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In the governing equation of motion of bond‐based peridynamics, the acceleration of a material point can be considered as the response function of all the displacements of material points in the horizon and a micro stiffness containing Young's modulus and length scale. A group method of data handling (GMDH) neural network is first developed to explicitly derive the discrete bond‐based peridynamic equation of motion based on measured data in this study rather than traditional complicated mathematical derivation. In order to discover the optimal structure more efficiently and to avoid exhaustive search, genetic algorithm is incorporated into GMDH structure. It is found that the prediction results obtained by GMDH model agree well with measured values both for training and testing data. Moreover, the derived equation of motion is expressed as the product of parameter composed of Young's modulus and length scale and linear combination of displacements of material points in the horizon, which is in accordance with the original bond‐based peridynamic formulation. Furthermore, numerical benchmarks associated with elastic deformation and crack problems are performed and compared with analytical solution or finite element analysis result to verify the validity and feasibility of the proposed model. [ABSTRACT FROM AUTHOR]

• Proposing field-enriched finite element method to simulate interface crack. • Using different forms of M -Integral to calibrate stress intensity factor. • F -criterion is extended to simulate the interface crack propagation path. • Effectiveness and accuracy of the proposed method are verified. • The proposed method has a relatively simple process of implementation. In this paper, a novel numerical method called field-enriched finite element method is proposed to investigate stress intensity factor, initiation angle and propagation path of interface crack. The features of the field-enriched finite element method are: (1) re-meshing is avoided during the process of crack propagation; (2) the physical position of crack can be located and the influence of crack on the physical field of whole model can be described by enriching the field variables; (3) the fracture criterion can be flexibly embedded in the field-enriched finite element method to predict the initiation angle and propagation path of interface crack. Some numerical examples are used to verify the effectiveness and accuracy of the field-enriched finite element method. The numerical results obtained by the field-enriched finite element method can be consistent with the theoretical solution, experimental observation and other numerical results obtained by traditional finite element method or extended finite element method. Therefore, the field-enriched finite element method can provide a new scheme to deal with the interface crack fracture problems. [ABSTRACT FROM AUTHOR]

The dynamic response and mechanical behaviors of rock masses are mainly governed by discontinuities. The field-enriched finite element method is proposed to study the mechanism of crack propagation in rock mass, and the multiaxial perfectly matched layer (M-PML) is introduced to absorb the reflected wave due to the existence of artificial boundary. The fundamental theory and numerical implementation of the proposed numerical method are described in detail. By comparing two numerical models, namely one with the absorbing boundary and the other without the absorbing boundary, the necessity of considering an absorbing boundary and the ability to verify the absorption effect of the absorbing boundary on the reflected waves are demonstrated. In addition, a numerical example of underground tunnel is established to investigate the influence of dynamic waves from the hole in underground space on the crack propagation in adjacent surrounding rocks of the tunnel. Finally, a numerical model of rock slope with cracks is considered, and the influence of the combination forms of rock bridge inclination angle and fissure spacing on the crack evolution patterns of rock slope with fissures under dynamic load is studied. The research in this paper demonstrates that the dynamic field-enriched finite element method with M-PML absorbing boundary can effectively simulate the dynamic behaviors of fractured rock masses under dynamic load. [ABSTRACT FROM AUTHOR]

Cracking is an important phenomenon in the failure of geomaterials. The prediction of crack paths is difficult and challenging because of the randomness and uncertainty in the cracking behaviors of geomaterials. In this paper, to predict crack paths based on 2D X‐ray computed tomography (CT) images, a digital energy grade‐based approach is proposed, and the corresponding energy principle is established. Excellent consistency of crack paths is found between the predicted crack path and the real crack path of the specimen. The numerical results indicate that the proposed approach provides a useful way to predict cracking paths in geomaterials. Meanwhile, the stress and displacement fields before and after the specimen fails can be obtained by combining the proposed method with finite element (FE) analysis. In total, this proposed method can be applied not only to monitoring the health of but also to the stability analysis of engineering structures during engineering activities. [ABSTRACT FROM AUTHOR]

In this paper, a novel geometric method combined with the piecewise linear function method is introduced into the extended finite element method (XFEM) to determine the crack tip element and crack surface element. Then, by combining with the advanced mesh technique, a novel method is proposed to improve the modelling of crack propagation in triangular 2D structure with the XFEM. The numerical tests show that the accuracy, the convergence, and the stability of the XFEM can be improved using the proposed method. Moreover, the applicability of the conventional multiple enrichment scheme is discussed. Compared with the proposed method, the conventional multiple enrichment scheme has deficiency in mixed mode I and II crack. Finally, a comparative study shows that the performance of the XFEM by using the proposed method to model the crack propagation can be greatly improved. [ABSTRACT FROM AUTHOR]

In this paper, a novel geometrical reconstruction model is proposed for numerical simulation of pore structure in rocks. The spatial configuration and geometrical information of the microstructure are firstly gathered from Chongqing sandstone by X-ray micro-CT observations, and experimental tests on Chongqing sandstone are applied to obtain the mechanical parameters. Then, on the basis of the gathered geometrical information, the surface geometrical model is established by using the modified Marching cubes algorithm. Next, the established surface geometrical model is extended to 3D tetrahedral model by using Delaunay refinement algorithm. Finally, the 3D tetrahedral model is transformed into finite element (FE) numerical model. Moreover, the relationship between the porosity, fractal dimension of pore structure and mechanical properties of Chongqing sandstone is also investigated. The comparison of the numerical results and the experimental data shows a good consistency. [ABSTRACT FROM AUTHOR]

The rock breakage process by a single disc cutter and the ejection speed of rock fragments are simulated using three-dimensional Finite Element Method (FEM) coupled with Smoothed Particle Hydrodynamics (SPH) method in this paper. Firstly, the rock penetration process can be divided into three stages including the formation stage of crushed zone, the formation stage of micro-cracks and the propagation stage of major cracks. Then, during the rock penetration process, three different zones beneath the cutter, namely crushed zone, cracked zone and intact rock zone, can be distinguished based on the degree of cracking. Finally, the ejection speed of fragments during rock penetration process is obtained using FEM-SPH method, which is a more convenient way to study the effect of the harmful ejection of rock fragments on TBM machine. Moreover, the three-dimensional numerical results are in good agreement with experimental observations. [ABSTRACT FROM AUTHOR]

• A field-enriched finite element method is proposed to simulate cracking behaviors of brittle solids containing cracks of complex geometries. • Three different coalescence types are considered by employing reasonable strategies. • A predictor-and-corrector strategy is developed to solve the problem of competing crack growth of multiple complex cracks. • Benchmark examples containing cracks of complex geometries are performed. A field-enriched finite element method (FE-FEM) is proposed to simulate cracking behaviors of brittle solids containing cracks of complex geometries. Three different coalescence types, i.e. the coalescence of crack tip and crack tip, crack tip and crack segment, crack tip and free boundary, are considered by employing reasonable strategies. Moreover, a predictor-and-corrector algorithm is developed to solve problem of competing crack growth. Three benchmark examples containing cracks of complex geometries are performed to validate the accuracy and correctness of the proposed numerical method. Finally, the evolution of complex cracks, including a tree-shaped crack, regularly distributed intersecting cracks, and randomly distributed intersecting cracks, are simulated and investigated. All numerical results show that the proposed numerical method can effectively handle complex cracks without any special treatment around junction points. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the strength envelope of rock masses is considered to follow a non-linear unified strength criterion that considers the effect of the intermediate principal stress. A unified slip line method for resolving the differential equation system that governs the stress field is established to research the ultimate bearing capacity, which can be adapted for a wide variety of rock masses. Through this new theory, a suitable characteristic method for rock masses of interest can be obtained, and the relationships between different types of characteristic methods are revealed. The characteristic methods are based on different strength criteria, such as the Hoek–Brown criterion, modified Hoek–Brown criterion, or non-linear twin-shear strength criterion; each of these criteria is a special case of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. In terms of the proposed theory, the ultimate bearing capacity with the Hoek–Brown criterion forms the lower bound; the ultimate bearing capacity with a non-linear twin-shear strength criterion forms the upper bound; and a series of the ultimate bearing capacities ranging between these two bounds may be derived from a non-linear unified strength criterion. A comparison is made between existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. It is shown that the present results are in good agreement with existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. [Copyright &y& Elsevier]

• Field-enriched finite element method to model composite lamina fracture is proposed. • Crack growth in constant stiffness and variable stiffness composite plate is studied. • Field-enriched finite element method is easier to implement. A field-enriched finite element method for crack propagation in fiber-reinforced composite lamina without remeshing is proposed. In the field-enriched finite element method, the propagation and evolution of cracks are controlled by fracture criteria, and the physical location of cracks and the influence on the whole model are realized by the field variables enriched at the nodes. Then, field-enriched finite element method is used to investigate the influence of fiber orientation on the constant stiffness and variable stiffness composite lamina under different loading conditions and configurations. The numerical results obtained by the field-enriched finite element method are in good agreement with those obtained by experimental observation and other numerical methods. Moreover, the crack propagation path is roughly along the fiber orientation direction, which means that for the fiber reinforced composite lamina, the crack propagation path is mainly dominated by the fiber orientation rather than the configuration and loading conditions of the specimen. Compared with the phase field method, the calculation efficiency of the proposed method is higher. Compared with the extended finite element method, the proposed method is easier to characterize cracks. Therefore, the field-enriched finite element method is a very promising method for simulating the fracture behavior of fiber-reinforced composite lamina. [ABSTRACT FROM AUTHOR]

• Novel method is proposed for simulating fracture in functionally graded materials. • Remeshing, level set function and enrichment function can be avoided in novel method. • The forms of governing equation and stiffness matrix in novel method are very simple. Stress intensity factors (SIFs) and propagation paths of cracks in functionally graded materials (FGMs) are simulated by a novel numerical method called the field-enriched finite element method (FE-FEM). In this novel numerical method, the fracture criterion is used to control crack propagation, the field variables enriched on nodes are employed to represent cracks and to describe the cracks' influence on the physical fields of the model. By comparing the FE-FEM simulation results with experimental observations or other numerical results in the literature, the FE-FEM can calibrate SIFs and simulate crack propagation paths in FGMs. Remeshing, the level set function and the enrichment function can effectively be avoided in the FE-FEM. Moreover, the FE-FEM takes the same concise form of governing equations and stiffness matrix as the traditional finite element method (FEM). Therefore, the FE-FEM is a simple and effective numerical method to simulate the fracture in FGMs. [ABSTRACT FROM AUTHOR]

• Field-enriched finite element method is proposed to simulate failure in rocks. • This proposed method can select the appropriate failure criteria for voids and crack. • Effectiveness and accuracy of proposed method are verified by numerical examples. • The proposed method has a higher calculation accuracy and efficiency in some case. A field-enriched finite element method is proposed in this paper to simulate the failure process of rocks. According to the different types of defects, the proposed method can select the appropriate failure criteria for voids and cracks. Field variables are used to characterize the crack location and to realize the influence of cracks on the physical field of the numerical model. The main features and the capability of the field-enriched finite element method to efficiently simulate the failure process of rocks with different defects are illustrated with some numerical examples. The results show that the field-enriched finite element method proposed in this paper can obtain the crack propagation path which is consistent with other numerical methods and experimental observations. Moreover, the numerical method proposed in this paper has the advantages of simple implementation process and higher computational efficiency and accuracy in some cases. Therefore, it is a promising numerical simulation method. [ABSTRACT FROM AUTHOR]

• A novel linearized elastic anisotropic constitutive model is proposed for continuum-kinematics-inspired peridynamics (CPD). • For the first time, the critical stretch-based failure criteria and critical micropotential energy-based failure criteria are incorporated into CPD. • The numerical convergence of the proposed anisotropic CPD models is studied. • A 2D orthotropic CPD formulation and a 3D transversely isotropic CPD formulations are obtained. • The eight-order double Fourier series is employed to achieve the anisotropy. In this work, linearized elastic isotropic continuum-kinematics-inspired-peridynamics (CPD) is further generalized to study the elastic, damage, and fracture behavior of anisotropic continua, focusing on 3D transversely isotropic and 2D orthotropic body. The anisotropy is generated by changing the material properties, including the micromodulus, critical stretch, and critical micropotential energy of basic finite kinematic elements with their direction in the principal material axes in terms of eight-order double Fourier expansion. It is critically proven that the volumetric micromodulus of finite volume elements in the 3D case is independent of their direction, which is similarly applied to the areal micromodulus in the 2D case. For this reason, the 2D orthotropic CPD formulation characterized by three independent elastic moduli and the 3D transversely isotropic CPD formulation characterized by four independent elastic moduli are distinguished. The accuracy of the computational models applied to elastic analysis is assessed by comparing the predicted displacement fields with the results from finite element analysis. Quantitative simulation of an orthotropic lamina with a central rectangular hole under a tensile load, eccentric three-point bending test for orthotropic lamina, and compact tension test for cortical bone are performed to verify the ability of the proposed model to describe the damage and fracture behavior of anisotropic materials. [Display omitted] [ABSTRACT FROM AUTHOR]

• The node-scheme method is firstly introduced into the XFEM to solve the frictional contact crack problems. • The stress redistribution is considered in the local part of the crack surface in the proposed method. • The proposed method has the ability to solve locking problems in the numerical simulation of the frictional contact crack. In this paper, based on the nodal displacement of the crack surface element, a novel node-scheme method is proposed to model the frictional contact problem in the framework of extended finite element method (XFEM). The paper systematically illustrates the novel node-scheme including the fundamentals of the proposed method, the coupled Coulomb's friction model. The novelty of the proposed method is that the node-scheme method is first introduced into the XFEM, it can consider the stress redistribution in the local part of the crack surface, and it has the advantage of solving the locking phenomenon in the numerical simulation of the frictional contact problem. The numerical results show that the proposed method is accurate and applicable to efficiently solve the frictional contact crack problem. [ABSTRACT FROM AUTHOR]

Abstract In natural rock masses, joints or flaws usually occur in sets that are more or less parallel and regularly spaced. Many problems occurred in tunnel engineering mainly result from the failure of joints or faults because they are weaker compared with the rock matrix. Therefore, it is important to study the interaction of joints with the tunnel, as well as the interactions between themselves. In this research, rock-like specimens of non-persistent jointed rock masses containing a circular hole are prepared and tested under uniaxial compression. The test results show that the peak strength and elastic modulus of the non-persistent jointed rock specimens display a "U" type variation with respect to the joint inclination. The multiple joints can be simplified and regarded as a combination of three types of two-joints relative location, and the crack coalescence types and failure modes are in accordance with the classic crack coalescence types of the two joints. The crack coalescence between the joints and a circular hole can be categorized into three modes with respect to the joint inclination. The Discrete Element Method (DEM) model of the jointed rock specimen that contains a circular hole is established in particle flow code 2D (PFC2D). The simulation results show a good agreement with the experiment results. Furthermore, the displacement fields at the crack zones reveal that the coalescence of joints is mainly caused by tensile cracks and that shear slipping cracks easily occur at the sidewalls of the circular hole. By comparing the parallel-bond force fields in jointed models containing a circular hole with no a circular hole, it is shown that the circular hole can change the stress state at the top and bottom. The joints at a joint inclination of 90° have the smallest effect on the mechanical behavior of the rock specimen. [ABSTRACT FROM AUTHOR]