Description
- Abstract:
- This thesis presents the applications of phase field modeling in fracture analysis. In this method, a diffusive crack zone controlled by a scalar auxiliary variable approximates the sharp crack surface topology in a solid. Because no interface tracking is necessary, the crack trajectories are automatically calculated as part of the solution in phase field modeling. Over the domain, the damage parameter changes continually. However, this flexibility comes with challenges because strong local gradients must be accurately represented by a very precise spatial discretization. The practical usefulness of phase field models is hence severely constrained. In this work, I have developed an attention mechanism integrated physics informed deep neural networks to solve brittle fracture. The network is trained using a method that minimizes the variational energy of a system that is characterized by general non-linear partial differential equations while adhering to any specified physical law. For effective network optimization, self-adaptive trainable weight parameters are linked to the loss terms (boundary loss and the variational energy loss). In contrast to traditional mesh-based discretization techniques, the suggested solution just requires a set of points to specify the geometry. An adaptive $\it{h}$-refinement scheme is integrated with this framework, where the refinement is based on a critical threshold value of $\phi$. In this work, we have considered displacement controlled loading conditions.
- Notes:
- Thesis (Sc. M.)--Brown University, 2022
Citation
Xin, Yuchen,
"Physics Informed Neural Network for Phase-field Modeling of Brittle Fracture"
(2022).
Mechanics of Solids Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:smfdmsfy/
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Collection:
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Mechanics of Solids Theses and Dissertations
Theses and Dissertations for the Mechanics of Solids department....