A multiscale fracture mechanics model for predicting damage evolution in laminated composites subjected to impact loading

Laminated polymeric composites are utilized in a variety of structural applications wherein impact loads are a common design consideration. In such circumstances damage is usually observed in the form of a variety of fracture modes including matrix cracking, delamination, and fiber fracture. Multiple cracks with significant energy dissipation are often observed experimentally before complete loss of structural integrity is attained. Therefore, since it is often possible to keep the part in service after the impact event, it is useful to develop models for predicting the post impact performance of the part. The interaction of crack propagation makes it essential to model the evolution of these damage events during impact loading. In order to capture the physics of all of the fracture events both accurately and efficiently, it is possible to develop a multi-scale continuum mechanics framework in which successively larger scales are utilized to model each of the fracture modes. This approach is taken in the current paper to account for microscale damage ahead of delaminations, mesoscale matrix cracking, local scale delaminations, and global scale part response. The resulting micro-meso-local-global methodology utilizes ductile fracture mechanics on each scale to effect crack growth of the three types described above, with the smaller two scales developed analytically, and the larger two developed computationally by means of the finite element method. Linking between the four different scales is obtained by utilizing damage dependent homogenization theorems that account for energy dissipation due to fracture on the smaller scales.