Study On Fracture Modeling Of Heterogeneous Quasi-brittle Materials Based On The Cohesive Crack Model

As a typical kind of quasi-brittle material, the concrete has relatively low tensile strength and instant softening response as well as random strength distribution due to the multi-scaled heterogeneity. The research on its fracture modeling is necessary for understanding the mechanism of crack initiation and propagation in quasi-brittle materials. The fracture modeling in heterogeneous materials was thoroughly reviewed, focused on the constitution of crack model and the algorithm of random fields. After an overall comparison among the present numerical models, a new method based on the cohesive zone model was proposed. In the proposed method, an auto-correlated random field was adopted to represent the spatial distribution of mechanical properties with an in-house algorithm to insert the cohesive elements into the boundaries of solid elements and another one to map the samples of random properties, i.e. the tensile strength, to cohesive elements.A two-dimensional concrete specimen under uni-axial tensile was firstly modeled with attentions on the effects of element type, mesh-dependence, crack surface characteristics and solvers of nonlinear equation. A few series of Monte Carlo Simulations (MCSs) of two-dimensional fracture modeling were then conducted. After verification of the convergence of the MCSs’results, the effects of variance and characteristic length in the random field on the structure’s carrying capacity were analyzed and the applications of the MCSs’results on reliability design and calculation of characteristic material strength were introduced. The method was then extended to three-dimension. Some static and dynamic fracture examples with deterministic material properties were carried on. Their numerical results were compared with experimental data or those from other numerical models. The same concrete specimen was modeled again in the context of three-dimensional methods and compared to the two-dimensional results. Finally, a Fiber Reinforced Concrete (FRC) model was introduced based on the proposed concrete model and adopted to simulate the fracture of FRC as well as some parametric study.The study shows that, the proposed method predicted the tortuous cracks with random spatial location in concrete; the carrying capacity decreases as the variance or characteristic length of random field of tensile strength increases; the three-dimensional model predicts higher carrying capacity than the two-dimensional model due to the interaction between the materials in thickness direction; the proposed method was proven to suit for static and dynamic modeling in complex structure as the numerical results agreed well with the experimental or numerical results in other references with little mesh-dependence; the proposed method, fulfilled in the context of a general-purposed finite element analysis package, provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength; the proposed FRC model predicts good loading-displacement curves compared to experimental data, and the comprehensive parametric study provides theoretical guide for improvement on FRC performance.