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• Novel OSB-PD model considering large deformation is proposed. • Drucker-Prager criterion is included in the novel OSB-PD model. • Plastic and damage behaviors under large deformation are captured precisely. In this paper, an ordinary state-based peridynamic (OSB-PD) plastic model is proposed to simulate the large deformation of geomaterials. The PD dilatation, which is equivalent to the volumetric strain in terms of the logarithmic strain in classical continuum mechanics (CCM), is proposed. The PD material parameters are obtained by equaling the assumed PD energy density to the energy density in terms of the Kirchhoff stress and logarithmic strain in CCM. The PD force, which is obtained by calculating the Frechet derivative of PD energy density, is naturally collinear with the deformed bond. The OSB-PD plastic model with the Drucker-Prager criterion considering geometric nonlinearity is subsequently established. Benchmark problems including the plate under large deformation and the l -shaped panel test are simulated, which has verified the proposed model. [ABSTRACT FROM AUTHOR]

• Non-uniform discretization peridynamic method is proposed to investigate cracking behavior. • A novel volume correction method is proposed to eliminate unbalance force. • The force loading condition is modified to replace the displacement loading. • The relationship between the material points discretization form and cracking behavior is defined. The proposed non-uniform discretization peridynamics reduces computational costs. Cracking behavior investigation is very important in solid mechanics. In this study, a non-uniform discretization bond-based peridynamic (NUD-BBPD) method is proposed to investigate the cracking behavior, in which the new volume correction method for regenerative family material points is proposed based on Monte Carlo statistical approach. When computational domain non-uniform discretization (NUD) is employed, the proposed method eliminates the need to use the variational horizon, and naturally solves the issue of unbalanced force in NUD. Additionally, the force loading condition is revised based on the energy conservation in the proposed method. This revision eliminates the need for fictitious material points when the displacement loading condition is used in simulation, and the drawback of the conventional force loading condition, in which the force is constrained, is also solved. The proposed method is then used to analyze the static and dynamic fractures of solids. The effects of the material points arrangement on the cracking behavior are obtained via a comprehensive comparison, and the numerical results obtained by the proposed method are in good agreement with those obtained by the conventional uniform discretizational peridynamics. Moreover, NUD peridynamics with constant horizon has higher computational efficiency than traditional peridynamics. [ABSTRACT FROM AUTHOR]

• A novel kinematic-constraint-inspired bond-associated non-ordinary state-based peridynamics is proposed. • The linear and angular momentum conservation is firstly and rigorously proved. • The ability of the proposed model to prevent unphysical deformation is analytically characterized. • Bond-associated stress state-based failure criteria are proposed for fracture analysis. • The advantage of the proposed model over other existing control methods is discussed. The non-ordinary state-based peridynamics (NOSBPD) is attractive because of its ability to incorporate available constitutive models. However, conventional NOSBPD suffers from numerical oscillation induced by zero-energy mode. Although the recently proposed bond-associated deformation gradient performs well with controlling the issues, the size of the bond-associated horizon is undetermined. The work is aimed to introduce kinematic constraints to redefine the classical bond-associated deformation gradient. Based on the kinematic constraints imposed by the symmetry of the bond-associated deformation gradient and non-local kinematic measures, a well-defined bond-associated horizon is derived for 1D, 2D, and 3D structures. In this way, a novel kinematic-constraint-inspired non-ordinary state-based peridynamics (KC-NOSBPD) is proposed, which completely differs from the previous continuum-kinematics-inspired peridynamics (CPD) extended from classical bond-based peridynamics (BBPD). The linear and angular momentum conservation is firstly and rigorously proved. The novel proposed model is proved capable of avoiding unphysical deformation modes that typically beset conventional formulation through several analytical examples. In addition, bond-associated stress-state-based failure criteria are proposed for fracture analysis. Several benchmarking tests verify the effectiveness of the proposed formulation in eliminating spurious oscillation of numerical solution and highlight the significance of kinematic constraints. The final crack pattern of sandstone specimens coincides with experimental observation, illustrating its suitability for solving crack propagation. [ABSTRACT FROM AUTHOR]

• A MPNN based graph network is proposed to learn the rules of the physical system behind the data. • The pre-trained model has the ability of forward prediction by considering the predicted value as input. • The crack propagation prediction under loading condition is realized by introducing edge updating module. In this paper, the message passage neural networks (MPNN) based graph networks is proposed for learning and prediction of boundary loading problem in solid mechanics. As a learnable physics engine, the proposed model is designed to learn from historical data to understand the rules of the physical system behind the data, and then to make predictions. By learning the historical displacement field sampling data of 2D intact plate, the proposed model successfully realizes its continuous displacement field prediction. On this basis, the trained model also achieves a good prediction in a plate containing holes under the same loading condition but without training, which verifies the generalization ability of the proposed model. Finally, the crack propagation can be realized by learning the historical data of the plate with prefabricated cracks subjected to tension, which shows the excellent predict ability and exciting prospect 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 traditional general particle dynamics (GPD) has been successfully applied in modeling fracture propagation, frictional contact and stick–slip problems in rocks. In this study, the updated Lagrangian nonlocal general particle dynamics (UL-NGPD) method is proposed to solve large deformation problems. In the UL-NGPD, the continuity equation and momentum equation are reformulated in the integro-differential formulation by introducing nonlocal theories in the updated Lagrangian framework. The artificial viscosity and artificial force state are utilized to enhance the numerical stability and accuracy in modeling large deformation. The nonlocal velocity gradient in the deformed configuration is used to update the Cauchy stress rate from the Drucker-Prager elasto-plastic constitutive model with strain-softening behaviour for solids. The UL-NGPD paradigm is numerically implemented through an explicit Predictor-Corrector scheme for high-performance computing. The stability and accuracy of the UL-NGPD are verified by numerical tests on compression test, slope stability analysis and aluminum bar collapse experiment. Thereafter, simulations of granular soil collapse and retrogressive landslide in sensitive clays are presented to demonstrate its efficacy and robustness in modeling challenging geotechnical problems involving large deformation. The numerical results show that the proposed UL-NGPD is powerful and suitable for analyzing large deformation problems in geotechnical engineering. [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]

For a full understanding of the cracking processes in granite, uniaxial compression tests are conducted on prismatic specimens with pre-existing flaws, and digital imaging and AE techniques are applied to monitor real-time rupture behaviors. The digital image correlation (DIC) method is used to detect the process zone nucleation characteristics in granite. A novel approach for representing AE data in terms of the inter-event time (IET) function F (τ) is employed to analyze fracture-related AE event rate characteristics. Based on the coupled analyses of the acousto-optic-mechanical characteristics, the complete cracking processes of granite are classified into six levels, which are distinguishable by five characteristic stresses. Process zone nucleation, which represents the clustering of micro-cracks, is incorporated into the classification for the first time. Process zone nucleation is visualized as a white patch and is either linear or diffuse. By DIC analysis, the maximum principal strain field reliably predicts a linear white patch, and the maximum shear strain field implies a diffuse white patch. The evolutionary rules of the IET function F (τ) strongly support the new classification of cracking levels in granite. For the identification of stress thresholds and cracking levels, a combined acousto-optic-mechanical methodology is established, in which the role of the IET function F (τ) is highlighted. • Acousto-optic-mechanical characteristics are analyzed in a coupled way to study the cracking process of granite. • Process zone nucleation is incorporated into the classification of cracking levels for the first time. • The DIC method is used to evaluate the process zone nucleation characteristics. • The inter-event time function F (τ) is first applied to identify the cracking processes of granite. • The combined acousto-optic-mechanical methodology is established to identify stress thresholds. [ABSTRACT FROM AUTHOR]