Multiscale modelling of strongly heterogeneous materials using geometry informed clustering

Abstract

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.

Topics & Concepts