Hyperelastic Shear Lag Model
Source abstract
Abstract
Abstract On the basis of the analysis of deformation of a representative volume element, a micromechanical model is derived to describe the elastic modulus of a unidirectional short-fiber composite under tension in the reinforcement direction. The analysis includes an exact solution to the hyperelastic equations for the deformed matrix and an approximate solution to the equations for the fiber material. The solution is provided for a neo-Hookean material. Formulas are derived to relate the elastic strain energy to the macroscopic longitudinal strain of the composite and to describe the longitudinal and radial deformation of the matrix and fiber material. The main result is a formula that relates the initial tangential elastic modulus of the composite (an analog of Young's modulus in linear elasticity) to the mechanical characteristics of the composite constituents (namely, the ratio of the elastic modulus of the matrix material to the elastic modulus of the fiber), as well as to the geometric characteristic (fiber length-to-diameter ratio) and volume fraction of fibers in the composite. The derived results are compared with other analytical models, as well as with the known results of finite element and boundary element modeling. The results generalize the well-known shear lag (SL) model to hyperelastic materials and are obtained via a more rigorous analysis than the original model.
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Research context
OpenAlex topics: Elasticity and Material Modeling · Composite Material Mechanics · Geotechnical Engineering and Soil Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (30)
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1. Fu, S.-Y., Lauke, B., Mäder, E., Yue, C.-Y., and Hu, X., Tensile Properties of Short-Glass-Fiber- and Short-Carbon-Fiber-Reinforced Polypropylene Composites, Composites Part A: Applied Science and Manufacturing, 2000, vol. 31, no. 10, pp. 1117–1125. https://doi.org/10.1016/S1359-835X(00)00068-310.1016/S1359-835X(00)00068-3 ↗
2. Liang, J.-Z., Predictions of Young's Modulus of Short Inorganic Fiber Reinforced Polymer Composites, Composites Part B: Engineering, 2012, vol. 43, no. 4, pp. 1763–1766. https://doi.org/10.1016/j.compositesb.2012.01.01010.1016/j.compositesb.2012.01.010 ↗
3. Jariwala, H. and Jain, P., A Review on Mechanical Behavior of Natural Fiber Reinforced Polymer Composites and its Applications, Journal of Reinforced Plastics and Composites, 2019, vol. 38, no. 10, pp. 441–453. https://doi.org/10.1177/073168441982852410.1177/0731684419828524 ↗
4. Facca, A.G., Kortschot, M.T., and Yan, N., Predicting the Elastic Modulus of Natural Fibre Reinforced Thermoplastics, Composites Part A: Applied Science and Manufacturing, 2006, vol. 37, no. 10, pp. 1660–1671. https://doi.org/10.1016/j.compositesa.2005.10.00610.1016/j.compositesa.2005.10.006 ↗
5. Migneault, S., Koubaa, A., Erchiqui, F., Chaala, A., Englund, K., and Wolcott, M.P., Application of Micromechanical Models to Tensile Properties of Wood–Plastic Composites, Wood Science and Technology, 2011, vol. 45, pp. 521–532. https://doi.org/10.1007/s00226-010-0351-510.1007/s00226-010-0351-5 ↗
6. Ratna Prasad, A.V. and Mohana Rao, K., Mechanical Properties of Natural Fibre Reinforced Polyester Composites: Jowar, Sisal and Bamboo, Materials & Design, 2011, vol. 32, no. 8-9, pp. 4658–4663. https://doi.org/10.1016/j.matdes.2011.03.01510.1016/j.matdes.2011.03.015 ↗
7. Eshelby, J.D., The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1957, vol. 241, pp. 376–396. https://doi.org/10.1098/rspa.1957.013310.1098/rspa.1957.0133 ↗
8. Tucker, C.L. and Liang, E., Stiffness Predictions for Unidirectional Short-Fiber Composites: Review and Evaluation, Composites Science and Technology, 1999, vol. 59, no. 5, pp. 655–671. https://doi.org/10.1016/S0266-3538(98)00120-110.1016/S0266-3538(98)00120-1 ↗
9. Withers, P.J., Stobbs, W.M., and Pedersen, O.B., The Application of the Eshelby Method of Internal Stress Determination to Short Fibre Metal Matrix Composites, Acta Metallurgica et Materialia, 1989, vol. 37, no. 11, pp. 3061–3084. https://doi.org/10.1016/0001-6160(89)90341-610.1016/0001-6160(89)90341-6 ↗
10. Shilko, S.V., Chernous, D.A., and Panin, S.V., A Mesomechanical Analysis of Short-Fiber Reinforced Composites with Account of the Interphase Layer, Mechanics of Composite Materials, 2012, vol. 48, pp. 171–178. https://doi.org/10.1007/s11029-012-9263-910.1007/s11029-012-9263-9 ↗
11. Roatta, A. and Bolmaro, R.E., An Eshelby Inclusion Based Model for the Study of Stresses and Plastic Strain Localization in Metal Matrix Composites II. Fiber Reinforcement and Lamellar Inclusions, Materials Science and Engineering: A, 1997, vol. 229, pp. 192–202. https://doi.org/10.1016/S0921-5093(96)10843-110.1016/S0921-5093(96)10843-1 ↗
12. Mori, T. and Tanaka, K., Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions, Acta Metallurgica et Materialia, 1973, vol. 21, no. 5, pp. 571–574. https://doi.org/10.1016/0001-6160(73)90064-310.1016/0001-6160(73)90064-3 ↗
13. Cox, H.L., The Elasticity and Strength of Paper and other Fibrous Materials, British Journal of Applied Physics, 1952, vol. 3, no. 3, pp. 72–79. https://doi.org/10.1088/0508-3443/3/3/30210.1088/0508-3443/3/3/302 ↗
14. Clyne, T.W., A Simple Development of the Shear Lag Theory Appropriate for Composites with a Relatively Small Modulus Mismatch, Materials Science and Engineering: A, 1989, vol. 122, no. 2, pp. 183–192. https://doi.org/10.1016/0921-5093(89)90629-110.1016/0921-5093(89)90629-1 ↗
15. Nairn, J.A., On the Use of Shear-Lag Methods for Analysis of Stress Transfer in Unidirectional Composites, Mechanics of Materials, 1997, vol. 26, no. 2, pp. 63–80. https://doi.org/10.1016/S0167-6636(97)00023-910.1016/S0167-6636(97)00023-9 ↗
16. Starink, M.J. and Syngellakis, S., Shear Lag Models for Discontinuous Composites: Fibre End Stresses and Weak Interface Layers, Materials Science and Engineering: A, 1999, vol. 270, no. 2, pp. 270–277. https://doi.org/10.1016/S0921-5093(99)00277-410.1016/S0921-5093(99)00277-4 ↗
17. Hsueh, C.-H., Young's Modulus of Unidirectional Discontinuous-Fibre Composites, Composites Science and Technology, 2000, vol. 60, no. 14, pp. 2671–2680. https://doi.org/10.1016/S0266-3538(00)00128-710.1016/S0266-3538(00)00128-7 ↗
18. Gao, X.-L. and Li, K., A Shear-Lag Model for Carbon Nanotube-Reinforced Polymer Composites, International Journal of Solids and Structures, 2005, vol. 42, no. 5-6, pp. 1649–1667. https://doi.org/10.1016/j.ijsolstr.2004.08.02010.1016/j.ijsolstr.2004.08.020 ↗
19. Kim, H.G. and Kwac, L.K., Evaluation of Elastic Modulus for Unidirectionally Aligned Short Fiber Composites, Journal of Mechanical Science & Technology, 2009, vol. 23, pp. 54–63. https://doi.org/10.1007/s12206-008-0810-110.1007/s12206-008-0810-1 ↗
20. Wang, J.-Y., Gu, C.-S., Gu, S.-T., Gao, X.-L., and Gu, H., Shear-Lag Model for Discontinuous Fiber-Reinforced Composites with a Membrane-Type Imperfect Interface, Acta Mechanica, 2020, vol. 231, pp. 4717–4734. https://doi.org/10.1007/s00707-020-02768-710.1007/s00707-020-02768-7 ↗
21. Halpin, J.C. and Kardos, J.L., The Halpin–Tsai Equations: A Review, Polymer Engineering & Science, 1976, vol. 16, pp. 344–352. https://doi.org/10.1002/pen.76016051210.1002/pen.760160512 ↗
22. Lewis, T.B. and Nielsen, L.E., Dynamic Mechanical Properties of Particulate-Filled Composites, Journal of Applied Polymer Science, 1970, vol. 14, no. 6, pp. 1449–1471. https://doi.org/10.1002/app.1970.07014060410.1002/app.1970.070140604 ↗
23. Pearson, A., Liao, W., Kazemi, Y., Duncan, M., Slingerland, E., Kakroodi, A., Heydrich, M., Hammami, A., and Naguib, H.E., Fiber-Matrix Adhesion between High-Density Polyethylene and Carbon Fiber, Polymer Testing, 2022, vol. 105, p. 107423. https://doi.org/10.1016/j.polymertesting.2021.10742310.1016/j.polymertesting.2021.107423 ↗
24. Galiotis, C., Young, R.J., Yeung, P.H.J., and Batchelder, D.N., The Study of Model Polydiacetylene/Epoxy Composites, Journal of Materials Science, 1984, vol. 19, pp. 3640–3648. https://doi.org/10.1007/BF0239693610.1007/BF02396936 ↗
25. Melanitis, N., Galiotis, C., Tetlow, P.L., and Davies, C.K.L., Monitoring the Micromechanics of Reinforcement in Carbon Fibre/Epoxy Resin Systems, Journal of Materials Science, 1993, vol. 28, pp. 1648–1654. https://doi.org/10.1007/BF0036336210.1007/BF00363362 ↗
26. Ingber, M.S. and Papathanasiou, T.D., A Parallel-Supercomputing Investigation of the Stiffness of Aligned, Short-Fiber-Reinforced Composites Using the Boundary Element Method, International Journal for Numerical Methods in Engineering, 1997, vol. 40, no. 18, pp. 3477–3491. https://doi.org/10.1002/(SICI)1097-0207(19970930)40:18<3477::AID-NME225>3.0.CO;2-B10.1002/(SICI)1097-0207(19970930)40:18<3477::AID-NME225>3.0.CO;2-B ↗
27. Hwang, S.J. and Gibson, R.F., Micromechanical Modeling of Damping in Discontinuous Fiber Composites Using a Strain Energy/Finite Element Approach, Journal of Engineering Materials and Technology – Transactions of the ASME, 1987, vol. 109, pp. 47–52. https://doi.org/10.1115/1.322593210.1115/1.3225932 ↗
28. Gibson, R.F., Principles of Composite Material Mechanics, CRC Press, Boca Raton, 2016. https://doi.org/10.1201/b1962610.1201/b19626 ↗
29. Gun, H. and Kose, G., Prediction of Longitudinal Modulus of Aligned Discontinuous Fiber-Reinforced Composites Using Boundary Element Method, Science and Engineering of Composite Materials, 2014, vol. 21, no. 2, pp. 219–221. https://doi.org/10.1515/secm-2013-005510.1515/secm-2013-0055 ↗
30. Krenchel, H., Fibre Reinforcement: Theoretical and Practical Investigations of the Elasticity and Strength of Fibre-Reinforced Materials, Akademisk Forlag, Copenhagen, 1964.