Computer Methods in Applied Mechanics and Engineering最新文献_第6页

A variational phase-field framework for multiphysics modeling of delayed hydride cracking in zirconium alloys 锆合金延迟氢化物裂纹多物理场模型的变分相场框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-20 DOI: 10.1016/j.cma.2026.118765

Wei Li , Han Zhao , Minghua Chi , Vincent Beng Chye Tan

Delayed hydride cracking (DHC) poses a significant integrity threat to zirconium nuclear cladding, arising from the cyclic interplay of hydrogen diffusion and hydride precipitation/dissolution, which leads to characteristic intermittent subcritical crack advance. This work develops a thermodynamically consistent variational phase-field framework that, in a unified formulation, couples hydrogen diffusion, stress- and temperature-regulated hydride evolution, thermo-elastoplasticity, and a ductile-to-brittle fracture transition. The model reproduces key experimental observations across temperatures—intermittent crack advance, DHC velocity, striation spacing, and incubation time—and quantifies how stress and temperature jointly govern hydride nucleation and cracking. Mechanistically, hydrostatic tension reduces the terminal solid solubility for precipitation/dissolution and concentrates hydrogen; ensuing precipitation relaxes and redistributes stresses, establishing a self-sustaining feedback loop that triggers hydride precipitation–fracture–dissolution–reprecipitation cycles. Parametric studies of pre-cracked cladding reveal a stress-dependent transition between diffusion-controlled and precipitation-controlled initiation. High applied stress induces pronounced thermal sensitivity via stress-assisted hydrogen accumulating, whereas low stress exhibits a weaker temperature response that manifests only above a critical hydride fraction. Beyond DHC, the framework is readily extensible to simulations of oxide–hydride synergistic delayed cracking under reactor-relevant conditions. It thus provides a physics-based foundation for mechanism identification, threshold assessment, and life prediction of zirconium cladding, and establishes a platform for future extensions to oxide–hydride interaction.

迟发性氢化物开裂（DHC）是由氢扩散和氢化物析出/溶解的循环相互作用引起的，对锆核包层的完整性构成了严重威胁，导致了典型的间歇性亚临界裂纹进展。这项工作开发了一个热力学一致的变分相场框架，在一个统一的公式中，耦合了氢扩散、应力和温度调节的氢化物演化、热弹塑性和韧性到脆性的断裂转变。该模型重现了不同温度下的关键实验观察结果——间歇性裂纹进展、DHC速度、条纹间距和孵化时间——并量化了应力和温度如何共同控制氢化物成核和开裂。从机械上讲，静水张力降低了沉淀/溶解的末端固溶度，并浓缩了氢；随后的沉淀松弛并重新分配应力，建立一个自我维持的反馈回路，触发氢化物沉淀-破裂-溶解-再沉淀循环。预裂包层的参数研究揭示了扩散控制和沉淀控制之间的应力依赖转变。高外加应力通过应力辅助的氢气积累导致明显的热敏性，而低外加应力表现出较弱的温度响应，仅在临界氢化物分数以上表现出来。除了DHC之外，该框架还可以很容易地扩展到反应器相关条件下氧化-氢化物协同延迟裂解的模拟。从而为锆包层的机理识别、阈值评估和寿命预测提供了物理基础，并为今后扩展到氧化氢化物相互作用建立了平台。

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引用次数: 0

The coupling of mixed and primal finite element methods for the coupled body-plate problem 耦合体板问题的混合有限元与原始有限元的耦合

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-20 DOI: 10.1016/j.cma.2026.118750

Jun Hu , Zhen Liu , Rui Ma

This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the plane direction and a plate bending model with Kirchhoff assumptions along the transverse direction. The Hellinger-Reissner formulation is adopted for the body by introducing the stress as an auxiliary variable, while the primal formulation is employed for the plate. The well-posedness of the new mixed weak formulation is established. This approach enables direct stress approximations and allows for non-matching meshes at the interface since the continuity condition of the displacement acts as a natural boundary condition for the body. Under certain assumptions, discrete stability and error estimates are derived for both conforming and nonconforming finite element methods. Two specific pairs of conforming and nonconforming finite elements are shown to satisfy the required assumptions, respectively. Furthermore, the problem is reduced to an interface problem based on the domain decomposition, which can be solved effectively by a conjugate gradient iteration. Numerical experiments are conducted to validate the theoretical results.

本文研究了三维弹性体与二维板在界面处刚性连接的耦合问题。该板包括沿平面方向的平面弹性模型和沿横向的基于基尔霍夫假设的板弯曲模型。体采用Hellinger-Reissner公式，将应力作为辅助变量引入，而板采用原始公式。建立了新的混合弱公式的适定性。由于位移的连续性条件作为物体的自然边界条件，这种方法可以实现直接的应力近似，并允许在界面处进行非匹配网格。在一定的假设条件下，导出了符合和不符合有限元方法的离散稳定性和误差估计。两对特定的符合和不符合的有限元分别满足所要求的假设。在此基础上，将该问题分解为基于区域分解的界面问题，并通过共轭梯度迭代有效地求解。通过数值实验对理论结果进行了验证。

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引用次数: 0

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces 使用再现核希尔伯特空间的可解释和灵活的非侵入性降阶模型

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-20 DOI: 10.1016/j.cma.2026.118734

Alejandro N. Diaz , Shane A. McQuarrie , John T. Tencer , Patrick J. Blonigan

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. The approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

本文发展了一种可解释的、非侵入性的、使用正则化核插值的降阶建模技术。现有的非侵入式方法通过求解低维矩阵算子的数据驱动最小二乘回归问题来近似降阶模型（ROM）的动力学。相反，我们的方法利用正则化内核插值，从用户定义的再现内核希尔伯特空间产生ROM动态的最佳近似值。我们表明，我们的基于内核的方法可以产生可解释的rom，其结构通过将明智选择的特征映射嵌入到内核中来反映全阶模型结构。该方法是灵活的，并且允许通过特征映射和闭包项在内核中通过更一般的非线性项进行知情结构的组合。我们还推导了一个可计算的后验误差界，该界结合了基于入侵投影的rom和核插值的标准误差估计。该方法在几个数值实验中得到了证明，包括使用适当的正交分解和二次维数降维与算子推理的比较。

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引用次数: 0

Discontinuous Galerkin cohesive zone modeling of toughness-controlled failure 韧性控制破坏的不连续Galerkin内聚带建模

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-20 DOI: 10.1016/j.cma.2025.118616

Daniel Pickard

A fracture analysis methodology is developed from the discontinuous Galerkin formalism, a simple failure locus, and the simple assumption of brittle unloading to the origin. For positive fracture energy, the semi-discrete system is a continuous function of the finite element nodal coordinate array, which renders the semi-discrete problem well-posed. In the perfectly brittle limit, the formulation reduces to the well-established discontinuous Galerkin/cohesive zone modeling paradigm. The robustness of the method is shown to stem from the blunting of the numerical flux at propagating crack tips, while its versatility is demonstrated through a series of large-scale fracture propagation problems.

从不连续的伽辽金形式、简单的破坏轨迹和简单的脆性卸荷假设出发，提出了一种断裂分析方法。对于正断裂能，半离散系统是有限元节点坐标阵的连续函数，使得半离散问题适定。在完全脆性极限下，公式简化为公认的不连续伽辽金/内聚区建模范式。该方法的鲁棒性源于裂纹尖端扩展处的数值通量的钝化，而通过一系列大规模断裂扩展问题证明了其通用性。

引用次数: 0

Graph neural networks with hybrid local-global attention for effective prediction of mechanical response in structures 局部-全局混合关注的图神经网络用于结构力学响应的有效预测

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-19 DOI: 10.1016/j.cma.2026.118753

Luca Patrignani, Silvestre T Pinho

Graph Neural Networks (GNNs) are emerging as a transformative approach for predicting mechanical response in structures by naturally encoding unstructured finite element meshes as graphs. While traditional finite element analysis (FEA) provides trusted solutions for mechanics problems, it encounters significant computational and scalability bottlenecks. Existing machine learning approaches using regular grids fail to capture the irregular nature of real-world meshes, whereas standard GNNs suffer from over-smoothing and limited long-range information propagation that compromise accuracy. To overcome these limitations, we present a Graph Transformer methodology that implements an encoder-processor-decoder framework augmented with a frequency-controlled hybrid local-global attention mechanism, which systematically bridges local mesh connectivity with global information awareness across the computational domain. Our approach integrates seamlessly with real-world FEA workflows through an automated FEM-to-GNN pipeline that converts FE simulations to graph representations and generates training datasets directly from commercial solvers, enabling rapid deployment across various engineering applications without manual preprocessing bottlenecks. We validate our approach on open holes Carbon Fibre Reinforced Polymer (CFRP) laminate plates under various loading conditions and geometric configurations, and extend validation to nonlinear woven composites exhibiting plasticity and progressive damage under shear-dominated loadings, employing systematic hyperparameter optimisation with Tree-structured Parzen Estimator (TPE) sampling and mesh convergence studies. The linear case demonstrates excellent predictive accuracy (

R^{2} = 0.98

,

R M S E = 0.00028

) with 70 ×  speedup over equivalent-accuracy FEA and

58 - 64 %

reduction in training and validation loss compared to standard message-passing GNN architectures without attention mechanisms, while the nonlinear case achieves

R^{2} = 0.97

(

R M S E = 0.0013

) with 660 ×  speedup.

图神经网络（gnn）正在成为一种变革性的方法，通过将非结构化有限元网格自然编码为图来预测结构的力学响应。虽然传统的有限元分析（FEA）为力学问题提供了可靠的解决方案，但它遇到了严重的计算和可扩展性瓶颈。使用规则网格的现有机器学习方法无法捕获现实世界网格的不规则性质，而标准gnn则存在过度平滑和有限的远程信息传播的问题，从而影响准确性。为了克服这些限制，我们提出了一种图形转换器方法，该方法实现了一个编码器-处理器-解码器框架，增强了频率控制的混合局部-全局注意机制，该机制系统地将局部网格连接与跨计算域的全局信息感知连接起来。我们的方法通过自动化的fem到gnn管道与现实世界的有限元工作流程无缝集成，该管道将有限元模拟转换为图形表示，并直接从商业求解器生成训练数据集，从而实现跨各种工程应用的快速部署，而无需手动预处理瓶颈。我们在各种载荷条件和几何构型下的开孔碳纤维增强聚合物（CFRP）层压板上验证了我们的方法，并将验证扩展到在剪切主导载荷下表现出塑性和渐进损伤的非线性编织复合材料，采用树结构Parzen Estimator （TPE）采样和网格收敛研究的系统超参数优化。线性情况显示出优异的预测精度（R2=0.98， RMSE=0.00028），比等效精度FEA加速70 × ，与没有注意机制的标准消息传递GNN架构相比，训练和验证损失减少58−64%，而非线性情况达到R2=0.97 (RMSE=0.0013)，加速660 × 。

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引用次数: 0

Discovering neural cohesive zone laws from displacement fields 从位移场发现神经内聚带规律

IF 7.3 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.2026.118733

Georgios Barkoulis Gavris, WaiChing Sun

Conventional inverse problems for cohesive zones often utilize homogenized responses of the effective media to identify a fixed set of material parameters prescribed a priori. However, the mixed-mode loading conditions of composites or natural materials may exhibit interfacial relations that are difficult to anticipate. This article presents a model-discovery framework for directly identifying cohesive zone models inferred from displacement fields across the interface, without fixing on a specific form of equations. We develop a differentiable version of the Material Point Method (MPM) with interface elements formulated to capture the traction-separation law at a pre-existing crack or bonded interface. Ensuring the differentiability of the MPM solver enables us to backpropagate the mismatch between simulated and measured (e.g., DIC/DVC) displacement fields through the time integrator and interface physics. Using only kinematics and equilibrium as constraints, numerical experiments suggest that the method may recover (i) a Mode-I traction-separation curve in a double-cantilever-beam test and (ii) a mixed-mode law for a circular interface shear test. These numerical results demonstrate that displacement-only experiments, combined with a differentiable solver, offer a promising pathway for identifying rich and potentially nonparametric cohesive laws.

传统的黏聚区反问题通常利用有效介质的均匀响应来识别一组先验规定的固定材料参数。然而，复合材料或天然材料的混合加载条件可能表现出难以预测的界面关系。本文提出了一个模型发现框架，用于直接识别从界面位移场推断的内聚区模型，而无需固定于特定形式的方程。我们开发了一种可微版本的物质点法（MPM），其中制定了界面元素，以捕获预先存在的裂纹或粘合界面的牵引分离规律。确保MPM求解器的可微性使我们能够通过时间积分器和界面物理反向传播模拟和测量（例如DIC/DVC）位移场之间的不匹配。仅使用运动学和平衡作为约束，数值实验表明，该方法可以恢复(i)双悬臂梁试验中的i型牵引-分离曲线和（ii）圆界面剪切试验的混合模式规律。这些数值结果表明，仅位移实验与可微求解器相结合，为识别丰富的潜在非参数内聚规律提供了一条有希望的途径。

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引用次数: 0

Generalized Eigenvalue stabilization for immersed explicit dynamics 浸入式显式动力学的广义特征值镇定

IF 7.3 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.2026.118727

Tim Bürchner , Lars Radtke , Sascha Eisenträger , Alexander Düster , Ernst Rank , Stefan Kollmannsberger , Philipp Kopp

Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass matrices of cut elements to cure their adverse impact on the critical time step size of the global system. We use spectral basis functions, specifically C⁰ continuous Lagrangian interpolation polynomials defined on Gauss-Lobatto-Legendre (GLL) points, which, in combination with its associated GLL quadrature rule, yield high-order convergent diagonal mass matrices for uncut elements. Moreover, considering cut elements, we combine the proposed GEVS approach with the finite cell method to guarantee definiteness of the system matrices. However, the proposed GEVS stabilization can directly be applied to other immersed boundary finite element methods. Numerical experiments demonstrate that the stabilization strategy achieves optimal convergence rates and recovers critical time step sizes of equivalent boundary-conforming discretizations. This also holds in the presence of weakly enforced Dirichlet boundary conditions using either Nitsche’s method or penalty formulations.

浸入式有限元离散化的显式时间积分严重受到切割不良单元的影响。在这篇贡献中，我们提出了一种广义特征值稳定（GEVS）策略，以消除切割单元质量矩阵对全局系统临界时间步长的不利影响。我们使用谱基函数，特别是定义在gass - lobatto - legendre （GLL）点上的C0连续拉格朗日插值多项式，结合其相关的GLL正交规则，生成未切割元素的高阶收敛对角质量矩阵。此外，考虑切割单元，我们将所提出的GEVS方法与有限单元法相结合，以保证系统矩阵的确定性。然而，该方法可直接应用于其他浸入式边界有限元方法。数值实验表明，该镇定策略能达到最优收敛速度，并能恢复等效边界一致性离散化的临界时间步长。这也适用于弱强制狄利克雷边界条件使用尼采的方法或惩罚公式。

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引用次数: 0

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 7.3 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

The Landau-de Gennes model for nematic liquid crystals provides the computational challenges of a second-order elliptic boundary value problem with reduced regularity in non-convex domains as well as exciting topological singularities called vortices for certain Dirichlet data of non-zero winding number for larger order parameter ℓ (named after Ginzburg). In two dimensions it simplifies to a Ginzburg-Landau model. The energy landscape in this non-convex minimisation problem is unexpectedly rich with many stationary points of the energy functional and the local solve faces severe difficulties. The nonconforming Crouzeix-Raviart finite elements have recently been shown to allow the computation of a guaranteed lower bound of the energy for sufficiently small meshes. We present an explicit residual-based a posteriori error estimate under the assumption that the discrete solution is sufficiently close to an isolated solution u. Our adaptive algorithm relies on a rigorous mathematical a posteriori error analysis for an asymptotic regime in the semi-linear problem and very small initial mesh-sizes that resolve the various stationary points of the energy. The emphasis is on the numerical verification of optimal convergence rates in computational benchmarks for the non-conforming Crouzeix-Raviart finite element method with lower-energy bounds. The validation of a physical model gives new insight into the energies of the two known global minimisers and four other local minimisers. The vortex localisation with adaptive mesh design is studied in a third example of winding number two. In all numerical experiments, the novel adaptive algorithm recovers optimal convergence rates.

向列液晶的Landau-de Gennes模型提供了非凸域上具有降低正则性的二阶椭圆边值问题的计算挑战，以及对于较大阶参数（以Ginzburg命名）的非零圈数Dirichlet数据（以Ginzburg命名）的令人兴奋的拓扑奇异点涡。在二维中，它简化为金兹堡-朗道模型。该非凸极小化问题的能量格局异常丰富，能量泛函的驻点众多，局部求解困难。非一致性的Crouzeix-Raviart有限元最近被证明允许计算足够小的网格的保证能量的下界。在假设离散解足够接近孤立解u的情况下，我们提出了一个显式的基于残差的后验误差估计。我们的自适应算法依赖于对半线性问题中渐近状态的严格数学后验误差分析和非常小的初始网格尺寸来解决能量的各个平稳点。重点对具有低能界的非一致性Crouzeix-Raviart有限元法在计算基准中的最优收敛速率进行了数值验证。物理模型的验证为两个已知的全局最小值和另外四个局部最小值的能量提供了新的见解。以卷绕数2为例，研究了自适应网格设计的涡定位问题。在所有的数值实验中，该自适应算法都恢复了最优的收敛速度。

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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