A physics-informed variational DeepONet for predicting the crack path in
brittle materials
- URL: http://arxiv.org/abs/2108.06905v1
- Date: Mon, 16 Aug 2021 05:31:05 GMT
- Title: A physics-informed variational DeepONet for predicting the crack path in
brittle materials
- Authors: Somdatta Goswami, Minglang Yin, Yue Yu, George Karniadakis
- Abstract summary: We propose a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis.
V-DeepONet is trained to map the initial configuration of the defect to the relevant fields of interests.
We demonstrate the effectiveness of V-DeepOnet through two benchmarks of brittle fracture, and we verify its accuracy using results from high-fidelity solvers.
- Score: 3.1196544696082613
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Failure trajectories, identifying the probable failure zones, and damage
statistics are some of the key quantities of relevance in brittle fracture
applications. High-fidelity numerical solvers that reliably estimate these
relevant quantities exist but they are computationally demanding requiring a
high resolution of the crack. Moreover, independent intensive simulations need
to be carried out even for a small change in domain parameters and/or material
properties. Therefore, fast and generalizable surrogate models are needed to
alleviate the computational burden but the discontinuous nature of fracture
mechanics presents a major challenge to developing such models. We propose a
physics-informed variational formulation of DeepONet (V-DeepONet) for brittle
fracture analysis. V-DeepONet is trained to map the initial configuration of
the defect to the relevant fields of interests (e.g., damage and displacement
fields). Once the network is trained, the entire global solution can be rapidly
obtained for any initial crack configuration and loading steps on that domain.
While the original DeepONet is solely data-driven, we take a different path to
train the V-DeepONet by imposing the governing equations in variational form
and we also use some labelled data. We demonstrate the effectiveness of
V-DeepOnet through two benchmarks of brittle fracture, and we verify its
accuracy using results from high-fidelity solvers. Encoding the physical laws
and also some data to train the network renders the surrogate model capable of
accurately performing both interpolation and extrapolation tasks, considering
that fracture modeling is very sensitive to fluctuations. The proposed hybrid
training of V-DeepONet is superior to state-of-the-art methods and can be
applied to a wide array of dynamical systems with complex responses.
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