Phase-field modelling of fracture in viscoelastic composite using isogeometric FCM

The damage of viscoelastic composites is a significant topic in industrial fields. Under external loads, the debonding of the coupling interfaces between the filler particles and the matrix can greatly reduce the reliability of viscoelastic composites. This study proposes a thermodynamically consistent phase-field model with the aim of predicting the quasi-brittle fracture of particle-reinforced linear viscoelastic composites. The main novelties of our model are as follows: (i) The quasi-brittle viscoelastic phase-field model and finite cell method (FCM) are integrated to predict viscoelastic composites with complex geometries, without creating boundary conforming meshes; (ii) An additional interface phase-field is introduced to smoothly transition the interface properties, while the governing equations are established in the framework of finite cell method by weak imposition of the Dirichlet boundary conditions. Based on the Mori-Tanaka method, we also derive a one-dimensional bi-material bar with adhesive interface to validate the effectiveness of the proposed model. The influence of two diffused formulas (Heaviside-like function and quadratic function) for the critical energy release rate of interface on the choice of length scale parameters are discussed in detail. Three cases of particle debonding are designed to demonstrate that the proposed model is capable of capturing the crack nucleation, propagation and intersection in the representative volume element (RVE) of viscoelastic composite.