Numerical and Analytical Modeling of Large Deflection with Local Indentation of Sandwich Beam Under Quasi-Static Transverse Loading

Document Type : Mechanics article

Author

Department of Mechanical Engineering, Bu Ali Sina University, Hammedan, Iran

Abstract

By taking local indention effect and foam core strength into account in the overall deflection process, a novel theoretical model is investigated to predict the large deflection with local indentation of sandwich beam under quasi-static lateral loading. The theoretical and numerical models of lateral crushing force and total plastic energy are proposed and the theoretical results agree well with numerical and experimental results of previous researches. The results conclude that local indention phase plays an important role in initial collapse deflection of sandwich beam when maximum deflection is greater than face sheets thickness. In addition, the theoretical results with and without local indention phase of total plastic energy are compared and it shows that total plastic energy of sandwich beam will be overestimated if local indention phase is neglected. The present analytical model can predict the large deflection behavior with local indention of sandwich beam reasonably.

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[1] M.F. Ashby, A.G. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson, and H.N.C. Wadley. "Metal foam: a design guide. " Washington: Butterworth, (2000).
[2] M.T. Tilbrook, V.S. Deshpande, and N.A. Fleck. "The impulsive response of sandwich beams: analytical and numerical investigation of regimes of behavior. " Journal of the Mechanics and Physics of Solids, no. 54 (2006): 2242–2280.
[3] S.Q. Li, X. Li, Z.H. Wang, G.Y. Wu, G.X. Lu, and L.M. Zhao. "Finite element analysis of sandwich panels with stepwise graded aluminum honeycomb cores under blast loading. " Composite Part A, no. 80 (2016): 1–12.
[4] Z.W. Zhou, Z.H. Wang, L.M. Zhao, and X.F. Shu. "Experimental investigation on the yield behavior of Nomex honeycombs under combined shear-compression. " Latin American Journal of Solids and Structures, no. 9 (2012): 515–530.
[5] T. Jin, Z.W. Zhou, Z.H. Wang, G.Y. Wu, and X.F. Shu. "Experimental study on the effects of specimen in-plane size on the mechanical behavior of aluminum hexagonal honeycombs." Material Science Engineering A, no. 635 (2015): 23–35.
[6] H.J. Rathbun, F.W. Zok, S.A. Waltner, C. Mercer, A.G. Evans, and D.T. Queheillalt. "Structural performance of metallic sandwich beams with hollow truss cores. " Acta Materialia, no. 54 (2006): 5509–5518.
[7] P.W. Zhang, Z.H. Wang, and L.M. Zhao. "Dynamic crushing behavior of open-cell aluminum foam with negative Poisson's ratio. "Journal of Applied Physics A, no. 123 (2017): 311-321.
[8] Z.F. Liu, W.Q. Hao, J.M. Xie, J.S. Lu, R. Huang, and Z.H. Wang. "Axial-impact buckling modes and energy absorption properties of thin-walled corrugated tubes with sinusoidal patterns." Thin Walled Structures, no. 94 (2015): 410–423.
[9] C. Kılıçaslan, İ.K. Odacı, and M. Güden. "Single- and double-layer aluminum corrugated core sandwiches under quasi-static and dynamic loadings." Journal of Sandwich Structures and Material, no. 18 (2016): 667–692.
[10] S.Q. Li, G.X. Lu, Z.H. Wang, L.M. Zhao, and G.Y. Wu. "Finite element simulation of metallic cylindrical sandwich shells with graded aluminum tubular cores subjected to internal blast loading." International Journal of Mechanical Sciences, no. 96 (2015): 1–12.
[11] H.W. Yang, J.X. Hu, L, Xu, and G.Y. Lu. "Peripheral deformation and buckling of stainless steel hemispherical shells compressed by a flat plate." Latin American Journal of Solids and Structures, no. 13 (2016): 257–271.
[12] P.W. Zhang, X. Li, T. Jin, Z.H. Wang, and L.M. Zhao. "Dynamic response of circular metallic sandwich panels under projectile impact. " Journal of Sandwich Structures and Material, no. 19 (2016): 572–594.
[13] J.J. Zhang, Z.H. Wang, and L.M. Zhao. "Dynamic response of functionally graded cellular materials based on the Voronoi model. " Composite Part B, no. 85 (2016): 176–187.
[14] S.Q. Li, X. Li, Z.H. Wang, G.Y. Wu, G..X Lu, and L.M. Zhao. "Sandwich panels with layered graded aluminum honeycomb cores under blast loading. " Composite Structures, no. 173 (2017): 242–254.
[15] T.M. McCormack, R. Miller, O. Kesler, and L.J. Gibson. "Failure of sandwich beams with metallic foam cores. " International Journal of Solids Structures, no. 38 (2001): 4901–4920.
[16] J.L. Yu, E.H. Wang, J.R. Li and Z.J. Zheng. "Static and low-velocity impact behavior of sandwich beams with closed-cell aluminum-foam core in three-point bending." International Journal of Impact Engineering, no. 35 (2008): 885–894.
[17] V.L. Tagarielli, N.A. Fleck and V.S. Deshpande. "Collapse of clamped and simply supported composite sandwich beams in three-point bending." Composite Part B, no. 35 (2004): 523–534.
[18] V.L. Tagarielli, and N.A. Fleck. "A comparison of the structural response of clamped and simply supported sandwich beams with aluminum faces and a metal foam core. " Journal of Applied Physics A, no. 72 (2005): 408-417.
[19] F. Zhu, Z.H. Wang, G.X. Lu, and L.M. Zhao. "Analytical investigation and optimal design of sandwich panels subjected to shock loading." Material Design, no. 30 (2009): 91–100.
[20] L. Jing, Z.H. Wang and L.M. Zhao. "An approximate theoretical analysis for clamped cylindrical sandwich shells with metallic foam cores subjected to impulsive loading." Composite Part B, no. 60 (2014):150–157.
[21] R.W. Mao, G.X. Lu, Z.H. Wang, G.X. Lu, and L.M. Zhao. "Large deflection behavior of circular sandwich plates with metal foam-core. " European Journal Mechanics A/Solids, no. 55 (2016): 57–66.
[22] Z.H. Wang, L. Jing, J.G. Ning, and L.M. Zhao. "The structural response of clamped sandwich beams subjected to impact loading." Composite Structures, no. 93 (2011): 1300–1308.
[23] Q. Qin, and T.J. Wang. "An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch." Composite Structures, no. 88 (2008): 509–518.
[24] F. Zhu, Z.H. Wang, G. Lu, and G. Nurick. "Some theoretical considerations on the dynamic response of sandwich structures under impulsive loading." International Journal of Impact Engineering, no. 37 (2010): 625–637.
[25] B. Castanié, J.J. Barrau, and J.P. Jaouen. "Theoretical and experimental analysis of asymmetric sandwich structures." Composite Structures, no. 55 (2002): 295–306.
[26] H. Hu, S. Belouettar, M. Potier-Ferry, E.M. Daya, and A. Makradi. "Multi-scale nonlinear modelling of sandwich structures using the Arlequin method." Composite Structures, no. 92 (2010): 515–522.
[27] H. Hu, S. Belouettar, M. Potier-Ferry, A. Makradi and Y. Koutsawa. "Assessment of various kinematic models for instability analysis of sandwich beams." Engineering Structures, no. 33 (2011): 572–579.
[28] H. Hu, S. Belouettar, M. Potier-Ferry and A. Makradi. "A novel finite element for global and local buckling analysis of sandwich beams." Composite Structures, no. 90 (2009): 270–278.
[29] H. Bart-Smith, J.W. Hutchinson, and A.G. Evans." Measurement and analysis of the structural performance of cellular metal sandwich construction. " International Journal of Mechanical Sciences, no. 43 (2001): 1945–1963.
[30] P.D. Soden. "Indentation of composite sandwich beams." Journal of Strain Analysis for Engineering Design, no. 31 (1996): 353–360.
[31] P.O. Bostrom. "Collapse modes of a rigid-plastic beam on a rigid-plastic foundation." International Journal of Mechanical Sciences, no. 17 (1975): 73– 84.
[32] R.E. Miller. "A continuum plasticity model for the constitutive and indentation behavior of foamed metals." International Journal of Mechanical Sciences, no. 42 (2000): 729–754.
[33] N. Jones. "Structural impact." 2nd ed. Cambridge: Cambridge University, (2011).
[34] T. Wierzbicki and M.S. Hoo Fatt. "Impact response of a string-on-plastic foundation." International Journal of Impact Engineering, no. 12 (1992): 21–36.
[35] V. Rubino, V.S. Deshpande and N.A. Fleck. "The three-point bending of Y-frame and corrugated core sandwich beams." International Journal of Mechanical Sciences, no. 52 (2010): 485–494.
[36] H. Hu, S. Belouettar, M. Potier-Ferry and E.M. Daya. "Review and assessment of various theories for modeling sandwich composites." Composites Structures, no. 84 (2008): 282–292.
[37] W.Q. Hao, J.M. Xie, F.H. Wang, Z.F. Liu and Z.H. Wang. "Analytical model of thin walled corrugated tubes with sinusoidal patterns under axial impacting." International Journal of Mechanical Sciences, no. 128 (2017): 1–16.
[38] W.Q. Hao, J.M. Xie and F.H. Wang. "Theoretical prediction of the progressive buckling and energy absorption of the sinusoidal corrugated tube subjected to axial crushing." Computer Structures, no. 191 (2017): 12–21.
[39] X. Qiu, V.S. Deshpande and N.A. Fleck. "Dynamic response of a clamped circular sandwich plate subject to shock loading." Journal of Applied Mechanics, no. 71 (2004): 637–645.
[40] Z.W. Zhou, Z.H. Wang, L.M. Zhao and X.F. Shu. "Loading rate effect on yield surface of aluminum alloy foams. " Material Science Engineering A, no. 543 (2012): 193–199.
[41] Z.W. Zhou, Z.H. Wang, L.M. Zhao and X.F. Shu. "Uniaxial and biaxial failure behaviors of aluminum alloy foams." Composite Part B, no. 61 (2014): 340–349.
[42] K. Yu, H. Hu, H. Tang, G. Giunta, M. Potier-Ferry and S. Belouettar. "A novel two dimensional finite elements to study the instability phenomena of sandwich plates." Computer Methods in Applied Mechanics and Engineering, no. 283 (2015): 1117–1137.
[43] Q. Huang, Y. Liu, H. Hu, Q. Shao, K. Yu and G. Giunta. "A Fourier-related double scale analysis on the instability phenomena of sandwich plates." Computer Methods in Applied Mechanics and Engineering, no. 318 (2017): 270–295.
[44] Y. Liu, K. Yu, H. Hu, S. Belouettar, M. Potier-Ferry and N. Damil. "A new Fourier related double scale analysis for instability phenomena in sandwich structures. " International Journal of Solids Structures, no. 49 (2012): 3077–3088.
[45] V.S. Deshpande and N.A. Fleck. "Isotropic constitutive models for metallic foams." Journal of the Mechanics and Physics of Solids, no. 48 (2000): 1253–1283.
[46] J.X. Zhang, Q.H. Qin, X.H. Han and W.L. Ai. "The initial plastic failure of fully clamped geometrical asymmetric metal foam core sandwich beams." Composite Part B, no. 87 (2016): 233–244.