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• An efficiently adaptive EFG for phase-field of brittle fracture of FGMs is developed. • The adaptive criterion for phase-field model of brittle fracture of FGMs is proposed. • Fracture mechanism of FGMs is revealed using phase-field model. Gradient distributions of material properties are taken into account in phase-field model of fracture and the adaptive consistent element-free Galerkin method (EFG) for the fracture analysis of functionally graded materials (FGMs) is presented. Considering the fact that both the moving least-square approximation and the consistent integration scheme contribute to producing the accurate stress fields, the phase-field model of fracture for FGMs is numerically solved by the consistent EFG method in this paper. The corresponding adaptive criterion is established and 2D and 3D crack propagation of FGMs is simulated. Numerical results indicate that the proposed method can accurately reflect the influence of different distributions of material parameters on the crack propagation and has high efficiency compared with the standard EFG method and linear FEM. At some level, the fracture mechanism that crack propagation is driven by both the strain energy history and the critical energy release rate is revealed using phase-field model. [ABSTRACT FROM AUTHOR]

• This paper presents a model to reveal the heat transfer mechanism and simulate the heat-flow coupling process in fractured rock masses. • The effects of fracture density and diameter on percolation probability are studied based on Monte-Carlo tests with each group for 10,000 times. • The effects of fracture density, roughness, and percolation of fracture network on heat-flow coupling in hot rock masses with embedded three-dimensional fracture network are studied. This paper presents a model to reveal the heat transfer mechanism and simulate the heat-flow coupling process in fractured rock masses. Specifically, effects of fracture density, roughness, and percolation on heat-flow coupling are investigated systematically. The fractured rock masses are composed of a discrete fracture network and a rock matrix. Regarding the mesh discretisation for finite element analysis, the rock matrix is discretised into three-dimensional (3D) solid elements, whereas the discrete fractures are modelled by zero-thickness elements. Fracture and matrix elements share the same nodes. Considering the effect of temperature on fluid density and dynamic viscosity, a heat-flow coupled model of fractured rock masses is established with an embedded 3D fracture network. The reliability of the model is verified by comparing it with the analytical solution of a two-dimensional single-fracture heat-flow coupling problem. The effects of fracture density and diameter on percolation probability are studied based on Monte-Carlo tests with each group for 10,000 times. Finally, numerical samples of the 3D discrete fracture network with different geometric parameters are generated to characterise fractured rock masses, and heat-flow coupling numerical simulation is conducted simultaneously. Results show that the percolation of the fracture network is the decisive factor affecting heat-flow coupling. The average outlet flow rate of the percolation network under the same fracture density is much larger than that of the nonpercolation fracture network, which results in a more rapid decrease in the outlet temperature. Other factors such as fracture roughness are also investigated. It is discovered that the effect of fracture roughness on heat-flow coupling is almost negligible for the nonpercolation fracture network model. [ABSTRACT FROM AUTHOR]

• Adaptive finite element method for hybrid phase-field model of 3D cracks is present. • Efficient and robust modelling of complex crack propagation in 3D is achieved. • Industrial application is demonstrated by modelling fracture of a turbine blade. Phase-field modeling of cracks in three dimensions (3D) is challenging due to expensive computational efforts caused by inefficient solution of non-linear governing equations as well as the requirement of extremely fine mesh for crack resolution. In this paper, a combination technique aiming at these two issues is presented. Firstly, a hybrid phase-field model is implemented in 3D with a simple and robust one-pass staggered solution scheme, yielding a linear system of governing equations which can be solved efficiently. Secondly, adaptive mesh refinement using the predictor-corrector algorithm is developed such that this hybrid model can be solved with minimal number of nodes. Numerical results show that computational cost of 3D phase-field modeling is dramatically reduced and complex crack events including initiation, mixed mode propagation, non-planar extension and twisting can be efficiently modeled with preferable robustness. Perfect agreement between numerical and experimental results on crack paths and application of the proposed method to the fracture of complicated engineering structures are demonstrated. [ABSTRACT FROM AUTHOR]

• Nonhomogeneous poisson distribution and annealing arithmetic was used to realize the clustering phenomenon of fractures. • The support-based connection was used to reduce the uncertainty errors caused by the lack of data. • Optimization of connectivity evaluation by considering the correlation between fracture parameters. • The potential seepage path can be predicted by this extended method, which is important for engineering applications. Connectivity evaluation of fracture networks is important in the design, assessment, and development of reservoirs in various engineering applications involving geothermal exploitation and the petroleum industry. By employing nonhomogeneous Poisson distribution and annealing arithmetic, this study generates fracture networks that fit well with actual outcrop fracture data. Based on Allard's definition of the connectivity index, a weighted factor is introduced, and an extended connectivity evaluation method is proposed to consider the effects of the aperture and its correlation with trace length. The results of the analysis show that the extended method improves the accuracy and reliability of connectivity evaluation compared with the traditional method. Moreover, the extended method is effective and accurate at predicting potential preferential flow paths in a practical example of the Dragon and Tiger Mountain (Jiangxi, China), and can better show the anisotropy with a change in the aperture. Hence, the proposed method extends the function of connectivity analysis and can benefit well location optimization in geothermal or petroleum exploration. [ABSTRACT FROM AUTHOR]