Zhou Jing, Lin Hang, Qiu Kaishun, Ou Ke, Nie Fenghua
School of Resources and Safety Engineering, Central South University, Changsha 410083, China.
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2BU, UK.
Materials (Basel). 2025 Jun 6;18(12):2674. doi: 10.3390/ma18122674.
Concrete is a highly heterogeneous composite material, and accurately predicting its elastic modulus remains a major challenge in mechanical analysis. To address this, this study systematically investigates the predictive performance of several classical homogenization methods for estimating the effective elastic modulus of concrete, including the dilute approximation, self-consistent method, generalized self-consistent method, Mori-Tanaka model, differential method, as well as the Voigt and Reuss models. To enhance prediction accuracy, an improved computational framework is proposed based on an iterative strategy that enables dynamic updating of model parameters. This approach combines principles of mesomechanics with numerical simulation techniques and is implemented using Mathematica for both symbolic and numerical computations. The performance of the models is evaluated under varying aggregate volume fractions and aggregate-matrix stiffness combinations, and validated using multiple experimental datasets from the literature. The results show that the iterative strategy significantly improves the predictive accuracy of several models, reducing the maximum error by up to 30%. Further analysis indicates that the dilute method performs best at low aggregate volume fractions, the Mori-Tanaka model yields the most accurate results when the aggregates are stiff and moderately concentrated, and the generalized self-consistent method outperforms the standard version when the elastic moduli of the aggregate and matrix are similar.
混凝土是一种高度非均质的复合材料，准确预测其弹性模量仍然是力学分析中的一项重大挑战。为解决这一问题，本研究系统地研究了几种经典均匀化方法在估计混凝土有效弹性模量方面的预测性能，包括稀释近似法、自洽方法、广义自洽方法、森田模型、微分法以及Voigt模型和Reuss模型。为提高预测精度，基于一种能够动态更新模型参数的迭代策略，提出了一种改进的计算框架。该方法将细观力学原理与数值模拟技术相结合，并使用Mathematica进行符号和数值计算。在不同的骨料体积分数和骨料-基体刚度组合下对模型性能进行评估，并使用文献中的多个实验数据集进行验证。结果表明，迭代策略显著提高了几种模型的预测精度，最大误差降低了30%。进一步分析表明，稀释法在低骨料体积分数下表现最佳，当骨料刚度大且浓度适中时，森田模型产生的结果最准确，当骨料和基体的弹性模量相似时，广义自洽方法优于标准版本。
