A UMAP-based clustering method for multi-scale damage analysis of laminates

In this study, a novel multi-scale damage model based on the parametric finite-volume direct averaging micromechanics theory (parametric FVDAM), extended finite element method (XFEM), and a clustering algorithm, is built, to describe the progressive damage evolution of laminates, where a uniform manifold approximation and projection (UMAP)-based clustering method is specially designed and incorporated with the FVDAM and XFEM for the first time. The subvolumes in the unit cell generated by FVDAM with similar mechanical responses were included in the same cluster using the UMAP-based clustering method. The semi-analytical framework of FVDAM allows the efficient generation of unit cells. The built-in advantage in the visualization of the proposed UMAP-based clustering method allows researchers in the field of mechanics to have a clear and intuitive understanding of the clustering results. The clustered unit cell is then conjugated to the XFEM, which allows the damage information to be transmitted between different scales. Three damage mechanisms of laminates under a three-dimensional (3D) stress state are considered, which include matrix damage, fiber breakage, and delamination. Furthermore, a shear nonlinear matrix D_s for a 3D element is derived and introduced in the model, which enables the description of the unique elastic nonlinear behavior of laminates. The model is implemented using UDMGINI and USDFLD subroutines in ABAQUS, which not only allows the calculation of the load–displacement curve, but also the simulation of clear and smooth crack propagation paths. To verify the effectiveness of the model, the experiments of [±60]_2s and [90]₈ notched glass-fiber/epoxy laminates under tension were performed by digital image correlation (DIC) monitoring, and the results compared were in good agreement with the simulations, thus proving the effectiveness of the proposed model. The code of the UMAP-based clustering method developed in this study can be downloaded from https://github.com/Danhui-Yang/MicroMechanicsUmapClustering.