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2024 | OriginalPaper | Chapter

Data-Driven Methodology to Extract Stress Fields in Materials Subjected to Dynamic Loading

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Abstract

Full-field stress determination is critical for dynamic loading condition when the stress fields are non homogeneous. Recent advances in high-speed experimental mechanics have led to methods that estimate stress from full-field deformation measurements. However, these methods require multiple numerical differentiation of displacement data, making them less accurate due to noise content in experimental measurements. In order to efficiently tackle noisy displacement data and predict accurate stress fields, a methodology based on neural networks is developed. Specifically, physics-informed neural networks are employed so that the information embedded in physical laws is also utilized along with the experimental measurements. The proposed method to inversely estimate the stress is illustrated by applying it to the impact of rigid mass on an elastic rod that generates a sharp stress discontinuity. A multi-network model is developed where independent feedforward neural networks approximate the displacement and stress. Physical laws are incorporated through equilibrium equations that effectively guide the method toward the right solution. It is shown that the method provides reliable estimates of stress even if the stress field is discontinuous and noise present in the data.

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Literature
1.
go back to reference Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016) Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016)
2.
go back to reference Lagaris, I.E.I.E., Likas, A., Fotiadis, D.I.D.I.: Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw. 9(5), 987–1000 (1998)CrossRef Lagaris, I.E.I.E., Likas, A., Fotiadis, D.I.D.I.: Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw. 9(5), 987–1000 (1998)CrossRef
3.
go back to reference Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019)MathSciNetCrossRef Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019)MathSciNetCrossRef
4.
go back to reference Sutton, M.A., Orteu, J.-J., Schreier, H.: Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications, 1st edn. Springer Publishing Company, Incorporated, New York (2009) Sutton, M.A., Orteu, J.-J., Schreier, H.: Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications, 1st edn. Springer Publishing Company, Incorporated, New York (2009)
5.
go back to reference Koohbor, B., Kidane, A., Lu, W.-Y., Sutton, M.A.: Investigation of the dynamic stress–strain response of compressible polymeric foam using a non-parametric analysis. Int. J. Impact Eng. 91, 170–182 (2016)CrossRef Koohbor, B., Kidane, A., Lu, W.-Y., Sutton, M.A.: Investigation of the dynamic stress–strain response of compressible polymeric foam using a non-parametric analysis. Int. J. Impact Eng. 91, 170–182 (2016)CrossRef
6.
go back to reference Ravindran, S., Koohbor, B., Malchow, P., Kidane, A.: Experimental characterization of compaction wave propagation in cellular polymers. Int. J. Solids Struct. 139–140, 270–282 (2018)CrossRef Ravindran, S., Koohbor, B., Malchow, P., Kidane, A.: Experimental characterization of compaction wave propagation in cellular polymers. Int. J. Solids Struct. 139–140, 270–282 (2018)CrossRef
7.
go back to reference Gupta, V., Miller, D., Kidane, A.: Numerical and experimental investigation of density graded foams subjected to impact loading. In: Dynamic Behavior of Materials, Volume 1 : Proceedings of the 2019 Annual Conference on Experimental and Applied Mechanics Conference Proceedings of the Society for Experimental Mechanics Series, pp. 31–35 (2020). https://doi.org/10.1007/978-3-030-30021-0_6CrossRef Gupta, V., Miller, D., Kidane, A.: Numerical and experimental investigation of density graded foams subjected to impact loading. In: Dynamic Behavior of Materials, Volume 1 : Proceedings of the 2019 Annual Conference on Experimental and Applied Mechanics Conference Proceedings of the Society for Experimental Mechanics Series, pp. 31–35 (2020). https://​doi.​org/​10.​1007/​978-3-030-30021-0_​6CrossRef
8.
go back to reference Graff, K.: Wave Motion in Elastic Solids. Dover Publications, New York (1975) Graff, K.: Wave Motion in Elastic Solids. Dover Publications, New York (1975)
9.
go back to reference Glorot, X., Y. B. B. T.-P. of the T. I. C. on A. I. and Statistics: Understanding the difficulty of training deep feedforward neural networks. Proc. Mach. Learn. Res. 9, 249–256 (2010) Glorot, X., Y. B. B. T.-P. of the T. I. C. on A. I. and Statistics: Understanding the difficulty of training deep feedforward neural networks. Proc. Mach. Learn. Res. 9, 249–256 (2010)
10.
go back to reference Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Program. 45(1–3), 503–528 (1989)MathSciNetCrossRef Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Program. 45(1–3), 503–528 (1989)MathSciNetCrossRef
11.
12.
go back to reference Gupta, V., Kidane, A., Sutton, M.: Closed-form solution for shock wave propagation in density-graded cellular material under impact. Theor. Appl. Mech. Lett. 11(5), 100288 (2021)CrossRef Gupta, V., Kidane, A., Sutton, M.: Closed-form solution for shock wave propagation in density-graded cellular material under impact. Theor. Appl. Mech. Lett. 11(5), 100288 (2021)CrossRef
Metadata
Title
Data-Driven Methodology to Extract Stress Fields in Materials Subjected to Dynamic Loading
Authors
Vijendra Gupta
Addis Kidane
Copyright Year
2024
DOI
https://doi.org/10.1007/978-3-031-50474-7_14

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