International Journal for Numerical Methods in Engineering最新文献

The piezoelectric effect in piezoelectric materials facilitates the transformation of mechanical energy into electrical energy, with significant applications in energy generation, aerospace, biomedical engineering and other sophisticated technologies. In this study, a Multi-field coupled Multiphase hybrid finite element method (MFCMHFEM) is discovered. The multiphase composite material enhances material properties while reducing fracture and fatigue characteristics. In the multiphase material element, independent force and electric displacement fields are established. For each phase, corresponding stress and electric displacement functions are constructed to analyze the piezoelectric composite material. Based on the principle of minimum complementary energy and using the Lagrange multiplier to implement several constraints, the modified complementary energy functional of the multiphase hybrid finite element is derived. The accuracy of the proposed method is ultimately validated by comparing the computational results of the piezoelectric MFCMHFEM model with those from the ABAQUS software through several numerical examples. The model is further employed to investigate the macroscopic equivalent physical and mechanical properties of piezoelectric composites in relation to microstructural details, including the volume ratio of the inclusion to the matrix, the number of inclusions, and the orientation of polarization. This method offers an effective approach to studying the micro- and macro-electromechanical coupling of piezoelectric composites with numerous inclusions.

The piezoelectric effect in piezoelectric materials facilitates the transformation of mechanical energy into electrical energy, with significant applications in energy generation, aerospace, biomedical engineering and other sophisticated technologies. In this study, a Multi-field coupled Multiphase hybrid finite element method (MFCMHFEM) is discovered. The multiphase composite material enhances material properties while reducing fracture and fatigue characteristics. In the multiphase material element, independent force and electric displacement fields are established. For each phase, corresponding stress and electric displacement functions are constructed to analyze the piezoelectric composite material. Based on the principle of minimum complementary energy and using the Lagrange multiplier to implement several constraints, the modified complementary energy functional of the multiphase hybrid finite element is derived. The accuracy of the proposed method is ultimately validated by comparing the computational results of the piezoelectric MFCMHFEM model with those from the ABAQUS software through several numerical examples. The model is further employed to investigate the macroscopic equivalent physical and mechanical properties of piezoelectric composites in relation to microstructural details, including the volume ratio of the inclusion to the matrix, the number of inclusions, and the orientation of polarization. This method offers an effective approach to studying the micro- and macro-electromechanical coupling of piezoelectric composites with numerous inclusions.

This paper develops a family of energy-conserving time integration methods for nonlinear conservative dynamical problems. Constructed within a unified, self-starting, and single-solve integration framework, the proposed methods avoid multi-stage or sub-step procedures, leading to improved computational efficiency while maintaining robust accuracy. By using a nonlinear conservative single-degree-of-freedom system as a benchmark, the proposed framework systematically derives the conditions under which higher-order consistency in conserving the total energy can be achieved. Three implicit integrators, called IA1-L, IA1-O, and IA1-E, are designed to minimize the local truncation error in displacement, overshoot at the first time step, and total energy error at the first time step, respectively. These three schemes are unconditionally stable and controllably dissipative, and exhibit third-order consistency in total energy conservation. To further enhance the accuracy in acceleration and total energy conservation, two identically second-order accurate implicit and explicit schemes, IA2 and EA2, are constructed to achieve fourth-order consistency in conserving the total energy. A range of numerical examples, including two linear multi-degree-of-freedom problems, a two-dimensional scalar wave propagation problem, the simple pendulum with distinct initial conditions, hardening/softening elastic springs, and the swinging wire rope with large-deformation and large-rotation, are solved and compared. The results demonstrate that the proposed methods significantly outperform the existing schemes, such as TPO/G-$��\alpha �$ and EG-$��\alpha �$, especially in terms of total energy conservation. Moreover, for spatially discretized nonlinear problems, introducing moderate numerical dissipation further improves energy conservation and numerical stability. Overall, the proposed methods provide some efficient implicit and explicit procedures for simulating nonlinear dynamics with energy-conserving requirements.

The Material Point Method (MPM) is widely used in simulating large-deformation problems, but it suffers from inherent contact-related issues, including premature contact, contact penetration, and poor adaptability to multi-resolution object contact. To address these challenges, this paper proposes an easily implementable embedded Lagrangian surface (ELS) contact algorithm and establishes a complete ELS-MPM solution framework. The core of the proposed method is the introduction of an ELS that moves synchronously with the boundary particles of deformable bodies. The contact interface is discretized using surface meshes; potential contact pairs are first filtered via a coarse search, and then accurate contact detection is achieved through fine distance calculation and penetration judgment. Contact forces are computed based on the penalty method and Coulomb friction model and integrated into MPM's grid-particle dynamic update via a two-step transfer process: “contact points to ELS nodes” and “ELS nodes to background grid.” Performance verification shows that ELS-MPM effectively eliminates premature contact and penetration by precisely defining the contact interface with ELS. It supports independent background grids for multi-resolution objects, breaking the resolution matching constraint of traditional MPM while maintaining compatibility with the traditional MPM core framework. A noted limitation is that the method cannot inherently handle material interface fracture, which requires integration with automatic surface mesh partitioning algorithms in future work. This study demonstrates the feasibility and advantages of ELS-MPM through theoretical analysis, framework construction, and case verification, providing an efficient and stable solution for MPM to address complex contact problems.

Geomaterials exhibit highly nonlinear plastic deformation and fracture behaviors. Deep learning offers a promising alternative by exploiting data-driven nonlinear mappings to bypass explicit equation construction. However, existing methods have difficulty in handling noisy small-sample geotechnical data and lack systematic integration of physical priors (e.g., energy conservation, yield conditions) to ensure consistency. In addition, most alternative models are limited to material-scale predictions and need to be combined with traditional numerical methods to solve problems related to boundary conditions, which affects efficiency. This study proposes a novel graph neural network (GNN)-based surrogate model for plasticity-fracture modeling, bridging data-driven learning and physical principles. The framework encodes state information (nodes) and interactions (edges) via a graph structure, enabling efficient evolution prediction of physical fields while embedding interpretable mechanical components. Three numerical examples validate the accuracy and computational efficacy of the proposed model.

Structural health monitoring (SHM) systems often face challenges due to missing or incomplete vibration signals caused by sensor failures, transmission disruptions, or environmental disturbances. To address these issues, we propose WaveNet_GRU, a novel deep learning (DL) model that integrates three key components: dilated causal convolutions for capturing multiscale temporal patterns, gated activation units to enhance nonlinearity and feature selection, and gated recurrent units (GRU) to model long-term temporal dependencies in structural dynamics. This unified architecture enables WaveNet_GRU to efficiently capture both local fluctuations and global temporal trends in vibration signals. We evaluate the model using two benchmark datasets: a laboratory-scale physical model of a cable-stayed bridge and the real-world Rach Mieu 1 Bridge in Vietnam, under varying missing data rates (10%–30%). Experimental results demonstrate that WaveNet_GRU consistently outperforms baseline models, including standalone GRU and WaveNet-based architectures. In particular, on the real-world Rach Mieu 1 Bridge dataset, WaveNet_GRU achieved the highest accuracy with a Coefficient of Determination (R²) exceeding 0.91 and the lowest Root Mean Square Error (RMSE) under 10% missing data conditions. Furthermore, the model demonstrated superior robustness by maintaining reliable performance even when data loss reached 30%, whereas baseline models exhibited significant degradation. By preserving subtle vibration features during reconstruction, WaveNet_GRU helps maintain continuous monitoring, supporting earlier damage indication and more cost-effective maintenance planning in practical SHM.

Accurately modeling crack propagation is critical for predicting failure in engineering materials and structures, where small cracks can rapidly evolve and cause catastrophic damage. The interaction of cracks with discontinuities, such as holes, significantly affects crack deflection and arrest. Recent developments in discrete particle systems with multibody interactions based on constitutive behavior have demonstrated the ability to capture crack nucleation and evolution without relying on continuum assumptions. In this work, we use data from Constitutively Informed Particle Dynamics (CPD) simulations to train operator learning models, specifically Deep Operator Networks (DeepONets), which learn mappings between function spaces instead of finite-dimensional vectors. We explore two DeepONet variants: vanilla and Fusion DeepONet, for predicting time evolving crack propagation in specimens with varying geometries. Three representative cases are studied: (i) varying notch height without active fracture; and (ii) and (iii) combinations of notch height and hole radius where dynamic fracture occurs on irregular discrete meshes. The models are trained using geometric inputs in the branch network and spatial-temporal coordinates in the trunk network. Results show that Fusion DeepONet consistently outperforms the vanilla variant, with more accurate predictions especially in non-fracturing cases. Fracture-driven scenarios involving displacement and crack evolution remain more challenging. These findings highlight the potential of Fusion DeepONet to generalize across complex, geometry varying, and time dependent crack propagation phenomena.

An efficient MPI-based parallel algorithm that preserves geometric structure is proposed, utilizing the field theory variational integrator (FTVI). The FTVI employs space-time finite elements for geometrically exact beams formulated on the Lie group SE(3), and the formulation has been validated to be naturally free of shear locking. Simulation results demonstrate that the FTVI offers good numerical convergence, and excellent long-term energy behavior. To further improve computational efficiency for large-scale simulations, an MPI (message passing interface)-based FTVI parallel algorithm is developed, utilizing the domain decomposition technique. Finally, a flexible cable net system with tens of thousands of degrees of freedom is given to validate the proposed MPI-based FTVI parallel algorithm, which includes reduced computational complexity, enhanced effectiveness and energy conservation.