Deep-Green Inversion to Extract Traction-Separation Relations at Material Interfaces


The traction-separation relationship of an interface is a critical component to understand and model the delamination behavior of multi-layer composites in situations where large scale bridging is active. Limited by current experimental techniques, the extraction of traction-separation relationships often relies on inverse approaches, where far field measurements are used as input data. In this article, a data-driven model based on Green's function embedded neural networks is proposed (namely Deep Green Inversion, or DGI), where the input consists of far field displacement fields while the output is the desired but initially unknown tractions and separations on the interface. Specifically, Green's functions are embedded as loss function terms along with other terms based on mean squared error and the field equations associated with loaded elastic bodies. The approach is first verified via analytical solutions to a simply supported beam subject to end moments and a non-uniform traction applied to a portion of one boundary of the beam. Hyperparameter training is included in order to elucidate the influence of weight factors that are applied to the different constraints that are considered. The developed approach is then successfully validated for mode-I and mixed-mode cohesive zone extraction problems using only far-field displacement synthetic data that are generated from numerical solutions to the problems. As part of the validation process and consideration of any limitations of the approach, the amount of displacement data required to produce robust traction-separation relations is deliberated. The tractions and separations within the cohesive zone are extracted with an average global error of 9.06 % and local error of 9.24%, using only 55–60% of the available experimental data. The proposed approach is then applied to double cantilever beam experiments with six different types of interaction between the beams, where the input displacement fields are obtained using digital image correlation. The traction-separation relationships extracted via the DGI neural network developed here agree very well with the results obtained via a direct extraction approach. These results suggest that the proposed approach is quite general, considering the range of traction-separation relations that were explored.


Civil, Architectural and Environmental Engineering

Keywords and Phrases

Boundary value problem; Cohesive zone; Green's function; Machine learning; Traction separation relationship

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Article - Journal

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Publication Date

15 Aug 2022