Phase field approach to fracture : massive parallelization and crack identification
The phase field method has proven to be an important tool in computational fracture mechanics in that it does not require complicated crack tracking and is able to predict crack nucleation and branching. However, the computational cost of such a method is high due to a small regularization length pa...
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| Formato: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | España |
| Recursos: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/396154 |
| Acesso em linha: | http://hdl.handle.net/10803/396154 https://dx.doi.org/10.5821/dissertation-2117-96365 |
| Access Level: | acceso abierto |
| Palavra-chave: | Àrees temàtiques de la UPC::Enginyeria civil 004 531/534 624 |
| Resumo: | The phase field method has proven to be an important tool in computational fracture mechanics in that it does not require complicated crack tracking and is able to predict crack nucleation and branching. However, the computational cost of such a method is high due to a small regularization length parameter, which in turns restricts the maximum element size that can be used in a finite element mesh. In this work, we developed a massively parallel algorithm on the graphical processing unit (GPU) to alleviate this difficulty in the case of dynamic brittle fracture. In particular, we adopted the standard finite element method on an unstructured mesh combined with second order explicit integrators. As the explicit methods fit nicely with the GPU paradigm especially in terms of thread and memory hierarchy, we solve an elastodynamic problem when the phase field update is based on a gradient flow, so that a fully explicit implementation is feasible. To ensure stability, we designed a time adaptivity strategy to account for the decreasing critical time step during the evolution of the fields. We demonstrated the performance of the GPU-implemented phase field models by means of representative numerical examples, with which we studied the effect of the artificial viscosity, an artificial parameter to be input, and compared the crack path branching predictions from three popular phase field models. Moreover, we verified the method with convergence studies and performed a scalability study to demonstrate the desired linear scaling of the program in terms of the wall time per physical time as a function of the number of degrees of freedom. One of the main ideas of the phase field method is to employ a smeared representation of discrete cracks. However, in some applications it is still convenient to have the explicit crack path available, or even to develop a mechanism to introduce crack paths to partially replace a smeared crack propagation model. In this work, we presents a variational method to identify the crack path from phase field approaches to fracture. The method is proven to be successful not only for a simple curved crack but also for multiple and branched cracks. The algorithm employs the non-maximum suppression technique, a procedure borrowed from the image processing field, to detect a bounding area which covers the ridge of the phase field profile. After that, it is continued with the step to determine a cubic spline to represent the crack path and to improve it via a constrained optimization process. To demonstrate the performance of our method, we provide the results with three sets of representative examples. The developed algorithm can be combined with one on crack opening, for more elaborate interpretation of phase field simulations. This is the topic of the next part of the work. In this dissertation, we also provide a variational way to calculate the crack opening from phase field approaches to fracture. We also demonstrate the performance of our method with three sets of representative examples, and verify the results with a proper benchmark. Having the crack geometry available from a phase field approach can provide more elaborate interpretation of the phase field simulations. It may also offer a possibility of developing less expensive numerical schemes for a fluid-driven crack propagation of impermeable solids. This will be the topic of our future work. |
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