To provide a more realistic and comprehensive description of the explosion process, this paper proposes a unified framework for modeling the explosion response of materials and structures using the coupled Lagrangian and Eulerian peridynamics. The primary contribution of this work lies in its ability to comprehensively model explosive detonation, propagation of explosive gas, interaction between gas and solid, and induced explosive failure of the solid within the unified framework. Specifically, the Lagrangian peridynamics is employed for the modeling of the solid, while the Eulerian peridynamics is utilized for the gas. Effective coupling between the solid and gas phases is also established within this framework, ensuring rational gas–solid interactions during the explosion process. Additionally, to address the issues of clustering and cavitation that arise from the intense motion of gas points, a displacement correction strategy is implemented for the gas phase. Furthermore, a GPU-accelerated algorithm is developed and integrated into the framework, significantly enhancing the numerical efficiency and scalability. The effectiveness of the proposed model and framework is validated through several typical examples, including the detonation propagation in a one-dimensional TNT slab, propagation of the explosive gas of a two-dimensional disk, and interactions between gas and solid, as well as the solid explosive failure in concrete explosive tests. The presented work offers a promising alternative for further in-depth investigation of explosive problems across diverse scenarios.

Fluid-structure interaction (FSI) involving structural damage and fracture is central to many engineering problems, yet remains difficult for numerical modeling because large free-surface deformation, moving fluid-solid interfaces, and spontaneous crack growth must be resolved simultaneously. This work develops the energy-robust Eulerian-Lagrangian peridynamics for FSI problems involving dynamic fracture, with emphasis on the treatment of internal energy under high-velocity impact. A dual internal energy description is introduced that maintains two independent energy evolution pathways simultaneously. One tracks total energy in conservative form, and the other directly evolves the thermodynamic internal energy through the pressure-work term. The internal energy used in the equation of state is then selected adaptively based on the local ratio of kinetic to thermal energy. In high-velocity regions, the directly evolved internal energy is preferentially employed to eliminate cancellation errors; in low-velocity regions, the conservative pathway is recovered to ensure thermodynamic consistency. The artificial viscosity is also reformulated to prevent excessive dissipation at high impact velocities. The proposed model is validated against a series of representative benchmark examples. In such cases, the present predictions are in good agreement with experimental observations and reference numerical results, demonstrating both the accuracy and the broad applicability of the proposed dual-energy peridynamic framework. Moreover, the model is further applied to pre-cracked rock subjected to a high-velocity water jet, investigating the effect of the notch size on the failure behavior of rock.

This study presents a reformulated Gurson-type peridynamic model for the numerical simulation of ductile fracture in high-strength metallic materials. The approach is built within a non-ordinary state-based peridynamics framework and tightly couples the Gurson–Tvergaard–Needleman (GTN) model at the bond level. Specifically, the proposed model directly couples porosity-driven softening with bond degradation based on microscopic damage mechanisms. Then, void-controlled plasticity is embedded into peridynamics, and a bond-level two-way coupling between yield behavior and damage is achieved. Meanwhile, the fracture criterion based on the GTN void volume fraction is established as well, effectively connecting the evolution of microscopic damage with macroscopic fracture behavior, from cavity initiation and growth to crack initiation and propagation. The methodology is validated against several typical examples, illustrating its effectiveness and capacity for tensile, shear, compressive, and impact problems. Overall, the proposed model offers a numerically unified and stable framework for ductile fracture in high-strength metals across diverse stress states and dynamic loading scenarios.

Multiferroic materials exhibit coexisting piezoelectric, piezomagnetic, and magnetoelectric couplings, enabling interactions among mechanical, electric, and magnetic fields. To accurately analyze the fracture and failure characteristics of multiferroic materials under complex multi-fields, especially when subjected to dynamic loadings, this paper presents the electro-magneto-mechanical coupling peridynamic model. The theoretical framework establishes nonlocal gradient operators for electric and magnetic fields, and derives constitutive relations for stress, electric displacement, and magnetic induction. An energy-based fracture criterion is proposed and implemented as well. Moreover, a block Gauss-Seidel iterative algorithm with diffusion smoothing is developed to solve the strongly coupled electromagnetic field equations. Through a series of systematic numerical simulations, the complicated interplay between the electromagnetic coupling field and the crack initiation and propagation for multiferroic materials is significantly investigated. We find that the electromagnetic coupling responses of multiferroic materials are not a simple superposition of the isolated electric-field and magnetic-field effects. Meanwhile, the effects of positive versus negative electromagnetic fields on the mechanical response are approximately antisymmetric and largely cancel when averaged. The framework developed herein is beneficial to provide new insights into intelligent structural design and the controlled fracture behavior of multiferroic materials.

The computational cost of peridynamics has historically limited its use to small-scale problems, despite its conceptual appeal for fracture modeling and failure analysis. This work introduces a revised peridynamic integration paradigm that enables high-fidelity simulations using substantially fewer integration points while maintaining accuracy. The key observation is that conventional peridynamic volume integration can be reformulated as two separable components, radial and angular, allowing independent numerical treatment of each. Building on this decoupling, we propose a peridynamic integration framework that couples Gauss- quadrature in the radial direction with Lebedev spherical quadrature for angular integration (PD-GL). This reformulation yields three main advances: (i) systematic reduction of integration points via structured projection algorithms, (ii) removal of repeated neighbor-search overhead through spatial hashing, and (iii) retention of high accuracy even for small horizons delta = 2 Delta x , where conventional peridynamics typically deteriorates. Across a range of horizon sizes ( delta = 2 Delta x to 4 Delta x ), PD-GL achieves more than a sevenfold speedup relative to standard implementations, with the advantage increasing as the horizon grows. By integrating multiple established acceleration strategies into a single unified scheme, PD-GL addresses the primary computational bottlenecks of peridynamic simulations and facilitates practical, high-fidelity fracture and failure modeling in engineering applications.

To investigate the ricochet phenomenon and failure characteristics for PMMA (Polymethyl-methacrylate) plates subjected to oblique penetration, an improved peridynamic contact model is proposed in this study. The proposed model incorporates the dynamic friction coefficient and shank friction force, complemented by a hybrid contact search strategy that combines grid search and KD-tree methods to enhance computational efficiency. To validate the model and approach, numerical simulations for the oblique impact tests on PMMA are conducted, where the peridynamic results have a satisfactory agreement with the corresponding experimental data. The ricochet phenomenon is accurately reproduced in the peridynamic simulations, underscoring that the proposed model and approach have the capability to effectively capture the intricate failure characteristics in PMMA under oblique penetration. Additionally, a systematic analysis is performed to investigate the influence of critical parameters, including the incidence angle, initial velocity, and attack angle, on the overall oblique penetration performance. These findings highlight the robustness and practical applicability of the proposed model and approach in predicting and analyzing intricate failure responses in PMMA under dynamic loading conditions.

Matrix cracks, serving as oxygen diffusion channels, are inevitable in Carbon/Silicon Carbide (C/SiC) ceramic matrix composites (CMCs). These cracks accelerate the oxidation of carbon reinforcements, significantly degrading the material’s mechanical performance under mechano-oxygenic coupling conditions. Applicable for addressing discontinuous mechanical problems induced by crack and oxidation, a peridynamic model on mechano-oxygenic coupling failures of CMCs is proposed. Notably, the competition between oxygen diffusion and reaction is incorporated, providing a unified description of the oxidation process governed by varying kinetics. Furthermore, a peridynamic simulation framework is established enabling simultaneous mechanical and oxidation analysis numerically. Model validation is performed via the proposed framework, including oxidation kinetics and mechano-oxygenic coupling responses. The model captures the linear recession process controlled by reaction and the parabolic recession process governed by diffusion under varying conditions. Additionally, the model successfully predicts the stress-oxidation behaviors of CMCs, with predictions corroborated by experimental data in terms of oxidation morphologies and mechanical degradation trends. Compared to existing simulation approaches, the proposed method, enabling both 2D and 3D analysis, offers more intuitive insights into the mechano-oxygenic coupling failure process. That will enhance the understanding of CMCs’ failure mechanisms and provide a promising tool for evaluating their mechanical performance in extreme environments.

The integrity of shrouds on turbine blades is essential for stable operations of turbines. But fatigue fractures can exist because of stress concentrations introduced by shroud flexure if insufficiently constrained. To address that, a blade-shroud-like structure is designed and tested to replicate failure process. Then, a peridynamic fatigue analysis method towards complex structures with irregular nonuniform discretization is proposed and adopted to the designed structure, also its variants. The method provides good predictions on structural fatigue failures, also accurate estimates of fatigue lifetimes. Such work provides connections between complex structures and peridynamics, making related engineering application forward.

To achieve a balance between computational efficiency and accuracy in the fracture and failure analyses of steel fiber reinforced concrete (SFRC) within the peridynamic framework, this study introduces a novel intermediately homogenized peridynamic model. The proposed model effectively links the mesoscale composition of SFRC with its macroscale fracture behavior by incorporating the steel fiber, matrix, and fiber-matrix interface, without incurring significant computational costs. Notably, the true volume fractions of steel fibers and fiber-matrix interface are accurately determined through fully discrete modeling, avoiding pseudo-interface errors caused by interfacial overlapping. A statistical method for the bond ratio of different phases based on Monte Carlo random sampling is employed for numerical implementation of the proposed intermediately homogenized model, eliminating inaccuracies arising from artificial interface overlaps while maintaining computational fidelity. The presented model is applied to several representative numerical examples of SFRC, including estimating the effective Young's modulus of SFRC and analyzing the quasi-static fracture and impact failure of SFRC. The peridynamic results are in great agreement with corresponding experimental data, demonstrating the proposed model's effectiveness.

This paper presents an innovative methodology that seamlessly integrates the peridynamic method with advanced deep learning techniques, specifically utilizing the Gated Recurrent Unit (GRU) neural network. This integration results in the development of a highly accurate and efficient model for predicting fatigue cracking and life. This model can effectively forecast the fatigue crack patterns and fatigue life, effectively addressing the limitations of existing data- driven models, which often struggle with accurately predicting fatigue crack growth. One of the key advancements of this study is the significant enhancement in numerical efficiency, reducing the computational cost to mere hundreds of seconds, a substantial improvement over traditional peridynamic simulations. The study begins by establishing a peridynamic fatigue damage model, which is used to generate a comprehensive dataset of mechanical behavior under fatigue loading. A strategy is developed to convert the mechanical data into a suitable format for deep learning, which enables the creation of well-structured training and testing datasets. The Peridynamic-Gated Recurrent Unit (PD-GRU) data-driven model is then proposed, demonstrating exceptional numerical performance and operational efficiency. Through a series of rigorous numerical analyses, the PD-GRU model's capabilities are validated, highlighting its potential as an innovative perspective and groundbreaking tool in the fatigue analysis of materials and structures.

The fatigue failure process is significantly accelerated in the presence of corrosion, a phenomenon widely observed in engineering practice. Accurately predicting the corrosion fatigue behaviours of materials remains challenging owing to the limited knowledge of the synergic effects of corrosion and fatigue loads. This paper proposes a new peridynamic simulation method to analyze corrosion fatigue problems based on authors' previous work, which considers mechanochemical effects to exhibit coupling between corrosion and material deformations. To validate the reasonability of the proposed method, corrosion fatigue tests on an iron-based (Febased) alloy are conducted to acquire experimental benchmarks. Then, numerical simulations based on the proposed method are conducted, whose results are compared with testing results, also simulation results obtained by previous simulation method. The proposed method not only provides accurate predictions on corrosion fatigue properties (the simulated fatigue limit is 249 MPa, the same with the tested one), but also increases accuracy on lifetime predictions by 66 % compared with authors' previous work. The proposed method not only provides a unified simulation method in dealing with complex mechanical problems considering both continuity and discontinuity, such as corrosion fatigue, but also provides good accuracy in predictions of corrosion fatigue properties, making such method both theoretical-meaningful and engineering-practical.

It is necessary to determine the input features and output results when constructing a surrogate model within the data-driven neural network. Since the law of features would be restrained when the surrogate mechanical model is employed, it is still a challenge to build a set of natural features to accurately describe the failure process of materials and structures within the traditional continuum mechanics framework. To address this challenge, a robust approach for constructing a surrogate model within the peridynamic-deep learning framework is proposed in this study, which is capable of representing material deformation and failure explicitly. The presented surrogate model integrates both reference and current configuration data to refine input features, enhancing model training. We incorporate a batch-normalization layer before the activation function to mitigate common issues such as slow convergence, low prediction accuracy, and overfitting due to the large numerical differences in the damage dataset. Additionally, numerical analyses on several typical examples are performed to validate the effectiveness and generality of the present model and methodology. The results demonstrate high accuracy in the training set as well as the testing set, confirming the model’s excellent generalization ability and significant potential for material failure analysis. According to this work, more peridynamic expressions can be further derived in the machine-learning-based peridynamic surrogate model by considering the reinforcement learning and symbol space, to potentially broaden its applicability to a wider range of mechanical issues.

A general three-dimensional anisotropic model is proposed within the non-ordinary state-based peridynamic framework in this work. Three-dimensional peridynamic formulations for anisotropic solids are formulated, and two types of stress rate solutions, Green-Naghdi and Jaumann stress rate are implemented in this model, respectively. Moreover, the equivalent bond stress and corresponding equivalent bond strain are presented and calculated. The 3D-Hashin failure criterion is used among the numerical analysis of anisotropic materials through the equivalent bond strain. Various typical cases are performed by the proposed anisotropic peridynamic model and approach, including the numerical analyses of quasi-static deformation and dynamic fracture for anisotropic materials. The effectiveness and applicability of the proposed model are verified by precisely characterizing the quasi-static deformation and dynamic failure behavior.

A coupling model of peridynamics and finite element method is proposed to study the interfacial delamination influenced by vertical crack density in thermal barrier coating (TBC) systems. Specifically, the progressive failure progress under static and fatigue loads in TBCs, including vertical cracks propagation, the evolution of vertical cracks to interfacial cracks, and interfacial delamination, is simulated by the proposed model. The difference between static failure mechanism and fatigue failure mechanism of TBCs is numerically elucidated. The simulated fracture morphology is in good agreement with the experiential observation. In both static and fatigue loads, a higher vertical crack density is found to correspond to a shorter delamination length, and there is no interfacial delamination when the vertical crack density is high enough. The results provide important insight of vertical crack density on interfacial delamination, and the durability of TBCs can be enhanced by ensuring an appropriately high vertical crack density.

Forced convection heat transfer occurs inside the steam turbine, and it is crucial for thermal and strength analysis to accurately estimate the convection heat transfer coefficients of the turbine rotor. This paper presents a hyper- reduced-order model for efficiently estimating the forced convection heat transfer coefficients of a steam turbine rotor. Unlike the full-order finite element method, the hyper-reduced-order model uses the discrete empirical interpolation method to approximate the domain integration of transient heat conduction simulations. This approach greatly reduces the degrees of freedom of numerical integration, thus substantially improving the computational efficiency of forward heat conduction problems. The hyper-reduced-order model and Levenberg-Marquardt algorithm are combined to minimize temperature errors between the numerical simulation results and remote sensor measurements and iteratively estimate the heat transfer coefficients of forced convection in the rotor. The accuracy and efficiency of the proposed model are verified through a transient heat conduction simulation. Moreover, the effects of the initial guess values and measurement errors are investigated to demonstrate the universality and robustness of the proposed approach in determining the convection heat transfer coefficient. Compared with the full-order finite element model, the proposed hyper-reduced-order model can increase the efficiency of forward heat conduction simulations of the turbine rotor by more than 10 times, and it only takes 0.87 s computer runtime in single transient step simulation, and then rapidly estimate the forced convection heat transfer coefficients. Furthermore, the performance of the proposed approach is insensitive to the initial guess values, and it exhibits great robustness under measurement error. The mean errors are 4.78 %, 2.67 % and 10.51 % when the initial values are 0.015 mW & sdot;mm- & sdot; mm- 3 & sdot;degrees C-1, & sdot; degrees C- 1 , 0.05 mW & sdot;mm- & sdot; mm- 3 & sdot;degrees C-1 & sdot; degrees C- 1 and 0.15 mW & sdot;mm- & sdot; mm- 3 & sdot;degrees C-1 & sdot; degrees C- 1 respectively. When there is no measurement error, the estimated error of the convection heat transfer coefficients is 2.67 %, and even if the measurement error reaches 5 %, and the accuracy loss is only 5.57 %. Consequently, this approach is highly suitable for estimating convection heat transfer coefficients during the dynamic operation of steam turbines, and this research provides reliable guidance for the optimization design and safe operation of steam turbines.

A peridynamic creep-fatigue model is proposed to study creep-fatigue mechanical responses and damage behaviors. A non-unified constitutive model is reformulated in a nonlocal form in the peridynamic-based framework. A probabilistic peridynamic damage criterion is proposed for characterizing creep-fatigue damage. The simulated mechanical responses are in good agreement with the results of creep-fatigue experiments conducted at high temperatures, which confirms the accuracy of the model. In addition, the damage evolution and morphology are well characterized by the model, and the damage mechanism is revealed. The model exhibits excellent potential for simulating nonlinear damage behaviors.

Superalloys suffer from attack of the hot corrosion, leading to degradation of their fatigue durability. Previous numerical studies, mostly by the finite element method (FEM), are rare in hot-corrosion-intervened fatigue problems. In this paper, the fatigue behaviors after pre-hot-corrosion of a Nickel-based superalloy are experimentally studied. The tests capture the specimen's fatigue lifetime reduction due to hot corrosion. Besides, a peridynamic-based model is built to analyze fatigue behaviors of specimens pre-subjected to hot corrosion. The fatigue failure process of the corroded specimen is numerically described, and the simulated fatigue lifetimes agree well with testing results, validating the effectiveness of the model.

A non-local correspondence peridynamic model is reformulated to describe the dynamic failure of ductile materials, under the framework of non-ordinary state-based peridynamics. To eliminate the zero-energy mode as well as to improve the numerical stability, the deformation gradient is updated on the bond level, which owns information including both the non-local deformation and the bond deviation. Peridynamic thermo-viscoplastic constitutive formulations are presented for the failure analyses of ductile materials. Moreover, a mixed strain-stress criterion describing the bond breaking and considering the temperature effect is presented on the bond level, in which the bonds can keep intact in calculations. Several comprehensive cases, including a notched tension test and Kalthoff-Winkler impact tests with different velocities, are investigated to verify the applicability of the proposed model for ductile fracture and impact failure. Numerical results, in terms of failure patterns, cracking switching and propagation, as well as adiabatic shear band propagation, show a reasonable agreement with corresponding experimental observations.

An enhanced adaptive coupling method of peridynamic (PD) theory and the finite element method (FEM) is performed that combines the advantages of both approaches and can be used to simulate quasi-static fracture problems. In the proposed model, PD is used to simulate crack initiation and propagation, whereas the FEM is used to simulate domains without damage to improve efficiency. The influence of ghost forces is reduced by introducing a transition subregion with a variable horizon, thereby significantly improving the accuracy of the model, which is verified by application to a plane stress problem. The conventional coupling model requires pre-partitioning of the solution domain, which is difficult to achieve when modeling certain problems, such as the initiation of cracks at unknown locations. Hence, the adaptive conversion criterion is introduced to ensure that subregions automatically evolve as cracks grow, thereby obviating the need for prior knowledge of crack propagation paths. The proposed model is applied to three standard laboratory tests of quasi-static fracture and its performance is validated by the good agreement of its results with reference solutions or experimental observations. The model accurately simulates complex fracture problems involving crack initiation, irregular crack propagation, and crack coalescence.

In this paper, an adaptive partitioning strategy and the proper orthogonal decomposition–Galerkin method are combined to formulate an adaptive partitioned reduced order model (APROM) for fast solution of peridynamic (PD) models involving fractures. A boundary layer separation approach is presented to tackle the inaccurate reproduction of nonlocal boundary conditions in the reduced order model (ROM). Cracks invariably make ROM results more sensitive to the snapshots, i.e. a set of high-fidelity solutions simulated by the full order model (FOM), and this challenge is overcome by an adaptive partitioning strategy. The internal computational domain is divided into two parts: the crack region is modeled by full PD model, and the remaining region is dimensionally reduced. The partitioned configuration is automatically updated with the damage evolution. Several numerical tests are executed to verify the performance of the APROM, which shows that the APROM is able to successfully simulate various fracture phenomena. A significant improvement in computational efficiency is found: the number of degrees of freedom in the full PD model is greatly reduced, leading to an approximately 10 times improvement in CPU time without loss of accuracy. This paper provides strong theoretical support for accelerating PD solutions, thereby promoting the practical application of PD theory in large-scale engineering projects.