Phase field method based on reduced-order-homogenization for fibrous composite material

Abstract

This manuscript proposes a novel multiscale phase field method (PFM) based on reduced-order-homogenization (ROH) approach to investigate the damage evolution for the fibrous composite material, namely the ROH-PFM. In the ROH-PFM, the matrix phase is described by the PFM, and the fiber phase could be modeled by some other classic constitutive model. The overall response of the fibrous composite material then is obtained by averaging and homogenization approaches through the ROH framework in order to obtain the macro-scopic stress and consistent material moduli. In the present work, we derive the governing equations in terms of the displacement field and the matrix phase field. Through the ROH and the Francfort–Marigo variational principle, we can obtain the governing elliptical partial differential equation for the matrix phase field in terms of the stress states of the matrix and fiber phases. The corresponding weak form is derived, and numerical algorithm through the finite element method is derived as well. Finally, three groups of numerical simulations are selected to verify the functionality of the ROH-PFM, while the fibers are assumed to follow an isotropic continuum damage model. The numerical examples show good performance of the ROH-PFM in stating various material degradation mechanism.