Computer Methods in Applied Mechanics and Engineering最新文献_第2页

Adaptive Crouzeix-Raviart finite elements for a non-convex Ginzburg-Landau model for nematic liquid crystals 向列液晶非凸Ginzburg-Landau模型的自适应Crouzeix-Raviart有限元

IF 7.2 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-17 DOI: 10.1016/j.cma.2025.118646

Carsten Carstensen, Asha K. Dond, Ruma R. Maity, Neela Nataraj, Lara Théallier

引用次数: 0

Numerical simulation of heat transfer across partial discontinuities using the peridynamic differential operator 局部不连续面传热的动态微分算符数值模拟

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-16 DOI: 10.1016/j.cma.2026.118749

Sunwoo Kim , Suyeong Jin , Jung-Wuk Hong

Simulating heat conduction has been studied using approaches including peridynamics. However, accurately capturing heat transfer across discontinuities such as cracks and material interfaces remains a major challenge. This study presents a computational framework for heat transfer that utilizes a peridynamic differential operator approach to offer a unified modeling approach for both continuous and discontinuous media. The classical heat conduction equation is computed by using peridynamic differential operators, enabling natural treatment of discontinuities. A bond-wise function is defined by the interaction state between nodes, enabling a consistent representation of heat transfer for both intact and broken bonds. For broken bonds, thermal contact conductance is incorporated into the bond-wise function to capture heat transfer across partial discontinuities. The framework is verified through numerical analyses of a two-panel contact problem and a three-dimensional L-shaped bimaterial panel. The results demonstrate accurate prediction of interfacial phenomena, including temperature drops and localized heat flux concentration. The analyses further show that the bond-wise function successfully captures the influence of the thermal contact conductance on both the degree of heat transfer across crack interfaces and the resulting alteration of singularity characteristics. Overall, the framework provides a general and computationally efficient tool for simulating heat conduction in heterogeneous systems with partial discontinuities and establishes a basis for fully coupled thermomechanical analyses.

模拟热传导已经用包括周动力学在内的方法进行了研究。然而，准确地捕捉裂缝和材料界面等不连续区域的传热仍然是一个主要挑战。本研究提出了一个传热计算框架，该框架利用周动力学微分算子方法为连续和不连续介质提供了统一的建模方法。经典的热传导方程是用周动力微分算子计算的，使得不连续的自然处理成为可能。键方向函数由节点之间的相互作用状态定义，使得完整键和断裂键的热传递一致。对于断裂的键，热接触电导被纳入键方向函数，以捕获部分不连续的热传递。通过两面板接触问题和三维l型双材料面板的数值分析验证了该框架。结果表明，该方法可以准确地预测界面现象，包括温度下降和局部热流密度。进一步分析表明，键向函数成功地捕获了接触热导对裂纹界面传热程度和由此产生的奇异特性变化的影响。总的来说，该框架为模拟具有部分不连续的非均质系统中的热传导提供了一个通用且计算效率高的工具，并为完全耦合的热-力学分析奠定了基础。

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引用次数: 0

Simulation of effective scale-size dependent heat conduction in rigid microgeometries 刚性微几何中有效尺度相关热传导的模拟

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-16 DOI: 10.1016/j.cma.2026.118752

Mario Setta, Eddie Wadbro, Grigor Nika

We present homogenization and simulation results for an enhanced heat equation model that captures thermal scale-size effects through higher-gradient corrections involving characteristic internal lengths. The resulting equation is a fourth-order parabolic equation that incorporates thermal scale effects inherent to microstructured materials. We derive effective thermal coefficients for the time-stationary problem using asymptotic homogenization. This enables accurate simulation via a quadratic B-spline-based finite element approach. Our results quantify the influence of microstructure shape and volume fraction on the effective thermal behavior, demonstrating how scale-size-induced phenomena critically affect heat transport in micro- and nanoscale devices.

我们提出了一个增强的热方程模型的均匀化和模拟结果，该模型通过涉及特征内部长度的更高梯度修正来捕获热尺度尺寸效应。所得方程是一个包含微观结构材料固有的热垢效应的四阶抛物方程。利用渐近均匀化方法导出了时间平稳问题的有效热系数。这使得通过基于二次b样条的有限元方法进行精确模拟成为可能。我们的研究结果量化了微观结构形状和体积分数对有效热行为的影响，展示了尺度尺寸诱导的现象如何严重影响微纳米级器件的热传输。

引用次数: 0

Locking-free monolithic FE2 frameworks for concurrent multiscale modeling 用于并发多尺度建模的无锁单片FE2框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-16 DOI: 10.1016/j.cma.2026.118751

Yehui Cui , Zhilang Zhang

Locking phenomena, including volumetric and shear locking, pose a critical challenge in conventional FE² modeling frameworks. Their nested solution schemes complicate the incorporation of classical locking-alleviation techniques, as scale-to-scale data transfer and multiscale boundary coupling often destabilize the solution. Their nested solution schemes complicate the incorporation of classical locking-alleviation techniques, as the macro–micro iterations require repeated exchange of strain/stress information and consistent enforcement of RVE boundary conditions, which increases implementation complexity and computational cost, and may hinder convergence for strongly nonlinear RVEs. Accordingly, while the locking mechanisms themselves are not unique to FE², systematic incorporation and benchmarking of locking remedies within coupled FE² implementations is less commonly reported. The Direct FE² (DFE²) method reformulates FE² into a monolithic solution scheme by employing a constraint matrix that couples macroscopic nodal forces with tractions on RVE boundaries. This structure not only improves computational efficiency but also provides a robust basis for integrating projection-based remedies. Leveraging this framework, this study develops three improved locking-free multiscale formulations: high-order model, stabilized selective relaxation (SSR) model, and enhanced B-bar (EB) model. These approaches systematically integrate projection methods into the concurrent multiscale setting to effectively suppress locking artifacts, thereby significantly improving the accuracy of DFE². Their performance is thoroughly evaluated against Direct Numerical Simulation (DNS) and fine-mesh DFE² across several 2D and 3D examples. Results show that the SSR-DFE² model effectively mitigates shear locking while maintaining the efficiency of the standard DFE² approach; however, it fails to alleviate volumetric locking, leading to errors in nearly incompressible cases. In contrast, the EB-DFE² model achieves a superior accuracy–efficiency balance, delivering solutions close to DNS while reducing computational costs by factors of 20–200 relative to DNS, 10–30 versus fine-mesh DFE² and 5–10 compared to the high-order model.

锁定现象，包括体积锁定和剪切锁定，对传统的FE2建模框架提出了严峻的挑战。由于尺度到尺度的数据传输和多尺度边界耦合经常破坏解的稳定性，它们的嵌套解决方案使经典的锁缓解技术的结合复杂化。由于宏观-微观迭代需要反复交换应变/应力信息和一致地执行RVE边界条件，这增加了实现的复杂性和计算成本，并可能阻碍强非线性RVE的收敛，因此它们的嵌套求解方案使经典锁定缓解技术的结合复杂化。因此，虽然锁定机制本身并不是FE2所独有的，但是在耦合FE2实现中对锁定补救措施的系统合并和基准测试很少被报道。直接FE2 （Direct FE2, DFE2）方法通过使用约束矩阵将宏观节点力与RVE边界上的牵引力耦合，将FE2重新表述为整体求解方案。这种结构不仅提高了计算效率，而且为整合基于投影的补救措施提供了坚实的基础。利用这一框架，本研究开发了三种改进的无锁定多尺度公式：高阶模型、稳定选择性松弛（SSR）模型和增强型B-bar （EB）模型。这些方法系统地将投影方法集成到并发多尺度设置中，有效地抑制锁定伪影，从而显著提高DFE2的精度。在多个2D和3D示例中，通过直接数值模拟（DNS）和细网格DFE2对其性能进行了全面评估。结果表明，SSR-DFE2模型在保持标准DFE2方法效率的同时，有效地缓解了剪切锁定；然而，它不能减轻体积锁定，在几乎不可压缩的情况下导致错误。相比之下，EB-DFE2模型实现了卓越的精度和效率平衡，提供接近DNS的解决方案，同时将计算成本相对于DNS降低20-200倍，相对于细网格DFE2降低10-30倍，相对于高阶模型降低5-10倍。

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引用次数: 0

The generalized shifted boundary method for geometry-parametric PDEs and time-dependent domains 几何参数偏微分方程和时变域的广义位移边界法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-15 DOI: 10.1016/j.cma.2026.118748

Oriol Colomés , Jan Modderman , Guglielmo Scovazzi

Many engineering and scientific problems require the solution of partial differential equations in complex geometries. Often, these problems involve parametrized geometries, e.g. design optimization, or moving domains, e.g. fluid-structure interaction problems. For such cases, traditional methods based on body-fitted grids require time-consuming mesh generation or re-meshing techniques. Unfitted finite element methods, e.g. CutFEM of AgFEM, are appealing techniques that address these challenges. However, they require ad-hoc integration methods and stabilization techniques to prevent instabilities for small cut cells. Recently, the Shifted Boundary Method (SBM), was introduced to prevent integration over cut cells and small cut-cell instabilities. An extension of the SBM was recently introduced, the Weighted Shifted Boundary Method (WSBM), where the variational form is weighted by the elemental active volume fraction, improving discrete mass/momentum conservation properties in simulations with moving domains. In this work we introduce the Generalized Shifted Boundary Method (GSBM), a geometry-agnostic generalization of the SBM and WSBM formulations that avoids the need of redefinition of integration domains and finite element spaces. The GSBM enables a unified formulation for problems with evolving geometries, supports gradient-based optimization of problems with varying geometries including topological changes, and unifies SBM, WSBM, and optimal-surrogate variants within a single framework. In this work we describe the formulation, and corresponding tests, for three model problems, namely: the Poisson problem, linear elasticity and transient Stokes flow.

许多工程和科学问题需要求解复杂几何中的偏微分方程。通常，这些问题涉及参数化几何，例如设计优化，或移动域，例如流固耦合问题。对于这种情况，传统的基于体拟合网格的方法需要耗时的网格生成或重新网格化技术。非拟合有限元方法，如AgFEM的CutFEM，是解决这些挑战的有吸引力的技术。然而，它们需要特别的集成方法和稳定技术来防止小切割细胞的不稳定。最近，引入了位移边界法（SBM）来防止切割细胞的积分和小切割细胞的不稳定性。最近引入了SBM的一种扩展，加权位移边界法（WSBM），其中变分形式由元素活性体积分数加权，改善了具有移动域的模拟中的离散质量/动量守恒特性。在这项工作中，我们介绍了广义位移边界法（GSBM），它是SBM和WSBM公式的一种几何不可知论的推广，避免了重新定义积分域和有限元空间的需要。GSBM支持对具有演化几何形状的问题进行统一表述，支持对具有不同几何形状（包括拓扑变化）的问题进行基于梯度的优化，并在单个框架内统一SBM、WSBM和最优代理变量。本文描述了泊松问题、线性弹性问题和瞬态斯托克斯流这三个模型问题的公式和相应的检验。

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引用次数: 0

Instabilities and phase transitions in architected metamaterials: a gradient-enhanced continuum approach 结构超材料的不稳定性和相变：梯度增强连续体方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-15 DOI: 10.1016/j.cma.2025.118719

Sarvesh Joshi , S. Mohammad Mousavi , Craig M. Hamel , Stavros Gaitanaros , Prashant K. Purohit , Ryan Alberdi , Nikolaos Bouklas

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transitions. Their macroscopic response–including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior–remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. We propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic–staggered strategy. Simulations capture densification fronts, forward and reverse transitions, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected metamaterials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.

结构超材料，如泡沫和晶格，表现出由微观结构不稳定性和新出现的相变所控制的广泛特性。它们的宏观响应——包括撞击过程中的能量耗散、大的可恢复变形、构型之间的变形和形变行为——仍然难以用传统的连续体模型捕获，这些连续体模型通常依赖于限制可扩展性的离散方法。我们提出了一种非局部连续体公式，可以捕获弹性结构超材料的稳定和不稳定响应。该框架通过引入非局部变量和反映微观结构特征的内部长度尺度扩展了各向异性超弹性。局部多凸自由能模型系统地扩充了两个非（多）凸能族，实现了亚稳态和双稳态响应。在有限元素框架中实现可以使用混合单块交错策略实现解决方案。模拟捕获致密化前沿，正向和反向转换，迟滞回路，不完善的灵敏度，和全局协调的辅助模式。总体而言，该框架为加速构建超材料中不稳定驱动现象的建模提供了坚实的基础，同时支持向各向异性、耗散和有源系统的扩展，以及与数据驱动和机器学习方法的集成。

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引用次数: 0

Structural optimization of a stack of elastic rings under gravity 重力作用下一叠弹性环的结构优化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-14 DOI: 10.1016/j.cma.2025.118698

Luis Andres Mollericon Titirico , Sylvain Lefebvre , Ole Sigmund , Jonàs Martínez

We study the structural optimization of a stack of elastic rings subjected to gravity. The aim is to optimize for minimum or maximum volume enclosing structures while preventing their collapse under their own weight. We formulate the problem using a parameterization of the cross-section geometry of the rings and a tailored optimization scheme that considers axisymmetric finite elements. As demonstrated through numerical examples, our method produces structurally sound shapes that can then be fabricated by stacking ring components or through extrusion-based manufacturing.

研究了一组受重力作用的弹性环的结构优化。目的是优化最小或最大体积的封闭结构，同时防止它们在自身重量下倒塌。我们使用环的横截面几何参数化和考虑轴对称有限元的定制优化方案来制定问题。通过数值例子证明，我们的方法产生结构合理的形状，然后可以通过堆叠环组件或通过挤压制造制造。

引用次数: 0

A vertex-centered finite volume method for solute transport in porous media on arbitrary polygonal meshes 任意多边形网格上多孔介质中溶质输运的顶点中心有限体积法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-14 DOI: 10.1016/j.cma.2026.118731

Yingzhi Qian , Xiaoping Zhang , Yan Zhu , Lili Ju , Jiesheng Huang

Accurately modeling solute transport in porous media is essential for effective agricultural water resource management. However, strong advection or localized sink/source terms often leads to steep local concentration gradients, posing significant challenges for numerical simulation. To address these issues, this paper proposes an efficient algorithm based on the Vertex-Centered Finite Volume Method (VCFVM). In this approach, the primary unknowns are defined at the mesh vertices, and the fluxes across dual edges are computed as weighted combinations of these vertex values. This formulation enables the advection-diffusion equation to be directly solved on arbitrary polygonal meshes-including nonmatching grids-without requiring complex preprocessing. The use of nonmatching grids allows for flexible local refinement, significantly enhancing the method’s ability to capture sharp concentration gradients. The proposed algorithm is particularly well-suited for simulating solute transport characterized by sharp gradients induced by strong advection or localized sink/source terms, and it has been validated through three representative benchmark cases. Numerical results show that the method accurately reproduces solute transport behavior in complex geometries, effectively maintains local Péclet numbers below 4, and successfully reduces numerical oscillations while suppressing excessive diffusion, as well as save about 50% CPU time in field scale simulation. This algorithm can be seamlessly integrated with existing groundwater and soil water flow models, offering a practical solution for managing sharp gradients in both water flow and solute transport.

准确模拟溶质在多孔介质中的运移对农业水资源的有效管理至关重要。然而，强平流或局部汇源项往往导致局部浓度梯度较大，给数值模拟带来重大挑战。为了解决这些问题，本文提出了一种基于顶点中心有限体积法（VCFVM）的高效算法。在这种方法中，主要未知数在网格顶点处定义，并且通过这些顶点值的加权组合计算跨双边的通量。该公式使平流扩散方程可以在任意多边形网格（包括不匹配网格）上直接求解，而不需要复杂的预处理。使用非匹配网格允许灵活的局部细化，显著增强了该方法捕捉尖锐浓度梯度的能力。该算法特别适合于模拟由强平流或局部汇源项引起的急剧梯度溶质输运，并通过三个代表性基准案例进行了验证。数值结果表明，该方法能准确再现复杂几何结构中的溶质输运行为，有效地将局部psamclet数维持在4以下，在抑制过度扩散的同时成功地减少了数值振荡，在现场尺度模拟中节省了约50%的CPU时间。该算法可以与现有的地下水和土壤水流模型无缝集成，为管理水流和溶质运移的急剧梯度提供了实用的解决方案。

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引用次数: 0

COMMET: Orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates 注释：通过批量化神经本构更新，有限元方法的数量级加速

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-14 DOI: 10.1016/j.cma.2026.118728

Benjamin Alheit , Mathias Peirlinck , Siddhant Kumar

Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs), i.e., neural network-based constitutive models, offer a highly expressive and flexible framework for modeling complex material behavior in solid mechanics. However, their practical adoption in large-scale FE simulations remains limited due to significant computational costs, especially in repeatedly evaluating stress and stiffness. NCMs thus represent an extreme case: their large computational graphs make stress and stiffness evaluations prohibitively expensive, restricting their use to small-scale problems. In this work, we introduce COMMET, an open-source FE framework whose architecture has been redesigned from the ground up to accelerate high-cost constitutive updates. Our framework features a novel assembly algorithm that supports batched and vectorized constitutive evaluations, compute-graph-optimized derivatives that replace automatic differentiation, and distributed-memory parallelism via MPI. These advances dramatically reduce runtime, with speed-ups exceeding three orders of magnitude relative to traditional non-vectorized automatic differentiation-based implementations. While we demonstrate these gains primarily for NCMs, the same principles apply broadly wherever for-loop based assembly or constitutive updates limit performance, establishing a new standard for large-scale, high-fidelity simulations in computational mechanics.

每当材料模型比较复杂时，本构评估往往是有限元模拟的主要计算成本。神经本构模型（ncm），即基于神经网络的本构模型，为固体力学中复杂材料行为的建模提供了一个高度表达和灵活的框架。然而，由于大量的计算成本，特别是在反复评估应力和刚度时，它们在大规模有限元模拟中的实际应用仍然有限。因此，ncm代表了一个极端的情况：它们的大型计算图使得应力和刚度评估过于昂贵，限制了它们在小规模问题中的应用。在这项工作中，我们介绍了COMMET，这是一个开源的FE框架，其架构已经从头开始重新设计，以加速高成本的本构更新。我们的框架具有一种新颖的装配算法，支持批处理和矢量化的本构评估，计算机图优化的导数取代自动微分，以及通过MPI实现分布式内存并行性。这些进步大大缩短了运行时间，相对于传统的基于非矢量化的自动微分实现，速度提高了三个数量级。虽然我们主要为ncm展示了这些增益，但同样的原理广泛适用于基于for-loop的装配或本构更新限制性能的地方，为计算力学中的大规模高保真模拟建立了新的标准。

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引用次数: 0

PACMANN: Point adaptive collocation method for artificial neural networks PACMANN：人工神经网络的点自适应配置方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-14 DOI: 10.1016/j.cma.2025.118723

Coen Visser , Alexander Heinlein , Bianca Giovanardi

Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual determined for a set of collocation points. Previous work has shown that the number and distribution of these collocation points have a significant influence on the accuracy of the PINN solution. Therefore, the effective placement of these collocation points is an active area of research. Specifically, available adaptive collocation point sampling methods have been reported to scale poorly in terms of computational cost when applied to high-dimensional problems. In this work, we address this issue and present the Point Adaptive Collocation Method for Artificial Neural Networks (PACMANN). PACMANN incrementally moves collocation points toward regions of higher residuals using gradient-based optimization algorithms guided by the gradient of the PINN loss function, that is, the squared PDE residual. We apply PACMANN to several forward and inverse problems, including one with a low-regularity solution and 3D Navier Stokes, and demonstrate that this method matches the performance of state-of-the-art methods in terms of the accuracy/efficiency tradeoff for the low-dimensional problems, while outperforming available approaches for high-dimensional problems. Key features of the method include its low computational cost and simplicity of integration into existing physics-informed neural network pipelines. The code is available at https://github.com/CoenVisser/PACMANN.

物理信息神经网络（pinn）已经成为逼近偏微分方程（PDEs）正解和逆解的一种工具。pinn最小化一个损失函数，它包含一组并置点确定的PDE残差。先前的工作表明，这些配点的数量和分布对PINN解的精度有显著影响。因此，这些搭配点的有效放置是一个活跃的研究领域。具体而言，已有的自适应配点采样方法在应用于高维问题时，在计算成本方面伸缩性较差。在这项工作中，我们解决了这个问题，并提出了人工神经网络的点自适应配置方法（PACMANN）。PACMANN使用基于梯度的优化算法，以PINN损失函数的梯度（即PDE残差的平方）为指导，逐步将搭配点向残差较高的区域移动。我们将PACMANN应用于几个正反问题，包括一个具有低正则解和3D Navier Stokes的问题，并证明该方法在低维问题的精度/效率权衡方面与最先进的方法相匹配，同时优于高维问题的可用方法。该方法的主要特点是计算成本低，易于集成到现有的物理信息神经网络管道中。代码可在https://github.com/CoenVisser/PACMANN上获得。

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引用次数: 0