Multiscale modelling of strongly heterogeneous materials using geometry informed clustering
Multiscale modelling of strongly heterogeneous materials using geometry informed clustering
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DOI：
10.1016/j.ijsolstr.2023.112369
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发表时间：
2023-09
影响因子：
3.6
通讯作者：
J. Selvaraj;Bassam El Said
中科院分区：
文献类型：
--
作者：
J. Selvaraj;Bassam El Said
在宏观尺度上对具有复杂内部结构的非均质材料进行计算高效且数值精确的建模是当前的一个问题。例如，在工程材料（如3D编织复合材料）中，保留材料结构的描述对于获得准确的刚度预测非常重要。然而，计算成本的增加成比例的中尺度细节的模拟水平。为了使结构尺度上的有效和准确的计算，提出了一种多尺度的方法，可以识别可重复的模式，在中尺度，并有效地在宏观尺度上表示它们。该方法具有两个重要的新颖性，（i）使用数据压缩算法k均值聚类以3D Voronoi单元的形式在离线阶段识别和存储可重复模式的方法。这提高了识别与最小数量的数据簇和最小化的网格尺寸的影响，和（ii）的方法来选择最相似的Voronoi细胞从中尺度数据库在在线阶段使用图像配准和k-d树数据结构。这使得计算不需要明确地模拟中尺度细节，并降低了计算成本，否则需要。所提出的方法进行了验证对三维编织单胞和三点弯曲的例子。此外，通过分析以前未存储在数据库中的编织架构来测试找到可重复模式的能力。
Computationally efficient and numerically accurate modelling of heterogeneous materials with complex internal architectures at the macroscale is a current problem. For instance, in engineering materials such as 3D woven composites, retaining the description of material architectures is important to obtain an accurate prediction of stiffness. However, computational cost increases in proportion to the level of mesoscale details modelled. To enable efficient and accurate calculations on the structural scale, a multiscale method that can identify repeatable patterns in the mesoscale and represent them efficiently at the macroscale is proposed. This method has two important novelties,(i) a method to identify and store repeatable patterns during offline stage in the form of 3D Voronoi cells using a data compression algorithm, k-means clustering. This improves the identification with a minimum number of data clusters and minimises the effects of mesh sizes, and (ii) a method to select most similar Voronoi cells from the mesoscale database during online stage using image registration and k-d tree data structure. This enables computations being performed without explicitly modelling mesoscale details and reduces the computational cost that are otherwise required. The proposed method is validated against 3D woven unit-cell and three-point bending examples. Furthermore, the ability to find repeatable patterns is tested by analysing a woven architecture previously not stored in the database.