AI 中文总结
研究针对传统方法在捕捉材料梯度特性不足的问题，提出两步均匀化方案，先将3D模型分解为2D层用微观力学模型估计行为，再用变分和方法重建3D环境行为，应用于薄板均匀化处理。
AI 中文摘要
本研究旨在开发一种可应用于非均质分层介质的数值均匀化方法。传统尺度转换方法在捕捉某些材料的基本梯度特性方面存在不足。因此，这项工作的重点是构建一个考虑材料特性梯度的均匀化模型。为此，提出了一种两步均匀化方案。首先，将三维模型分解为多个二维非均质层，并使用诸如Hashin-Shtrikman界等微观力学模型估计每层的行为。其次，使用变分和方法重建三维环境的行为。最后，将该方法应用于对具有孔隙率梯度的薄板进行均匀化处理。
英文摘要
This study aims to develop a numerical homogenization method that can be applied to a heterogeneous stratified medium. Traditional scale transition methods are inadequate in capturing the essential gradient properties of some materials. Therefore, the focus of this work is to construct a homogenized model that considers the material property gradient. To achieve this, a two-step homogenization scheme is proposed. Firstly, the 3D model is decomposed into multiple 2D heterogeneous layers, and the behavior of each layer is estimated using a micro-mechanical model such as the Hashin-Shtrikman bounds. Secondly, a variational sum method is used to rebuild the behavior of the 3D environment. Finally, the method is applied to homogenize a thin plate with a porosity gradient.
