useful for the model parameters calibration. The proposed model is used to simulate the laboratory tests on Westerly granite under true triaxial stresses. Comparing the numerical simulation results provided by the models with associated/non-associated plastic flow rule and experimental results, it is clear that the proposed non-associated model gives a better prediction than the previous associated model.
Highlights
Constitutive model and simulation of the mechanical behaviors of heterogeneous rocks under general stress conditions have a great significance on the investigation of the safety and stability of rock engineering
A series of researches [33,34] have shown that the crack damage stress σcd is defined as the volume compressibility dilatancy (C/D) transition stress
A new micromechanical anisotropic damage model with a nonassociated plastic flow rule has been developed for describing the true triaxial compression behaviors for brittle rocks
Summary
Constitutive model and simulation of the mechanical behaviors of heterogeneous rocks under general stress conditions have a great significance on the investigation of the safety and stability of rock engineering. In 1967, [8] firstly developed an experimental apparatus that combined torsion and triaxial compression It provided general triaxial stress states but did not produce the conditions of homogeneous triaxial stress. Geomaterials, such as rocks and concrete, display stress-induced anisotropy in their mechanical properties Considering it difficult in modeling the anisotropy, few researchers have established anisotropic theoretical models with physical meaning for simulating the true triaxial stress-strain curve of rocks. A large number of experimental and theoretical results show that a nonassociated plastic flow rule must be adopted to more accurately describe the inelastic deformation of rocks To this end, a micromechanical anisotropic damage model with a non-associated plastic flow rule will be developed, which will be used to simulate laboratory tests on Westerly granite under true triaxial stresses. The following tensorial product notations are used throughout this paper: (A ⊗ B)ijkl AijBkl, (A ⊗ B)ijkl (AikBjl + AilBjk)/2, (a ⊗ b)ij aibj, (a ⊗s b)ij (aibj + ajbi)/2
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