Peridynamic Modeling of Fracture Mechanism in Quasi-brittle Materials

准脆性材料斷裂機理的近場動力學研究

Student thesis: Doctoral Thesis

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Award date13 Aug 2021

Abstract

Crack is a primary threat to the safety and durability of engineering structures made of quasi-brittle materials, such as many rocks and cementitious composites. Except for experimental techniques, numerical methods have become indispensable tools to explore the failure mechanism and to predict complex crack problems with the increased computational resources. The traditional computational methods are mostly based on the classical continuum mechanics (CCM), which can be classified into two categories: cohesive zone model (CZM)-based discontinuous approaches and continuum damage model-based continuous approaches. Even though these computational methods have largely promoted the development of computational fracture mechanics, accurate prediction of complex crack problems, such as crack coalescence, bifurcation and fragmentation, is still an active challenge. The reason is that remeshing or crack tracking is required to explicitly describe cracks in the former approaches, while the latter approaches suffer from mesh-dependence which needs to be carefully avoided using different regularization methods. Peridynamics (PD) is a reformulated nonlocal version of the CCM. Instead of using partial-differential equations, the motion equation of PD is in an integro-differential form, which is valid even when cracks or discontinuities occur. Thanks to its inherent capability to capture complex crack phenomenon, PD becomes increasingly attractive in the field of computational fracture mechanics.

The primary focus in the present dissertation is the development of robust, accurate and efficient PD-based numerical method for the fracture analysis of quasi-brittle materials under mode-I and mixed mode loading conditions. Accurate damage models are proposed in the framework of PD to determine the damage initiation and damage evolution in quasi-brittle materials. Besides, both explicit and implicit implementations are performed to robustly solve the tension softening-induced physical nonlinear problems. The proposed method is validated through predicting many typical benchmark tests. Main parts of this dissertation are presented as follows.

First, a simple feasible coupling approach of PD and the finite element method (FEM) is developed to utilize the respective advantages of both two methods and at the same time avoid the respective drawbacks. The FEM nodes near the PD zone are simultaneously regarded as virtual PD particles, and PD grids are directly coupled with FEM meshes through coupling PD bonds. The proposed coupling approach is validated by comparing with FEM results and pure PD results through presenting several elastic cases and brittle fracture cases under both quasi-static and dynamic loading conditions.

Together with the proposed PD-FEM coupling approach, a peridynamics-based CZM (PD-CZM) is proposed to accurately predict mode-I dominated cohesive crack propagation problems. The proposed PD-CZM is a nonlocal CZM established in the frame of PD through introducing an objective and precise damage model based on the energy equivalence. Several numerical examples are presented to validate the proposed PD-CZM. The results show that the proposed PD-CZM can well predict mode-I failure, and it is not sensitive to the grid size. However, it becomes not accurate enough when simulating quasi-brittle fracture under shear-dominated mixed-mode loading.

Furthermore, a novel damage model is proposed in the PD-CZM to accurately predict quasi-brittle failure under quasi-static mixed-mode loading, especially shear-dominated loading. Instead of using existing bond stretch-based failure criterion, a new damage criterion obtained by combining bond stretch and dilatational bond potential is firstly proposed to determine the damage initiation. Besides, to robustly solve the physical nonlinear characteristics, especially tension softening-induced snap-back phenomenon, the robust implicit implementation of the PD-CZM is performed. Three challenging benchmarks are simulated to validate the proposed damage model robustness of the implicit implementation.

Finally, a concurrent multiscale model is proposed and established in the framework of peridynamics for accurately and effectively simulating fracture process of concrete. The proposed multiscale model consists of two sub-domains, i.e., macroscale sub-domain for linear elastic bulks and mesoscale sub-domain for damage and failure analysis. Three phases including the mortar matrix, aggregates and interfacial transition zones are considered in the mesoscale sub-domain to represent heterogeneous internal structure of concrete. A three-point bending test is predicted by the proposed multiscale model. The numerical results are in good agreement with the experimental observations. More importantly, micromechanical processes, such as crack nucleation are well captured in the proposed multiscale model.