An extended cohesive damage model for simulating crack propagation in fibre reinforced composies

摘要

This thesis presents an extended cohesive damage model (ECDM) for simulating crack propagation in fibre reinforced composites. By embedding the cohesive zone model (CZM) into the eXtended Finite Element Method (XFEM)and eliminating the enriched degree of freedoms (DoFs), the ECDM defines the cohesive crack path in an implicit way in equilibrium equations and enables the local enrichments of approximation spaces without additional DoFs. The contribution from additional DoFs can be accounted via the DoFs elimination,which allows discontinuities to exist within a finite element rather than the element boundaries. To account for the evolution of cohesion before crack propagation, in this developed ECDM, a new equivalent damage variable with respect to strain field is introduced to avoid the appearance of enriched DoFs,and to substitute the conventional characterization in the approximation of displacement jump. This variable is achieved based on the energy dissipation during post-failure process to characterize the damage evolution. Therefore,the constant dissipation of fracture energy during failure process is guaranteed.Eliminating the enrichment by adopting a condensation technique, the ECDM is expected to provide significant superiority in computational efficiency when modelling crack propagation in materials.The performance of the present ECDM is demonstrated by the initial applications in simulation of crack propagation in homogeneous and heterogonous structures, which show that the developed ECDM works well when comparing to experiment work and XFEM analysis. Regarding the computational cost, the ECDM can ease the computational burden by more than 60% reduction in terms of CPU time without sacrificing numerical accuracy and robustness. The feasibility of the ECDM in capturing delamination migration within fibre reinforced laminated composites is verified. Good agreements with experimental work are obtained and the present model’s advantage in accuracy and numerical efficiency comparing to CZM based model is demonstrated.This work makes contribution to academic knowledge and technology translation by the following points: 1. It is the first time to theoretically derive the fully condensed equilibrium equations of the ECDM based on the framework of XFEM; 2. An equivalent damage variable with respect to strain field is introduced for characterizing the effects from enriched DoFs and cohesive traction, which avoids physical displacement jump in presenting strong discontinuities; 3. A significant improvement of computing efficiency in non-linear fracture analysis is achieved through eliminating the enriched DoFs required by XFEM; 4. The developed ECDM provides a highly efficient tool for academics and engineers in predicting detailed multicrack failure mechanism in engineering materials and structures; 5. The ECDM is developed using common computer language FORTRAN, which can be easily integrated into other FEM commercial packages.