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Multigrid methods for 3D composite material simulation and crack propagation modelling based on a phase field method

Abstract : With the development of imaging techniques like X-Ray tomography in recent years, it is now possible to take into account the microscopic details in composite material simulations. However, the composites' complex nature such as inclined and broken fibers, voids, requires rich data to describe these details and thus brings challenging problems in terms of computational time and memory when using traditional simulation methods like the Finite Element Method. These problems become even more severe in simulating failure processes like crack propagation. Hence, it is necessary to investigate more efficient numerical methods for this kind of large scale problems. The MultiGrid (MG) method is such an efficient method, as its computational cost is proportional to the number of unknowns. In this thesis, an efficient MG solver is developed for these problems. The MG method is applied to solve the static elasticity problem based on the Lame's equation and the crack propagation problem based on a phase field method. The accuracy of the MG solutions is validated with Eshelby's classic analytic solution. Then the MG solver is developed to investigate the composite homogenization process and its solutions are compared with existing solutions in the literature. After that, the MG solver is applied to simulate the free-edge effect in laminated composites. A real laminated structure using X-Ray tomography is first simulated. At last, the MG solver is further developed, combined with a phase field method, to simulate the brittle crack propagation. The MG method demonstrates its efficiency both in time and memory dimensions for solving the above problems.
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Hanfeng Gu. Multigrid methods for 3D composite material simulation and crack propagation modelling based on a phase field method. Materials. Université de Lyon, 2016. English. ⟨NNT : 2016LYSEI090⟩. ⟨tel-02001087⟩

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