A novel coupled clustering FFT² multiscale method for modeling the nonlinear behavior and failure of composites

We propose a novel FFT² parallel multiscale computational method to predict the nonlinear behavior and failure of composite materials. Unlike traditional multiscale methods, the proposed approach reformulates the mechanical boundary value problem into Lippmann-Schwinger type integral equations at both the micro- and macro-scale, thereby leveraging the numerical efficiency of the fast Fourier transform (FFT) method at both scales. The application of generic (e.g. non-periodic) boundary conditions at the macro-scale is carried out by using the virtual boundary technique and buffer zones. In addition, the introduction of a clustering algorithm further improves the computational efficiency of the numerical method during the information transfer between scales. To ensure accurate damage prediction and mitigate spurious strain localization at both scales, suitable regularization techniques are employed. The proposed multiscale method is applied to investigate the transverse tension of unidirectional composite dog-bone specimens. After experimental verification, the method is applied to simulate 2D and 3D brittle fracture, elasto-plastic damage, and examples with non-uniform material orientation. The results demonstrate the robustness and adaptability of the clustering approach, which achieves up to 65.90-fold speedup and 81.62-fold reduction in memory usage compared to non-clustered multiscale methods, while maintaining a comparable level of accuracy.