Energetically-consistent multiscale analysis of fracture in composites materials

Two distinct length scale transition methodologies are developed to establish effective traction-separation relations for fracture in composite materials within a hierarchical multiscale framework. The two methodologies, one kinetics-based and the other kinematics-based, specify effective fracture properties that satisfy a surface-based Hill-Mandel consistency condition. Correspondingly, the total amount of energy dissipated is the same whether a crack is described in detail with micro quantities or in terms of an effective macroscopic crack. Though both methods guarantee consistency in terms of energy rates across length scales, they provide in general distinct effective traction-separation relations. Several representative samples of fiber reinforced composites are analyzed numerically, including the formation and propagation of cracks at mid-ply locations as well as (idealized) ply interfaces. Through post-processing of the microscale results, it is shown that the kinematics-based averaging method provides a macroscopic traction that is prone to rapid fluctuations while the kinetics-based averaging method shows a more smooth response but with openings that can deviate from the surface average of the microscale openings. The two methods are also compared with a previously-proposed scale transition methodology, which is a hybrid method that only satisfies the Hill-Mandel condition approximately. The suitability of the three methods is discussed in light of the results obtained from the simulations.