Finite Elements in Analysis and Design最新文献_第6页

Derivative-enhanced Bayesian optimization for broad-bandgap phononic metamaterials with hypercomplex automatic differentiation 具有超复杂自动微分的宽带隙声子超材料的导数增强贝叶斯优化

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-20 DOI: 10.1016/j.finel.2025.104461

Juan C. Velasquez-Gonzalez , Juan David Navarro , Mauricio Aristizabal , Harry Millwater , David Restrepo

The design of Phononic Metamaterials (PM) with unique dynamic behaviors and wave propagation characteristics remains a significant challenge due to the highly non-linear relationships between design parameters and response. The arrangement of the periodic unit cells within PM is crucial for determining their dynamic behavior, making optimization methods essential for the design and development of these materials. These methods are used to tailor bandgap characteristics such as bandwidth and frequency location by optimizing the unit cell’s geometric parameters. However, existing approaches often suffer from slow convergence rates, entrapment in local minimum, or require numerous expensive evaluations of the objective function. To address these challenges, this work proposes using a novel derivative-enhanced Bayesian optimization (DEBO) framework that integrates Hypercomplex Automatic Differentiation (HYPAD) with a Gradient-Enhanced Gaussian Process (GEGP) interpolator surrogate model. This combination enables the accurate and efficient computation of objective function sensitivities, resulting in more reliable and data-efficient surrogate models. As a result, DEBO significantly improves the robustness of BO against local minima, which is particularly beneficial for the non-convex optimization problem characteristic of PM design. The framework is applied to optimize the geometry of a two-dimensional cross-shaped unit cell, maximizing bandgap width at low mid-frequencies. By consistently converging to the global optimum, we demonstrate that DEBO outperforms traditional methods, including derivative-free Bayesian optimization, gradient-based numerical optimization, and metaheuristics. Furthermore, experimental validation of the optimized geometry aligns closely with numerical predictions, confirming the effectiveness of the approach.

由于设计参数与响应之间的高度非线性关系，具有独特动态行为和波传播特性的声子超材料（PM）的设计仍然是一个重大挑战。周期单元胞在PM内的排列对于确定其动态行为至关重要，因此优化方法对于这些材料的设计和开发至关重要。这些方法通过优化单元的几何参数来定制带隙特性，如带宽和频率位置。然而，现有的方法往往存在收敛速度慢、陷入局部最小值或需要对目标函数进行大量昂贵的评估的问题。为了解决这些挑战，本研究提出了一种新的导数增强贝叶斯优化（DEBO）框架，该框架将超复杂自动微分（HYPAD）与梯度增强高斯过程（GEGP）插值器代理模型集成在一起。这种组合使得目标函数灵敏度的精确和高效的计算，从而产生更可靠和数据高效的代理模型。因此，DEBO显著提高了BO对局部极小值的鲁棒性，特别有利于PM设计的非凸优化问题。该框架被应用于优化二维十字形单元电池的几何形状，最大化中低频带隙宽度。通过持续收敛到全局最优，我们证明了DEBO优于传统方法，包括无导数贝叶斯优化，基于梯度的数值优化和元启发式。此外，优化几何形状的实验验证与数值预测密切一致，证实了该方法的有效性。

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引用次数: 0

Uzawa methods for the coupling of free flow and porous medium flow 自由流动与多孔介质流动耦合的Uzawa方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-19 DOI: 10.1016/j.finel.2025.104460

Qingzhou Wang, Guangzhi Du

In this paper, two kinds of Uzawa algorithms are proposed and investigated to solve the coupling of free flow and porous medium flow, which is modeled by the mixed Stokes-Darcy problem with the Beavers-Joseph-Saffman interface condition. The first Uzawa method as an iterative method can avoid solving the saddle point problem at each iteration step. The second method aims to optimize the first one by combining the two-grid strategy. Rigorously theoretical analysis is established for these two algorithms. Some numerical experiments are carried out to verify the theoretical findings.

本文提出并研究了两种Uzawa算法来解决自由流动和多孔介质流动的耦合问题，该问题由带有beaver - joseph - saffman界面条件的混合Stokes-Darcy问题建模。第一种Uzawa方法作为一种迭代方法，可以避免在每个迭代步骤都求解鞍点问题。第二种方法旨在通过结合两网格策略对第一种方法进行优化。对这两种算法进行了严格的理论分析。通过数值实验对理论结果进行了验证。

引用次数: 0

The polytopal composite element method for finite strain hyperelastic problems 有限应变超弹性问题的多面体复合元法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-18 DOI: 10.1016/j.finel.2025.104436

Y. Li , B.W. Wang , Z.Q. Feng

Polygonal elements have emerged as a cutting-edge discretization paradigm in computational solid mechanics, demonstrating significant potential for linear elasticity analyses. This work pioneers a robust computational framework extending polytopal composite elements to finite-strain hyperelasticity. The key idea by constructing a polynomial projection using least squares approximation for linear-compatible strain fields, followed by extending the derived linear operator to large deformation cases involving nonlinear strain. The computational framework of this method is fundamentally consistent with finite elements, allowing it to adapt and extend to various nonlinear problems. Through several numerical investigation we show that this approach maintains the excellent accuracy, convergence and stability, and is potentially offering new insights and references for polygonal elements in future nonlinear problems.

在计算固体力学中，多边形单元已经成为一种前沿的离散化范式，在线性弹性分析中显示出巨大的潜力。这项工作开创了一个强大的计算框架，将多面体复合元素扩展到有限应变超弹性。关键思想是利用最小二乘近似构造线性相容应变场的多项式投影，然后将导出的线性算子推广到涉及非线性应变的大变形情况。该方法的计算框架与有限元基本一致，使其能够适应和扩展到各种非线性问题。数值研究表明，该方法保持了良好的精度、收敛性和稳定性，为今后求解多边形单元的非线性问题提供了新的思路和参考。

引用次数: 0

Statistical topology optimization for damage identification for orthotropic and cellular structures 基于统计拓扑优化的正交各向异性和细胞结构损伤识别

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-17 DOI: 10.1016/j.finel.2025.104459

Jae Yeop Na, Sol Ji Han, EunBin Park, Gil Ho Yoon

This study aims to enhance the accuracy and robustness of structural damage identification by extending the statistical topology optimization (STO) framework. While previous STO research has primarily focused on isotropic materials, its applicability to orthotropic and cellular structures has not been fully explored. To broaden its scope, the approach applies the STO framework to models with directional stiffness and periodic microstructures. Multiple topology optimization runs are performed under varied frequency excitations, and consistent damage patterns are extracted using density-based spatial clustering (DBSCAN). Unlike earlier studies, this work introduces genetic algorithm-based tuning of DBSCAN parameters to improve clustering reliability and reduce user dependency. Damage is modeled differently according to the structure type: through density reduction or principal direction rotation in orthotropic models, and by adjusting the void size within cellular unit cells, from which the effective material properties are derived through polynomial-based numerical homogenization. Numerical examples confirm that the framework accurately localizes damage under complex material conditions and achieves superior performance compared to conventional methods.

本研究旨在通过扩展统计拓扑优化（STO）框架来提高结构损伤识别的准确性和鲁棒性。虽然之前的STO研究主要集中在各向同性材料上，但其对正交异性和细胞结构的适用性尚未得到充分探索。为了扩大其范围，该方法将STO框架应用于具有定向刚度和周期性微观结构的模型。在不同频率激励下进行多次拓扑优化运行，并使用基于密度的空间聚类（DBSCAN）提取一致的损伤模式。与早期的研究不同，这项工作引入了基于遗传算法的DBSCAN参数调优，以提高聚类可靠性并减少用户依赖性。根据结构类型的不同，对损伤进行了不同的建模：在正交异性模型中，通过密度减小或主方向旋转，以及通过调整细胞单元胞内的空隙大小，通过基于多项式的数值均匀化推导出有效的材料特性。数值算例验证了该框架在复杂材料条件下的损伤定位精度，取得了优于传统方法的性能。

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引用次数: 0

Using Gappy-POD to derive a reduced quadrature rule 利用Gappy-POD导出了一种简化正交规则

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-17 DOI: 10.1016/j.finel.2025.104439

Shigeki Kaneko

Among various reduced-order modeling techniques, the combination of low-dimensional approximation using proper orthogonal decomposition (POD) and the Galerkin method is a promising approach. However, the POD–Galerkin method has a well-known drawback that the computation of the Galerkin projection is heavy, which overshadows the reduction of computational cost for solving simultaneous equations. To speed up the reduced-order model analysis, a hyper-reduction method, which approximately calculates the Galerkin projection, has been introduced. Although several hyper-reduction methods have been proposed up to date, currently, a reduced quadrature (RQ) method is widely used because of its stability. In the conventional RQ method, a sparse representation problem with

ℓ_{0}

pseudo-norm minimization under the non-negativity constraint is solved to derive an RQ rule. However, it is difficult to control the number of non-zero entries in the weight vector of RQ and the error of least-squares fitting. The purpose of the present study was to develop a new RQ derivation method to overcome this difficulty. The formulation of the new method is not based on the sparse representation but on Gappy-POD, which is a sparse sampling technique and was originally proposed for image reconstruction. To demonstrate the new method, we applied it to nonlinear dynamic structural analysis with geometrical nonlinearity and to incompressible viscous flow analysis. The results confirmed that the new method can provide a more accurate RQ rule than can the conventional method.

在各种降阶建模技术中，利用适当正交分解（POD）的低维近似与伽辽金方法相结合是一种很有前途的方法。然而，POD-Galerkin方法有一个众所周知的缺点，即Galerkin投影的计算量很大，这掩盖了求解联立方程的计算成本的降低。为了加快降阶模型的分析速度，引入了一种近似计算伽辽金投影的超约简方法。虽然目前已经提出了几种超还原方法，但目前，还原正交法（RQ）因其稳定性被广泛应用。在传统的RQ方法中，求解了非负性约束下具有0伪范数最小化的稀疏表示问题，导出了RQ规则。然而，很难控制RQ的权向量中非零条目的个数和最小二乘拟合的误差。本研究的目的是开发一种新的RQ推导方法来克服这一困难。新方法的制定不是基于稀疏表示，而是基于Gappy-POD， Gappy-POD是一种稀疏采样技术，最初是为图像重建而提出的。为了证明新方法的有效性，我们将其应用于具有几何非线性的非线性动力结构分析和不可压缩粘性流动分析。结果表明，该方法能提供比传统方法更精确的RQ规则。

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引用次数: 0

Integrating multiplicative Nitsche's method with HIGA platform: Isogeometric analysis of hydraulic tunnels lining thickness 基于HIGA平台的乘Nitsche法积分：水工隧洞衬砌厚度等几何分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-17 DOI: 10.1016/j.finel.2025.104445

Mingchao Li , Yixin Wang , Mengxi Zhang , Ang Li , Stéphane P.A. Bordas , Peng Yu , Yinpeng He

Isogeometric Analysis (IGA) is a novel numerical analysis method that can occupy the gap between geometrical and analytical models. IGA, when integrated with splicing algorithms, enables the splicing and coupling of multiple computational domains. This approach offers a novel solution for simulating complex hydraulic tunnels and similar practical engineering applications involving complex computational models. In this paper, a multiplicative Nitsche's method is proposed. The method determines the stabilization parameter

α

for contact models through a precise control coefficient computation equation, based on a chosen weighting parameter

γ

, and is integrated into the Hydraulic IsoGeometric Analysis (HIGA) platform. This method addresses the instability issues typically associated with the traditional Nitsche's method, which arise from empirically selected control parameters. Compared with the conventional Nitsche's method, multiplicative Nitsche's method significantly enhances the accuracy and stability of IGA while maintaining computational efficiency, according to the results of several 2D and 3D numerical examples. To demonstrate the engineering application prospects of multiplicative Nitsche's method, the proven applicability of IGA with the multiplicative Nitsche's method is showcased through a static analysis of a hydraulic tunnel model with complex geological features. The results demonstrate the method's capability to handle large-scale, multi-patch engineering problems, underscoring its potential for simulating and analyzing hydraulic tunnels under complex topographical and geological conditions.

等几何分析（IGA）是一种新颖的数值分析方法，可以填补几何模型与解析模型之间的空白。当IGA与剪接算法集成时，可以实现多个计算域的剪接和耦合。该方法为复杂水工隧道的模拟和涉及复杂计算模型的类似实际工程应用提供了一种新的解决方案。本文提出了一种乘法Nitsche方法。该方法基于选定的加权参数γ，通过精确的控制系数计算方程确定接触模型的稳定参数α，并集成到液压等几何分析（HIGA）平台中。该方法解决了通常与传统Nitsche方法相关的不稳定性问题，这些问题源于经验选择的控制参数。若干二维和三维数值算例结果表明，与传统的Nitsche方法相比，乘法Nitsche方法在保持计算效率的同时，显著提高了IGA的精度和稳定性。为了证明乘法Nitsche方法的工程应用前景，通过对具有复杂地质特征的水工隧道模型进行静力分析，证明了IGA与乘法Nitsche方法的适用性。结果表明，该方法具有处理大规模、多地块工程问题的能力，强调了其在复杂地形和地质条件下模拟和分析水工隧洞的潜力。

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引用次数: 0

An implicit coupled method of scaled boundary finite element and peridynamics for fracture analysis 断裂分析的尺度边界有限元与周动力隐式耦合方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-16 DOI: 10.1016/j.finel.2025.104453

Wei Yu , Jun Liu , Haibo Wang , Lei Qin , Lei Gan , Quansheng Zang , Wenbin Ye

In this paper, firstly, an innovative multi-scale coupled method based on scaled boundary finite element (SBFEM) and peridynamics (PD) is proposed for predicting fracture propagation of elastic bodies in static/quasi-static problems. The coupled process in this method is established not by transition regions (overlapping regions), but by force equilibrium conditions at common points, which greatly reduces the complexity of modeling. The SBFEM is introduced to model the non-cracked domain and the PD is applied to model the cracked domain in this method. This reduces a great deal of computational time compared to the PD method. Moreover, the limitations of surface effects and troublesome load conditions for the PD calculation can be eliminated or mitigated. The SBFEM is different from FEM in that only the boundary of elastic bodies is discretized. Therefore, the computational efficiency is further improved compared with the coupled method of the FEM and PD. The SBFEM is also different from BEM in that it does not need to provide the fundamental solution and compute the singular integrals. Hence, the method is more convenient for solving complex problems compared with the coupled method of the BEM and PD. The accuracy of this coupled method is demonstrated by one example of accuracy analysis for single coupled and multiple coupled interfaces, and three examples of fracture propagation analysis (two pre-determined cracks and one spontaneous crack). The results show that the coupled method has a high accuracy. Furthermore, it is recommended that the spacing of the common points be set equal to the spacing of the PD material points so that the accuracy of the coupled method can be maximized. Finally, the cracking forms of a square plate with different shaped holes are explored. It shows that the proposed coupled method has potential for engineering applications.

本文首先提出了一种基于尺度边界有限元（SBFEM）和周动力学（PD）的多尺度耦合方法，用于静力/准静力问题中弹性体断裂扩展的预测。该方法不是通过过渡区域（重叠区域）建立耦合过程，而是通过共同点处的力平衡条件建立耦合过程，大大降低了建模的复杂性。该方法引入SBFEM对非裂纹区域进行建模，并采用局部局部化方法对裂纹区域进行建模。与PD方法相比，这大大减少了计算时间。此外，可以消除或减轻表面效应的限制和PD计算的麻烦负载条件。SBFEM与有限元法的不同之处在于它只对弹性体的边界进行离散化。因此，与有限元与PD耦合方法相比，进一步提高了计算效率。SBFEM与边界元法的不同之处在于，它不需要提供基本解和计算奇异积分。因此，该方法比边界元与PD的耦合方法更便于求解复杂问题。通过1个单耦合和多耦合界面精度分析算例以及3个断裂扩展分析算例（2个预定裂纹和1个自发裂纹）验证了该耦合方法的准确性。结果表明，该耦合方法具有较高的精度。此外，建议将公共点的间距设置为与PD材料点的间距相等，以使耦合方法的精度最大化。最后，探讨了不同孔型的方形板的开裂形式。表明所提出的耦合方法具有工程应用的潜力。

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引用次数: 0

Comparison of parametric model order reduction methods to solve magneto-quasistatic and electro-quasistatic problems 参数模型降阶方法解决磁准静态和电准静态问题的比较

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-15 DOI: 10.1016/j.finel.2025.104444

Wei Chen, Thomas Henneron, Stéphane Clénet

In this paper, we compare two parametric model order reduction methods, the multi-moment matching method and the interpolation of projection subspaces method for the magneto-quasistatic (MQS) and electro-quasistatic (EQS) problems derived from Maxwell’s equations and discretized with the Finite Element (FE) method. The two problems considered are both governed by the differential–algebraic equations. The material characteristic parameters as well as the geometry parameters have been considered. The applications are two realistic test cases: an EQS model of a transformer bushing under insulation defect uncertainty and a MQS model of a planar inductor with geometric and material variations. The result shows that both methods approximate well global quantities, such as the current or the voltage, as well as the local quantities like field distributions. The multi-moment matching method remains always faster in the online stage, since the reduced basis is not parameter dependent, requiring no reduced basis calculation. The multi-moment matching method requires an affine decomposition of the FE model, which is not easy to obtain when considering geometry parameters. A hybrid method is proposed and tested leading to more accurate results than the interpolation of projection subspaces method but much easier to implement than the multi-moment matching method.

本文比较了两种参数模型降阶方法，即多矩匹配法和投影子空间插值法，用于求解由麦克斯韦方程组导出并用有限元法离散的磁准静态（MQS）和电准静态（EQS）问题。所考虑的两个问题都由微分代数方程控制。考虑了材料的特性参数和几何参数。应用了两个实际的测试案例：绝缘缺陷不确定情况下变压器套管的EQS模型和具有几何和材料变化的平面电感器的MQS模型。结果表明，这两种方法都能很好地逼近电流或电压等全局量以及场分布等局部量。多矩匹配方法在在线阶段总是更快，因为约简基不依赖于参数，不需要计算约简基。多矩匹配方法需要对有限元模型进行仿射分解，在考虑几何参数的情况下，这种方法不容易得到。提出并测试了一种混合方法，其结果比投影子空间插值法更精确，但比多矩匹配法更容易实现。

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引用次数: 0

Mesoscale FEM model of concrete: Statistical assessment of inherent stress concentrations in dependence on phase heterogeneity 混凝土的中尺度有限元模型：依赖于相非均质性的固有应力集中的统计评估

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-13 DOI: 10.1016/j.finel.2025.104442

Jan Mašek, Petr Miarka

Concrete heterogeneity originates from its production process, which involves bonding aggregates with a binder matrix. This study presents a mesoscale finite element model (MFEM) that offers detailed insights into the fracture process at the aggregate–cement matrix interface, focusing on one of concrete’s key properties: its mechanical response. Unlike discrete models, which often average out critical stress concentrations within the mesostructure, the MFEM approach captures detailed stress distributions, revealing localized effects crucial for understanding damage evolution. Although computationally more demanding, the MFEM leverages modern high-performance computing (HPC) to provide a detailed description of the stress field and material damage across different phases and interfaces. The proposed modeling framework integrates a collision-checked aggregate generation procedure, Voronoi-based mesostructure construction, and adaptive 3D meshing, forming a reusable methodology for stress analysis in heterogeneous composites. This approach offers transparent, physically interpretable parameterization of phase properties in contrast to black-box discrete models. Another methodological contribution is the statistical post-processing of stress data using histogram-based analysis across cross-sectional planes. This enables quantitative evaluation of stress concentration distributions, providing valuable insights into the mesoscale mechanical response and serving as a useful visualization tool for researchers working on heterogeneous material modeling. Various matrix-to-aggregate stiffness ratios are considered to evaluate the influence of material heterogeneity on the stress field. The results are based on a statistical evaluation of stress concentrations arising from variations in material stiffness. The model is applied to investigate the impact of using recycled crushed bricks as aggregates in concrete, with particular emphasis on the stiffness mismatch between the matrix and aggregates. The study examines how this stiffness contrast affects stress distribution and ultimately influences the composite’s failure mechanisms. Beyond this application, the MFEM framework provides a foundation for further investigations into nonlinear fracture processes, fatigue analysis, and mechanical optimization of alternative aggregate-matrix systems.

混凝土的非均质性源于其生产过程，该过程涉及将骨料与粘结剂基体粘合。本研究提出了一个中尺度有限元模型（MFEM），该模型提供了对骨料-水泥基体界面断裂过程的详细见解，重点关注混凝土的关键特性之一：力学响应。与离散模型不同，离散模型通常在细观结构中平均临界应力集中，而MFEM方法可以捕获详细的应力分布，揭示对理解损伤演变至关重要的局部效应。尽管计算要求更高，但MFEM利用现代高性能计算（HPC）提供了不同阶段和界面的应力场和材料损伤的详细描述。所提出的建模框架集成了碰撞检查聚合生成程序、基于voronoi的细观结构构建和自适应3D网格划分，形成了一种可重复使用的方法，用于异质复合材料的应力分析。与黑盒离散模型相比，这种方法提供了透明的、物理上可解释的相位特性参数化。另一个方法上的贡献是利用基于直方图的跨横截面分析对应力数据进行统计后处理。这可以定量评估应力集中分布，为中尺度力学响应提供有价值的见解，并为研究异质材料建模的研究人员提供有用的可视化工具。考虑不同的基体-骨料刚度比来评估材料非均质性对应力场的影响。结果是基于由材料刚度变化引起的应力集中的统计评估。该模型用于研究在混凝土中使用再生碎砖作为骨料的影响，特别强调基质和骨料之间的刚度不匹配。该研究考察了这种刚度对比如何影响应力分布并最终影响复合材料的破坏机制。除此之外，MFEM框架还为进一步研究非线性断裂过程、疲劳分析和替代集料基质系统的力学优化提供了基础。

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引用次数: 0

A simplified gradient-enhanced damage model based on energy limiters for crack propagation under time-dependent loading 基于能量限制器的时效加载下裂纹扩展梯度增强损伤简化模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-13 DOI: 10.1016/j.finel.2025.104443

Hung Thanh Tran

This paper presents the development and investigation of a simplified energy limiter-based nonlocal damage model for dynamic crack propagation in brittle media. The key idea underlying the proposed model is that crack growth under impact loading is primarily influenced by the tensile component of the strain tensor. Consequently, the energy-based damage-driving term is simplified to a strain-based counterpart, which is integrated using the first principal strain. This simplification leads to a model that is not only easier to implement but also more effective in capturing dynamic crack propagation compared to the original theory. In addition, the computational framework incorporates an energy limiter-based gradient damage formulation with a damage threshold, enabling natural crack initiation and propagation while significantly reducing spurious damage. One of the distinctive features of the proposed approach is the treatment of the nonlocal crack field as a primary unknown, alongside displacements. This allows the use of identical shape functions for both fields within the finite element analysis, enhancing consistency and computational efficiency. Consistent with classical continuum damage mechanics, the model can accurately simulate arbitrary and complex multiple crack paths, including three-dimensional (3D) crack propagation. Furthermore, to provide a more efficient numerical framework under time-dependent loading conditions with complex crack patterns, an explicit dynamic fracture algorithm is employed. This algorithm utilizes the central difference method, the row-sum technique for mass lumping, and a consistent procedure for updating the kinematic and damage-related terms. The advantages and modeling capabilities of the proposed strain-based gradient-enhanced damage formulation are demonstrated through representative numerical examples of dynamic fracture under shear, tension, and compression loading scenarios.

本文提出了一种基于能量限制器的脆性介质动态裂纹扩展非局部损伤简化模型。提出的模型的关键思想是，裂纹在冲击载荷下的扩展主要受应变张量的拉伸分量的影响。因此，基于能量的损伤驱动项被简化为基于应变的对应项，并使用第一主应变进行积分。与原始理论相比，这种简化导致的模型不仅更容易实现，而且在捕获动态裂纹扩展方面也更有效。此外，该计算框架结合了一个基于能量限制器的梯度损伤公式，该公式具有损伤阈值，可以实现自然裂纹的起始和扩展，同时显着减少虚假损伤。该方法的一个显著特点是将非局部裂纹场与位移一起作为主要未知数处理。这允许在有限元分析中对两个领域使用相同的形状函数，增强一致性和计算效率。该模型与经典连续介质损伤力学一致，能够准确模拟任意复杂的多重裂纹路径，包括三维裂纹扩展。此外，为了在具有复杂裂纹模式的时变加载条件下提供更有效的数值框架，采用了显式动态断裂算法。该算法利用中心差分法、行和技术进行质量集总，并采用一致的程序更新运动学和损伤相关项。通过具有代表性的剪切、拉伸和压缩加载情景下的动态断裂数值实例，证明了所提出的基于应变的梯度增强损伤公式的优势和建模能力。

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引用次数: 0