Finite Elements in Analysis and Design最新文献_第7页

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

POD-RBF hyper-reduction method for fast finite element analysis of nonlinear dynamic problems 非线性动力问题快速有限元分析的POD-RBF超约简方法

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.2025.104455

Lam Vu-Tuong Nguyen, Hyun-Gyu Kim

This paper proposes a new hyper-reduction method for fast finite element analysis of nonlinear dynamic problems using proper orthogonal decomposition (POD) and radial basis function (RBF) interpolation. In the offline stage, displacement and internal force snapshots are collected from full-order FE simulations of nonlinear dynamic problems with training load cases. POD basis vectors are extracted from the displacement snapshots using the singular value decomposition (SVD). RBF coefficients for the internal force snapshots are also computed in the offline stage. The proposed POD-RBF hyper-reduction method efficiently estimates the reduced internal force vectors and the reduced tangent stiffness matrices using RBF interpolation with respect to reduced generalized coordinates. A snapshot selection strategy combining K-means clustering and greedy sampling algorithms is used to reduce the size of solution snapshots, which further enhances the efficiency of the present method. Numerical results show that the POD-RBF hyper-reduction method can be efficiently and effectively used to quickly solve nonlinear dynamic problems in a reduced-order space.

本文提出了一种利用正交分解和径向基函数插值的超约化方法，用于非线性动力问题的快速有限元分析。在离线阶段，从具有训练载荷的非线性动力问题的全阶有限元模拟中获取位移和内力快照。利用奇异值分解（SVD）从位移快照中提取POD基向量。在脱机阶段还计算了内力快照的RBF系数。提出的POD-RBF超约简方法利用RBF插值在广义约简坐标下有效地估计约简内力矢量和约简切刚度矩阵。采用k均值聚类和贪婪采样算法相结合的快照选择策略，减小了解快照的大小，进一步提高了方法的效率。数值结果表明，POD-RBF超约简方法可以高效、有效地快速求解降阶空间中的非线性动态问题。

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引用次数: 0

Sensitivity analysis of any hyperelastic evaluation functions coupled with adjoint method and automatic differentiation 结合伴随法和自动微分的超弹性评价函数敏感性分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-12 DOI: 10.1016/j.finel.2025.104440

S. Ogawa, K. Yonekura, K. Suzuki

This study introduces a new sensitivity analysis method for the topology optimization of a static hyperelastic material, which combines the adjoint variable method with automatic differentiation (AD). The adjoint variable method, frequently used in sensitivity analysis, requires mathematical formulations. Therefore, any changes in the design problem require reformulating the sensitivity analysis and updating the calculation program. The proposed method allows for the calculation of design sensitivities without being tied to specific evaluation functions, constitutive laws, or interpolation methods. This method effectively addresses the considerable memory requirements often associated with AD. To showcase the versatility of the proposed approach, we assessed both the compliance and the maximum von Mises stress of the second Piola–Kirchhoff stress tensor. We examined two hyperelastic materials: St. Venant-Kirchhoff, Neo-Hookean, and Mooney–Rivlin. For broader applicability, we used the discrete material optimization (DMO) method to address multimaterial problems, evaluating the adaptability in the interpolation of material properties based on the design variables. Through numerical examples, we validated the sensitivity analysis, analyzed the computational time and memory usage, and confirmed the efficacy of the proposed method. Examples involving two-dimensional problems highlight the practical application of this method in topology optimization.

提出了一种将伴随变量法与自动微分法相结合的静态超弹性材料拓扑优化灵敏度分析新方法。伴随变量法在灵敏度分析中经常使用，它需要数学公式。因此，设计问题的任何变化都需要重新制定灵敏度分析和更新计算程序。提出的方法允许计算设计灵敏度，而不需要绑定到特定的评估函数，本构律，或插值方法。这种方法有效地解决了通常与AD相关的大量内存需求。为了展示所提出方法的通用性，我们评估了第二Piola-Kirchhoff应力张量的顺应性和最大von Mises应力。我们研究了两种超弹性材料：St. Venant-Kirchhoff， Neo-Hookean和Mooney-Rivlin。为了更广泛的适用性，我们使用离散材料优化（DMO）方法来解决多材料问题，评估基于设计变量的材料性能插值的适应性。通过数值算例验证了灵敏度分析，分析了计算时间和内存使用情况，验证了所提方法的有效性。涉及二维问题的例子突出了该方法在拓扑优化中的实际应用。

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引用次数: 0

Geometric compensation of process-induced deformation in hybrid unidirectional/woven CFRP composites with multi-layup sequence using a physics-driven reverse deformation approach 基于物理驱动反向变形方法的复合材料过程变形几何补偿

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-11 DOI: 10.1016/j.finel.2025.104446

Dong-Hyeop Kim , Sang-Woo Kim

This study proposes a novel physics-based geometric compensation methodology to mitigate process-induced deformation (PID) in hybrid unidirectional/woven CFRP composite structures. Reverse deformation to compensate PID is induced by inverting the layup sequence, while the deformation magnitude is precisely adjusted using scaling factors, which are determined via fitting-based optimization and applied to thermochemical strain coefficients. The methodology is implemented through thermo-mechanical simulations using the finite element method, integrating cure-dependent material behavior, effective material properties, and thermal and chemical strains to accurately predict PID. The capability of the proposed methodology is demonstrated through extensive simulations of hybrid CFRP laminates, specifically incorporating multiple layup sequences and thickness configurations within a single laminate to reflect realistic structural design configurations encountered in composite manufacturing. In all simulation results, the optimized compensation reduced nodal displacements by more than 93%, resulting in significant improvements in both local and global geometric accuracy. The proposed methodology comprehensively considers complex cure-induced physical behaviors, enabling accurate, robust, and highly efficient nodal-level deformation compensation and providing practical applicability across a wide range of composite structures, including both unidirectional and textile-reinforced laminates.

本研究提出了一种新的基于物理的几何补偿方法来减轻单向/编织复合材料结构的过程诱导变形。通过反转铺层序列引起的逆变形补偿PID，通过基于拟合优化确定的比例因子精确调节变形大小，并将其应用于热化学应变系数。该方法是通过使用有限元方法进行热力学模拟来实现的，集成了固化相关材料行为，有效材料特性以及热应变和化学应变，以准确预测PID。所提出的方法的能力通过对混合CFRP层压板的广泛模拟得到了证明，特别是在单个层压板中结合了多个层叠序列和厚度配置，以反映复合材料制造中遇到的实际结构设计配置。在所有仿真结果中，优化后的补偿将节点位移减少了93%以上，从而显著提高了局部和全局几何精度。所提出的方法全面考虑了复杂的固化诱发的物理行为，实现了精确、鲁棒和高效的节点级变形补偿，并提供了广泛的复合材料结构的实际适用性，包括单向和纺织品增强层压板。

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引用次数: 0

Coupled crystal plasticity-cohesive zone modeling of rock salt viscoplasticity 岩盐粘塑性耦合晶体塑性-黏结区建模

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-09 DOI: 10.1016/j.finel.2025.104438

Nour Habib, Saber El Arem, Amine Ammar

Rock salt, owing to its viscoplastic behavior and structural integrity under high pressure, is a promising candidate for safe and large-scale underground energy storage. This study presents a comprehensive numerical framework for modeling the viscoplastic deformation of rock salt, accounting for both intragranular and grain boundary (GB) deformation mechanisms. Intragranular deformation is modeled using a crystal plasticity approach governed by a power-law relation, capturing the activity of crystallographic slip systems. Concurrently, a cohesive zone model (CZM) is introduced to simulate grain boundary sliding (GBS) and opening via a rate-dependent traction–separation law. This modeling strategy enables a detailed analysis of the coupled interplay between crystal plasticity and intergranular decohesion phenomena.

岩盐由于其在高压下的粘塑性特性和结构完整性，是安全、大规模地下蓄能的理想选择。本研究提出了一个综合的数值框架来模拟岩盐的粘塑性变形，同时考虑了粒内和晶界（GB）变形机制。使用幂律关系控制的晶体塑性方法来模拟晶内变形，捕捉晶体滑移系统的活动。同时，引入内聚带模型（CZM），通过速率相关的牵引分离规律来模拟晶界滑动（GBS）和打开。这种建模策略可以详细分析晶体塑性和晶间脱黏现象之间的耦合相互作用。

引用次数: 0

An expandable local and parallel two-grid finite element scheme for Stokes problem Stokes问题的可扩展局部并行双网格有限元格式

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-08 DOI: 10.1016/j.finel.2025.104375

Hongwei Song , Jianping Zhao , Yanren Hou

A novel locally parallel finite element algorithm for addressing the Stokes problem has been developed, leveraging the two-grid method and the unit splitting technique. This innovative algorithm boasts several key advantages: (1) it operates independently of the hyperapproximation property, enhancing its applicability across various scenarios; (2) the decomposition of regions is solely dependent on the unit splitting technique, simplifying the computational process; and (3) by incorporating constraints on local corrections, the algorithm employs the penalized form of the Stokes problem. This strategic choice facilitates the exclusive resolution of the velocity field function under specific assumptions, thereby streamlining the solution process and potentially reducing computational complexity.

利用双网格法和单元分裂技术，提出了一种求解Stokes问题的局部并行有限元算法。该创新算法具有以下几个关键优势：(1)它独立于超逼近性质运行，增强了其在各种场景中的适用性；(2)区域分解完全依赖于单元分裂技术，简化了计算过程；(3)通过对局部修正的约束，该算法采用Stokes问题的惩罚形式。这种策略选择有助于在特定假设下对速度场函数进行独家解析，从而简化求解过程并可能降低计算复杂性。

引用次数: 0

An efficient higher-order triangulation based micromechanical model for fiber composites 基于高阶三角剖分的纤维复合材料细观力学模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-07 DOI: 10.1016/j.finel.2025.104441

Jamal F. Husseini , Eric J. Carey , Evan J. Pineda , Brett A. Bednarcyk , Farhad Pourkamali-Anaraki , Scott E. Stapleton

Composite microstructures are susceptible to localized stress concentrations between close or touching fibers where failure can initiate and propagate. Typically, representative volume elements are used to predict mechanical response by simulating random microstructure arrangements under different loading configurations. However, these simulations can be prohibitively expensive when considering large microstructures or closely packed fibers. The current work aims to provide a computationally efficient method for predicting homogenized and local properties of composite microstructures through a novel finite element mesh referred to as the fixed triangulation-mesh model. This triangulation-based meshing algorithm uses configured element sizes where the highest stresses occur and higher order elements to capture stress gradients between closely packed fibers. An efficient homogenization technique to fully characterize the stiffness matrix of the composite without the need for individual load perturbations or stress integration was derived and implemented. A progressive damage model using the smeared crack approach was implemented with higher order elements to simulate post-peak softening. The results for stiffness, transverse strength, and in-plane shear strength were verified against the high fidelity generalized method of cells for different microstructures of varying fiber volume fractions. Then, a comparison was made to a refined mesh finite element model with linear elements and a toughened matrix. The fixed triangulation-mesh model showed good agreement between the high fidelity generalized method of cells and linear element models, and computation time was reduced by approximately 104 times for the low-toughness matrix, and 55 times for the toughened matrix.

复合材料微结构容易受到紧密或接触纤维之间的局部应力集中的影响，在那里破坏可以开始和传播。通常，代表性体积单元通过模拟不同加载配置下的随机微观结构排列来预测力学响应。然而，当考虑到大型微观结构或紧密堆积的纤维时，这些模拟可能会非常昂贵。目前的工作旨在通过一种称为固定三角网格模型的新型有限元网格，提供一种计算效率高的方法来预测复合材料微结构的均质和局部特性。这种基于三角的网格划分算法使用最高应力发生的配置单元尺寸和高阶单元来捕获紧密排列的纤维之间的应力梯度。推导并实现了一种无需单独载荷扰动或应力积分即可充分表征复合材料刚度矩阵的有效均匀化技术。采用涂抹裂纹法建立了渐进式损伤模型，采用高阶元模拟峰后软化。采用高保真广义胞元法对不同纤维体积分数的微观结构进行了刚度、横向强度和面内抗剪强度的验证。在此基础上，对线性单元和增韧矩阵的精细化网格有限元模型进行了比较。所建立的固定三角网格模型与线形单元模型具有较好的一致性，低韧性矩阵计算时间缩短约104倍，增韧矩阵计算时间缩短约55倍。

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引用次数: 0