International Journal for Numerical Methods in Engineering最新文献

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.

To tackle the challenge of structural boundary blurring in density-based topology optimization, a sensitivity dynamic filtering method incorporating density penalization is proposed. By enhancing the traditional sensitivity filtering framework, element relative densities are penalized to rapidly drive them toward binary states (0 or 1). Concurrently, during the topology iteration, the filtering radius is adaptively reduced according to structural discreteness, thereby minimizing the sensitivity influence of surrounding elements within the shrunk radius on the central element. The proposed method is integrated with the Solid Isotropic Material with Penalization (SIMP) method and validated through numerical examples. Results demonstrate that the proposed method can effectively suppress intermediate-density elements, generate structures with sharp boundaries, and support topological optimization that accounts for element stress while circumventing numerical instabilities like checkerboard patterns—ultimately achieving substantial improvements in topology optimization efficiency.

This work introduces a reduced-order model (ROM) for plate structures with periodic microstructures by coupling the self-consistent clustering analysis (SCA) method with the Lippmann-Schwinger equation, thereby enabling rapid multi-scale homogenisation of heterogeneous plates. For the first time, a plate-specific SCA scheme is derived featuring two key components: (i) an offline-online strategy that combines Green's functions with k-means data compression, and (ii) an online self-consistent update that exploits the weak sensitivity of the reference medium. The framework handles both linear and non-linear problems in classical plate theory (CPT) and first-order shear deformation theory, and its performance is verified on linear isotropic perforated plates and woven composites, as well as on non-linear elasto-plastic perforated plates and woven composites with damage. Across all cases, the proposed model matches the accuracy of fast Fourier transform (FFT)-based direct numerical simulation (DNS) while reducing computational cost by over an order of magnitude. Furthermore, the potential of dynamic adaptive clustering to balance improved computational accuracy with associated increased computational cost is discussed.