Virtual clustering analysis for long fiber reinforced composites

Virtual clustering analysis (VCA) is an effective data-driven numerical homogenization method. In its original version (Tang et al. in Comput Mech 62(6):1443–1460, 2018), a homogeneous reference material is selected, and the governing system of heterogeneous material is reformulated into a Lippmann–Schwinger equation. For effective treatment of representative volume element (RVE) where long fibers penetrate the matrix, we propose to introduce an inhomogeneous reference material in this work. Since analytical expressions are not available in general, the interaction tensor and reference strain field are computed numerically. We validate the consistency with the original version of VCA in the first example, and demonstrate the effectiveness of the proposed strategy by several numerical examples. While better resolving the boundary traction, the proposed virtual clustering analysis for long fiber reinforced composites (VCA-L) algorithm correctly predicts homogenized properties in numerical tests.