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| 基于快速傅里叶变换方法的混凝土有效弹性模量高效数值预测 |
| Efficient Numerical Prediction of Concrete Effective Elastic Modulus Based on the Fast Fourier Transform Method |
| 投稿时间：2025-09-14 修订日期：2025-10-10 |
| DOI： |
| 中文关键词: 混凝土 弹性模量 快速傅里叶变换 数值均质化方法 RSE建模 |
| 英文关键词:Concrete Elastic Modulus Fast Fourier Transform Numerical Homogenization Method RSE Modeling |
| 基金项目:安徽省自然科学基金；湖北省自然科学基金；国家自然科学基金 |
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| 中文摘要: |
| 基于代表体积单元（Representative Volume Element，RVE）的均质化方法可在细观尺度上实现对混凝土宏观力学性能的有效预测，传统有限元方法（Finite Elem Method，FEM）在实现时依赖于网格划分数量，在需要划分精细网格时其计算效率将显著下降。文章基于快速傅里叶变换（Fast Fourier Transform，FFT）数值均质化方法，构建网格像素点离散模型，成功规避了网格划分与刚度矩阵迭代过程，较好地克服了这一问题。首先基于随机顺序展开（RSE）算法建立了包含骨料、砂浆、界面过渡区（ITZ）及孔隙的四相细观结构模型，其次通过单轴拉伸与纯剪切载荷下的数值模拟，对FFT与FEM的计算精度进行对比验证。具体讨论了骨料体积分数（20%-50%）、ITZ体积分数（1%-7%）及孔隙率（0%-5%）对有效弹性模量的影响规律，结果表明：骨料体积分数每增加10%，弹性模量提升9.3%-10%；随着孔隙增加弹性模量呈线性下降。通过与经典解析模型、渐近均质化方法及实验数据对比，FFT方法预测结果相对误差均小于5%。研究成果为混凝土多相复合材料性能预测提供了高效可靠的数值分析工具。 |
| 英文摘要: |
| The homogenization method based on the Representative Volume Element (RVE) enables the prediction of macroscopic effective mechanical properties of concrete at the mesoscopic scale. Traditional Finite Element Method (FEM) implementations exhibit significant computational inefficiency when requiring fine mesh discretization due to their inherent dependence on mesh density. This study addresses this limitation by employing a Fast Fourier Transform (FFT)-based numerical homogenization approach, which establishes a pixel-discretized model that effectively circumvents both mesh generation and stiffness matrix iteration processes. A four-phase mesostructural model incorporating aggregates, mortar, Interface Transition Zone (ITZ), and pores was first developed using the Random Sequential Expansion (RSE) algorithm. Subsequently, numerical simulations under uniaxial tension and pure shear loading were conducted to compare and validate the computational accuracy of FFT and FEM. The study specifically investigated the influence patterns of aggregate volume fraction (20%-50%), ITZ volume fraction (1%-7%), and porosity (0%-5%) on the effective elastic modulus. Key findings indicate: a 10% increase in aggregate volume fraction enhances elastic modulus by 9.3%-10%; elastic modulus exhibits linear degradation with increasing porosity. Comparative analyses with classical analytical models, asymptotic homogenization methods, and experimental data confirm that FFT predictions maintain relative errors below 5%. This research establishes an efficient and reliable numerical framework for performance prediction of multi-phase concrete composites, demonstrating significant advantages in computational effectiveness and predictive accuracy over conventional approaches. The methodology provides critical insights for microstructure-property relationship analysis in heterogeneous materials. |
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