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Computer methods in applied mechanics and engineering
North-Holland Pub. Co.
Computer methods in applied mechanics and engineering

North-Holland Pub. Co.

周刊

0045-7825

Computer methods in applied mechanics and engineering/Journal Computer methods in applied mechanics and engineeringSCIISTP
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    Time series clustering adaptive enhanced method for time-dependent reliability analysis and design optimization

    Zhang D.Zhao Y.Yang M.Han X....
    1.1-1.30页
    查看更多>>摘要：© 2025Adaptive Kriging model has gained growing attention for its effectiveness in reducing the computational costs in time-dependent reliability analysis (TRA). However, the existing methods struggle to identify critical sample regions, leverage parallel computational resources, and assess the value for sample trajectories, thus restricting improvement in accuracy and efficiency. To address the challenges, this study proposes a time series clustering adaptive enhanced method (TSCM). TSCM first employs the time series clustering technique to partition the sample region efficiently. A novel time-dependent Kriging occurrence learning function is then introduced to account for both the uncertainty of sample trajectories and its influence on the approximated limit state boundary. Subsequently, an adaptive sampling strategy is developed to select training samples in parallel, guided by an uncertainty-based assessment of sample regions. After that, a time-dependent error-based stopping criterion is introduced to determine the training stage and terminate the update process. Finally, TSCM is extended to time-dependent reliability-based design optimization problems. Several numerical examples and an engineering case study demonstrate the superior computational efficiency and accuracy of the proposed method.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Constitutive model-constrained physics-informed neural networks framework for nonlinear structural seismic response prediction

    Wu Y.Yin Z.Gao Y.Yang S....
    1.1-1.18页
    查看更多>>摘要：© 2025Seismic response prediction presents a significant challenge in earthquake engineering, particularly in balancing computational efficiency with physical accuracy. Traditional numerical methods are computationally expensive for performing large-scale nonlinear analyses, while data-driven machine learning approaches, though computational efficiency, often lack physical constraints and sufficient training data. Physics-Informed Neural Networks (PINNs), an emerging approach that integrates physical laws with deep learning techniques to solve complex scientific and engineering problems, show great potential. However, incorporating nonlinear constitutive models to accurately describe the structural behavior under seismic loading remains a challenge. In this study, a new framework, constitutive model-constrained physics-informed neural networks (CM-PINNs), is proposed to address this issue. This framework enhances prediction accuracy and physical interpretability by incorporating nonlinear constitutive constraints into the loss function. It also uses a fully connected skip LSTM architecture and implements an adaptive loss weight initialization strategy. Numerical validation demonstrates the superior performance of the CM-PINNs framework in simulating single-degree-of-freedom nonlinear seismic responses. Under limited training data conditions, CM-PINNs demonstrates notably superior performance compared to existing methods such as physics-informed multi-LSTM networks (PhyLSTM). Additionally, the scalability of CM-PINNs is verified through its application to multi-layer shear building structures. The results demonstrate that CM-PINNs provide a computationally efficient and reliable approach for seismic response prediction.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Adaptive phase-field cohesive-zone model for simulation of mixed-mode interfacial and bulk fracture in heterogeneous materials with directional energy decomposition

    Bian P.-L.Liu Q.Zhang H.Yu T....
    1.1-1.31页
    查看更多>>摘要：© 2025 Elsevier B.V.Interfacial debonding, a critical failure mechanism in heterogeneous materials, is often characterized by mixed-mode fracture. This study develops a numerical framework to simulate bulk and interfacial fractures in composite materials. A phase-field cohesive zone model, incorporating a directional energy decomposition scheme and a modified toughness method, is employed to capture complex fracture behaviors. A level-set method explicitly defines interface positions, while an adaptive mesh refinement strategy enhances computational efficiency. Numerical examples validate the model's accuracy and efficiency in predicting mixed-mode crack propagation and interfacial debonding. This work provides a robust and efficient approach to simulate complex fracture phenomena in heterogeneous materials, especially for the mixed-mode fracture.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Adaptive phase-field modeling for electromechanical fracture in flexoelectric materials using multi-patch isogeometric analysis

    Li H.Yu T.Liu Z.Sun J....
    1.1-1.31页
    查看更多>>摘要：© 2025 Elsevier B.V.The fracture of flexoelectric materials involves strain gradients, which pose challenges for theoretical and numerical analysis. The phase-field model (PFM) is highly effective for simulating crack propagation. However, PFM within the finite element method (FEM) framework faces certain challenges in simulating the fracture behavior of flexoelectric materials since the conventional FEM can only provide C0 continuity. In this study, an adaptive PFM within multi-patch isogeometric analysis using polynomial splines over hierarchical T-meshes (PHT-splines) is proposed to simulate electromechanical fracture in flexoelectric materials. The PHT-splines functions feature higher-order continuity and can effectively discretize the strain gradient. All computational models are accurately modeled using multiple PHT-splines patches. The continuity of field variables such as displacement, electric potential, and phase field at the coupling edge is ensured using Nitsche's method. To effectively compute the crack-driving force, the generalized Miehe decomposition method is employed. To alleviate the computational burden, a mesh refinement adaptive scheme based on user-defined thresholds for the phase field is used. The proposed method's accuracy, reliability, and robustness are demonstrated using several fracture simulations.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    A partitioned Lagrangian finite element approach for the simulation of viscoelastic and elasto-viscoplastic free-surface flows

    Rizzieri G.Ferrara L.Cremonesi M.
    1.1-1.27页
    查看更多>>摘要：© 2025 The AuthorsMany materials, such as clays, fresh concrete, and biological fluids, exhibit elasto-viscoplastic (EVP) behaviour, transitioning between solid and fluid states under varying stress conditions. Among EVP models, Saramito's constitutive law stands out for its thermodynamic consistency, smooth solid-to-fluid transition, and ability to accurately represent diverse materials with only four easily determinable parameters. However, computational challenges have mainly confined its application to 2D or axisymmetric confined flows. This work presents an innovative partitioned Lagrangian FEM approach for the simulation of transient free-surface viscoelastic and EVP flows. The Lagrangian framework allows to naturally track free surfaces and simplifies the constitutive equation by eliminating the convective term. The solver decouples the Navier–Stokes equations (solved implicitly) from the EVP constitutive law (solved explicitly), employing an adaptive sub-stepping procedure. An advantageous splitting of the Cauchy stress tensor is used in combination with the Both Sides Diffusion (BSD) stabilization technique to prevent issues linked to the ellipticity loss in the momentum equation, also for low solvent-polymer viscosity ratios. The FEM solver has been integrated within the Particle Finite Element Method (PFEM), an updated Lagrangian formulation equipped with an efficient re-meshing scheme, to simulate free-surface flows, large deformations in soft solids, and topological changes of the domain. Benchmark tests in 2D and 3D, including gravity-induced spreading, impacting drops, and dam-break scenarios are used to validate the framework and highlight the versatility of Saramito's model, which can also successfully reproduce a wide range of simpler sub-cases, including viscoelastic, viscoplastic, and EVP behaviours.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Point cloud neural operator for parametric PDEs on complex and variable geometries

    Zeng C.Zhang Y.Zhou J.Wang Y....
    1.1-1.29页
    查看更多>>摘要：© 2025Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses significant challenges, particularly in handling geometrically complex and variable domains, which are often discretized as point clouds. In this work, we systematically investigate the formulation of neural operators — maps between infinite-dimensional function spaces — on point clouds to better handle complex and variable geometries while mitigating discretization effects. We introduce the Point Cloud Neural Operator (PCNO), designed to efficiently approximate solution maps of parametric PDEs on such domains. We evaluate the performance of PCNO on a range of pedagogical PDE problems, focusing on aspects such as boundary layers, adaptively meshed point clouds, and variable domains with topological variations. Its practicality is further demonstrated through three-dimensional applications, such as predicting pressure loads on various vehicle types and simulating the inflation process of intricate parachute structures.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Learning physics-consistent material behavior from dynamic displacements

    Han Z.Pundir M.Kammer D.S.Fink O....
    1.1-1.16页
    查看更多>>摘要：© 2025 The AuthorsAccurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress–strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed to learn the constitutive law from deformation data. Nonetheless, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on boundary force data for training which are unavailable in many in-situ scenarios. Here, we introduce a machine learning approach to learn physics-consistent constitutive relations solely from material deformation without boundary force information. This is achieved by considering a dynamic formulation rather than static equilibrium data and applying an input convex neural network (ICNN). We validate the effectiveness of the proposed method on a diverse range of hyperelastic material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations. It is, due to its design based on dynamics, particularly suited for applications to strain-rate-dependent materials and situations where constitutive laws need to be inferred from in-situ measurements without access to global force data.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    The Fast Forward Quantum Optimization Algorithm: A study of convergence and novel unconstrained optimization

    Singh P.
    1.1-1.31页
    查看更多>>摘要：© 2025 Elsevier B.V.The Fast Forward Quantum Optimization Algorithm (FFQOA) is a novel quantum-inspired heuristic search algorithm, drawing inspiration from the movement and displacement activities of wavefunctions associated with quantum particles. This algorithm has demonstrated remarkable effectiveness in predicting time series, clustering biomedical images, and optimizing the performance of convolutional neural networks. However, there has been no comprehensive study to investigate the convergence behavior and performance of FFQOA on standard optimization test functions. Motivated by this gap, we extend our research in three significant directions. First, we analyze the convergence behavior of FFQOA by studying the local and global displacements of its wavefunctions. To achieve this, martingale theory is employed to analyze the sequence of displacements, and we establish a necessary and sufficient condition for attaining the global convergence state of FFQOA. Second, we introduce 20 novel unconstrained optimization test functions, termed the Singh optimization functions. The mathematical properties of these functions are rigorously derived and comprehensively discussed. Finally, leveraging these optimization functions, the performance of FFQOA is evaluated and compared against well-established metaheuristic algorithms, including the Genetic Algorithm, Simulated Annealing, Cultural Algorithm, Particle Swarm Optimization, Ant Colony Optimization, Firefly Algorithm, and Grey Wolf Optimizer. Our analysis reveals that most existing algorithms struggle to effectively balance exploration and exploitation in the early stages of iterations, often failing to achieve global convergence. In contrast, FFQOA not only satisfies the global convergence criteria but also consistently identifies the global optimal solutions for the proposed Singh optimization functions. [Source Code: The source code for this study is available upon request by contacting the author via emails at drpritpalsingh82@gmail.com, pritpal@curaj.ac.in].
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Accelerating crash simulations with Finite Element Method Integrated Networks (FEMIN): Comparing two approaches to replace large portions of a FEM simulation

    Thel S.Greve L.van der Smagt P.Karl M....
    1.1-1.26页
    查看更多>>摘要：© 2025 The AuthorsThe Finite Element Method (FEM) is a widely used technique for simulating crash scenarios with high accuracy and reliability. To reduce the significant computational costs associated with FEM, the Finite Element Method Integrated Networks (FEMIN) framework integrates neural networks (NNs) with FEM solvers. We discuss two different approaches to integrate the predictions of NNs into explicit FEM simulation: A coupled approach predicting forces (f-FEMIN) and a newly introduced, uncoupled approach predicting kinematics (k-FEMIN). For the f-FEMIN approach, we introduce a novel adaption of the Deep Variational Bayes Filter (DVBF). The adapted DVBF outperforms deterministic NNs from a previous study in terms of accuracy. We investigate the differences of the two FEMIN approaches across two small-scale and one large-scale load case. Although the adaptation of the DVBF and the f-FEMIN approach offers good accuracy for the small-scale load cases, the k-FEMIN approach is superior for scaling to large-scale load cases. k-FEMIN shows its excellent acceleration of the FEM crash simulations without overhead during runtime and keeps compute costs during training low.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Physics-informed non-intrusive reduced-order modeling of parameterized dynamical systems

    Dave H.Cotteleer L.Parente A.
    1.1-1.19页
    查看更多>>摘要：© 2025 Elsevier B.V.In this study, we present a new framework of physics-informed non-intrusive reduced-order modeling (ROM) of dynamical systems modeled by parametric, partial differential equations (PDEs). Given new time and parameter values of a PDE, the framework utilizes trained physics-informed ML models to quickly estimate high-fidelity solutions while simultaneously observing the constraints and dynamics of the system. In the offline training phase, proper orthogonal decomposition (POD) decomposes a training database of high-fidelity solutions into POD modes and POD coefficients. A feed-forward neural network is trained to map time-parameter values to the few dominant POD coefficients. The loss function is composed of two terms: (1) error between original data and reconstructed data and (2) PDE residuals where each term of the PDE is expressed using Galerkin expansion on the reduced basis composed of the most dominant POD modes. The PDE residuals are not evaluated using POD–Galerkin (reduced-order) equations. The novelty of this work lies in the construction of PDE residual term and an a priori analysis that allows one to select weighting factor (or Lagrange multiplier) ahead of it. It has been found that a physics-informed ROM minimizing the two terms generates new solutions orders-of-magnitude accurate than a vanilla ROM that minimizes only the first error term. Besides estimating reconstruction error on a database, the framework also allows estimation of reconstruction quality of different terms such as advection and diffusion in the PDE. This is expected to promote better integration and interpretation of ML in reduced-order modeling of dynamical systems. During the online prediction phase, given new values of time and parameters, the generalized coordinates are quickly estimated and used in reconstruction. High-fidelity solutions are thus obtained orders-of-magnitude faster than a conventional numerical simulation. The framework is demonstrated on 1D and 2D Burgers’ equations and an incompressible flow over a backward facing step.
      原文链接:
    • NETL
    • NSTL
    • Elsevier