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Discovering Failure Criteria of Composites by Sparse Identification and Compressed Sensing



A reliable design of a composite structure needs to consider the failure of the composites. Hashin failure criterion is one of the most popular phenomenological models in engineering practice due to its simplicity of application. Although remarkable success has been achieved from the Hashin failure criterion, it does not always fit the experimental results very well. Over the past few years, a few experimental failure data have been collected. It would be of interest to leverage the existing data to improve the prediction of failure criteria. In this paper, we proposed to apply a framework that combines sparse regression with compressed sensing to discover failure criteria from data. Following the phenomenological failure models, we divided the failure of composites into tensile and compressive fiber modes, tensile and compressive matrix modes. Two examples were studied with the proposed framework. The first example was presented to demonstrate the capability of the framework. The data was generated by the Hashin failure criterion and added various magnitudes of noise. The proposed framework was implemented to discover the failure criterion from the noised data. For the second example, the proposed method was used to discover failure criteria from the experimental data which are collected from the first world wide failure exercise (WWFE I). Both examples show that the proposed method can discover the failure criteria accurately.


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J. Gu and P. Chen, “Some modifications of hashins failure criteria for unidirectional

composite materials,” Composite Structures, vol. 182, pp. 143–152, 2017.

C. H. Wang and C. N. Duong, Bonded joints and repairs to composite airframe structures.

Academic Press, 2015.

S.W. Tsai and E. M.Wu, “A general theory of strength for anisotropic materials,” Journal

of Composite Materials, vol. 5, no. 1, pp. 58–80, 1971.

L. Kroll and W. Hufenbach, “A physically based failure criterion for laminated composites,”

Mechanics of Composite Materials, vol. 35, no. 4, pp. 277–284, 1999.

Z. Hashin, “Failure criteria for unidirectional fiber composites,” Journal of Applied Mechanics,

Z. Hashin and A. Rotem, “A fatigue failure criterion for fiber reinforced materials,” Journal

of Composite Materials, vol. 7, no. 4, pp. 448–464, 1973.

A. Puck and H. Sch¨urmann, “Failure analysis of frp laminates by means of physically

based phenomenological models,” in Failure criteria in fibre-reinforced-polymer composites,

pp. 832–876, Elsevier, 2004.

R. Cuntze, “The predictive capability of failure mode concept-based strength criteria for

multi-directional laminatespart b,” Composites Science and Technology, vol. 64, no. 3-4,

pp. 487–516, 2004.

S. T. Pinho, C. G. D´avila, P. P. Camanho, L. Iannucci, and P. Robinson, “Failure models

and criteria for frp under-in-plane or three-dimensional stress states including shear nonlinearity,”

M. Hinton and A. Kaddour, “The background to the second world-wide failure exercise,”

Journal of Composite Materials, vol. 46, no. 19-20, pp. 2283–2294, 2012.

D. Z. Huang, K. Xu, C. Farhat, and E. Darve, “Predictive modeling with learned constitutive

laws from indirect observations,” arXiv preprint arXiv:1905.12530, 2019.

K. Xu, D. Z. Huang, and E. Darve, “Learning constitutive relations using symmetric

positive definite neural networks,” arXiv preprint arXiv:2004.00265, 2020.

X. Liu, F. Tao, H. Du,W. Yu, and K. Xu, “Learning nonlinear constitutive laws using neural

network models based on indirectly measurable data,” Journal of Applied Mechanics,

pp. 1–10, 04 2020.

P. Liu and J. Zheng, “Recent developments on damage modeling and finite element analysis

for composite laminates: A review,” Materials & Design, vol. 31, no. 8, pp. 3825–

, 2010.

F. Tao, X. Liu, H. Du, and W. Yu, “Learning composite constitutive laws via coupling

abaqus and deep neural network,” Composite Structures, p. 114137, 2021.

F. Tao, X. Liu, H. Du, and W. Yu, “Learning damage constitutive law of composites

via lamination theory enhanced abaqus-pdnn mechanics system,” in AIAA Scitech 2021

Forum, p. 2022, 2021.

S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data

by sparse identification of nonlinear dynamical systems,” Proceedings of the national

academy of sciences, vol. 113, no. 15, pp. 3932–3937, 2016.

S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Data-driven discovery of partial

differential equations,” Science Advances, vol. 3, no. 4, p. e1602614, 2017.

D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to linear regression analysis.

John Wiley & Sons, 2021.

R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal

Statistical Society: Series B (Methodological), vol. 58, no. 1, pp. 267–288, 1996.

J. Friedman, T. Hastie, R. Tibshirani, et al., The elements of statistical learning, vol. 1.

Springer series in statistics New York, 2001.

W.-X.Wang, R. Yang, Y.-C. Lai, V. Kovanis, and C. Grebogi, “Predicting catastrophes in

nonlinear dynamical systems by compressive sensing,” Physical review letters, vol. 106,

no. 15, p. 154101, 2011.

D. L. Donoho, “Compressed sensing,” IEEE Transactions on information theory, vol. 52,

no. 4, pp. 1289–1306, 2006.

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate

measurements,” Communications on Pure and Applied Mathematics: A Journal

Issued by the Courant Institute of Mathematical Sciences, vol. 59, no. 8, pp. 1207–1223,

M. Schmidt and H. Lipson, “Distilling free-form natural laws from experimental data,”

science, vol. 324, no. 5923, pp. 81–85, 2009.

P. D. Soden, M. J. Hinton, and A. Kaddour, “Lamina properties, lay-up configurations

and loading conditions for a range of fibre reinforced composite laminates,” in Failure

criteria in fibre-reinforced-polymer composites, pp. 30–51, Elsevier, 2004.

M. Hinton, A. Kaddour, and P. Soden, “The world-wide failure exercise: Its origin, concept

and content,” in Failure criteria in fibre-reinforced-polymer composites, pp. 2–28,

Elsevier, 2004.

R. W. Schafer, “What is a savitzky-golay filter?[lecture notes],” IEEE Signal processing

magazine, vol. 28, no. 4, pp. 111–117, 2011.

U. Hutter, H. Schelling, and H. Krauss, “An experimental study to determine failure

envelope of composite materials with tubular specimens under combined loads and comparison

between several classical criteria,” AGARD Specialists Meeting on Failure Modes

of Composite Mater, 1975.

F. Tao, X. Liu, H. Du, and W. Yu, “Physics-informed artificial neural network approach

for axial compression buckling analysis of thin-walled cylinder,” AIAA Journal, vol. 58,

no. 6, pp. 2737–2747, 2020.


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