An adaptive clustering FE² multiscale framework for heterogeneous materials with localized damage

An adaptive clustering FE² (ACFE²) method is developed to accelerate the multiscale damage and failure analysis of heterogeneous materials. Firstly, a feature vector which is composed by the strain components and damage rates of each macro integration point is applied for macro model reduction. Then based on the feature vector, an elbow-based k -means clustering method is used to find the optimal number of clusters for macrostructure in each numerical increment. Once local damage behavior appears, an adaptive local enhancement scheme is applied in the region where damage evolves rapidly, so that the corresponding elements are directly coupled with RVE calculations, improving the accuracy of localized damage prediction. By comparing with the experimental and numerical results, the accuracy of ACFE² method for predicting the damage evolution of heterogeneous materials with various microstructures and microscale constituents is validated. Regarding the computational costs, the ACFE² method is about 10-50 times more efficient than the traditional FE² method, and 3-5 times more efficient than the k -means FE² (KMFE²) method, which demonstrates a great improvement in computational efficiency for multiscale problems.