Parametric study of Sandwich Plates with Viscoelastic, Auxetic Viscoelastic and Orthotropic Viscoelastic Core Using a New Higher Order Global-Local Theory

Document Type : Research Paper


1 Renewable Energies Department, Niroo Research Institute (NRI), Tehran, Iran

2 Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran



In this paper, sandwich plates with flexible core and composite surfaces as well as viscoelastic and auxetic core is investigated under dynamic loading. A new higher order global-local theory is used for simulation of the dynamic behavior of sandwich plate. Ability of simulation the thickness changes of the plate and calculation of exact transverse stresses which are so crucial for studying of thick sandwich plate especially by soft core are some of the important features of the presented theory. Furthermore, in terms of solving equations, an iterative incremental method based on the formulation of transient nonlinear finite element as well as a real time algorithm was employed to simulate viscoelastic behavior accurately. The results indicate a significant increase in the stiffness of the sandwich plate due to the auxetic properties of the core materials, leading consequently to the reduction of the vibration amplitude and stresses level. Some of the innovations belonging to this paper are: 1) presenting a global-local higher-order theory while considering the changes in the thickness of the sandwich plates; 2) calculating transverse stresses using the three-dimensional elasticity method as well as modifying the results obtained from displacement and inertial effects based on this method; 3) simulating sandwich plate with viscoelastic and auxetic cores; 4) taking orthotropic properties for the viscoelastic core into account.


[1]        Z. Hashin, Viscoelastic behavior of heterogeneous media, 1965.
[2]        R. S. Lakes, A. Wineman, On Poisson’s ratio in linearly viscoelastic solids, Journal of Elasticity, Vol. 85, No. 1, pp. 45-63, 2006.
[3]        B. K. Eshmatov, Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates, Journal of Sound and Vibration, Vol. 300, No. 3-5, pp. 709-726, 2007.
[4]        R. Alex, L. Schovanec, An anti-plane crack in a nonhomogeneous viscoelastic body, Engineering fracture mechanics, Vol. 55, No. 5, pp. 727-735, 1996.
[5]        L. Schovanec, J. R. Walton, The quasi-static propagation of a plane strain crack in a power-law inhomogeneous linearly viscoelastic body, Acta mechanica, Vol. 67, No. 1-4, pp. 61-77, 1987.
[6]        G. H. Paulino, Z.-H. Jin, Correspondence principle in viscoelastic functionally graded materials, J. Appl. Mech., Vol. 68, No. 1, pp. 129-132, 2001.
[7]        A. Assie, M. Eltaher, F. Mahmoud, Modeling of viscoelastic contact-impact problems, Applied Mathematical Modelling, Vol. 34, No. 9, pp. 2336-2352, 2010.
[8]        G. Cederbaum, J. Aboudi, Dynamic response of viscoelastic laminated plates, Journal of sound and vibration, Vol. 133, No. 2, pp. 225-238, 1989.
[9]        T. M. Chen, The hybrid Laplace transform/finite element method applied to the quasi‐static and dynamic analysis of viscoelastic Timoshenko beams, International Journal for Numerical Methods in Engineering, Vol. 38, No. 3, pp. 509-522, 1995.
[10]      M. Ilyasov, Dynamic stability of viscoelastic plates, International journal of engineering science, Vol. 45, No. 1, pp. 111-122, 2007.
[11]      F. Abdoun, L. Azrar, E. Daya, M. Potier-Ferry, Forced harmonic response of viscoelastic structures by an asymptotic numerical method, Computers & Structures, Vol. 87, No. 1-2, pp. 91-100, 2009.
[12]      A. Assie, M. Eltaher, F. Mahmoud, Behavior of a viscoelastic composite plates under transient load, Journal of mechanical science and technology, Vol. 25, No. 5, pp. 1129, 2011.
[13]      M. Shariyat, S. Khalili, I. Rajabi, A global–local theory with stress recovery and a new post-processing technique for stress analysis of asymmetric orthotropic sandwich plates with single/dual cores, Computer Methods in Applied Mechanics and Engineering, Vol. 286, pp. 192-215, 2015.
[14]      C. Wanji, W. Zhen, A selective review on recent development of displacement-based laminated plate theories, Recent patents on mechanical engineering, Vol. 1, No. 1, pp. 29-44, 2008.
[15]      R. Moreira, J. D. Rodrigues, A layerwise model for thin soft core sandwich plates, Computers & structures, Vol. 84, No. 19-20, pp. 1256-1263, 2006.
[16]      D. Elmalich, O. Rabinovitch, A high-order finite element for dynamic analysis of soft-core sandwich plates, Journal of Sandwich Structures & Materials, Vol. 14, No. 5, pp. 525-555, 2012.
[17]      O. Rabinovitch, Y. Frostig, High-order behavior of fully bonded and delaminated circular sandwich plates with laminated face sheets and a “soft” core, International journal of solids and structures, Vol. 39, No. 11, pp. 3057-3077, 2002.
[18]      M. Ćetković, D. Vuksanović, Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model, Composite structures, Vol. 88, No. 2, pp. 219-227, 2009.
[19]      W. Zhen, C. Wanji, Free vibration of laminated composite and sandwich plates using global–local higher-order theory, Journal of Sound and Vibration, Vol. 298, No. 1-2, pp. 333-349, 2006.
[20]      A. Ghaznavi, M. Shariyat, Higher-order global-local theory with novel 3D-equilibrium-based corrections for static, frequency, and dynamic analysis of sandwich plates with flexible auxetic cores, Mechanics of Advanced Materials and Structures, Vol. 26, No. 7, pp. 559-578, 2019.
[21]      H. Wan, Y. Li, L. Zheng, Vibration and damping analysis of a multilayered composite plate with a viscoelastic midlayer, Shock and Vibration, Vol. 2016, 2016.
[22]      Y. Zhai, Y. Li, S. Liang, Free vibration analysis of five-layered composite sandwich plates with two-layered viscoelastic cores, Composite Structures, Vol. 200, pp. 346-357, 2018.
[23]      B. Liu, L. Zhao, A. Ferreira, Y. Xing, A. Neves, J. Wang, Analysis of viscoelastic sandwich laminates using a unified formulation and a differential quadrature hierarchical finite element method, Composites Part B: Engineering, Vol. 110, pp. 185-192, 2017.
[24]      J. S. Moita, A. L. Araújo, V. F. Correia, C. M. M. Soares, J. Herskovits, Active-passive damping in functionally graded sandwich plate/shell structures, Composite Structures, Vol. 202, pp. 324-332, 2018.
[25]      M. Filippi, E. Carrera, S. Valvano, Analysis of multilayered structures embedding viscoelastic layers by higher-order, and zig-zag plate elements, Composites Part B: Engineering, Vol. 154, pp. 77-89, 2018.
[26]      S. Ren, G. Zhao, S. Zhang, A layerwise finite element formulation for vibration and damping analysis of sandwich plate with moderately thick viscoelastic core, Mechanics of Advanced Materials and Structures, Vol. 27, No. 14, pp. 1201-1212, 2020.
[27]      A. Ghaznavi, M. Shariyat, Non-linear layerwise dynamic response analysis of sandwich plates with soft auxetic cores and embedded SMA wires experiencing cyclic loadings, Composite Structures, Vol. 171, pp. 185-197, 2017.
[28]      G. Imbalzano, P. Tran, T. D. Ngo, P. V. Lee, Three-dimensional modelling of auxetic sandwich panels for localised impact resistance, Journal of Sandwich Structures & Materials, Vol. 19, No. 3, pp. 291-316, 2017.
[29]      M. Mansouri, M. Shariyat, Biaxial thermo-mechanical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations, Composites Part B: Engineering, Vol. 83, pp. 88-104, 2015.
[30]      G. Imbalzano, S. Linforth, T. D. Ngo, P. V. S. Lee, P. Tran, Blast resistance of auxetic and honeycomb sandwich panels: Comparisons and parametric designs, Composite Structures, Vol. 183, pp. 242-261, 2018.
[31]      J. Zhang, G. Lu, D. Ruan, Z. Wang, Tensile behavior of an auxetic structure: Analytical modeling and finite element analysis, International Journal of Mechanical Sciences, Vol. 136, pp. 143-154, 2018.
[32]      Y. Wang, W. Zhao, G. Zhou, C. Wang, Analysis and parametric optimization of a novel sandwich panel with double-V auxetic structure core under air blast loading, International Journal of Mechanical Sciences, Vol. 142, pp. 245-254, 2018.
[33]      J. Zhang, X. Zhu, X. Yang, W. Zhang, Transient nonlinear responses of an auxetic honeycomb sandwich plate under impact loads, International Journal of Impact Engineering, Vol. 134, pp. 103383, 2019.
[34]      J. N. Reddy, 2003, Mechanics of laminated composite plates and shells: theory and analysis, CRC press,
[35]      J. L. Schoner, J. Lang, H. P. Seidel, Measurement‐based interactive simulation of viscoelastic solids, in Proceeding of, Wiley Online Library, pp. 547-556.
[36]      J.-M. Schwartz, D. Laurendeau, M. Denninger, D. Rancourt, C. Simo, Modeling Techniques For Liver Tissue Properties and Their Application in Surgical Treatment of Liver Cancer,  in: Biomechanical Systems Technology: Volume 4: General Anatomy, Eds., pp. 45-81: World Scientific, 2007.
[37]      G. Debunne, M. Desbrun, M.-P. Cani, A. H. Barr, Dynamic real-time deformations using space & time adaptive sampling, in Proceeding of, 31-36.
[38]      M. Sedef, E. Samur, C. Basdogan, Real-time finite-element simulation of linear viscoelastic tissue behavior based on experimental data, IEEE Computer Graphics and Applications, Vol. 26, No. 6, pp. 58-68, 2006.
[39]      M. Alipour, M. Shariyat, Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations, Mechanics Research Communications, Vol. 38, No. 8, pp. 594-601, 2011.
[40]      M. Shariyat, M. Alipour, A novel shear correction factor for stress and modal analyses of annular FGM plates with non-uniform inclined tractions and non-uniform elastic foundations, International Journal of Mechanical Sciences, Vol. 87, pp. 60-71, 2014.
[41]      M. Cho, K.-O. Kim, M.-H. Kim, Efficient higher-order shell theory for laminated composites, Composite Structures, Vol. 34, No. 2, pp. 197-212, 1996.
[42]      W. Zhen, C. Wanji, A global-local higher order theory including interlaminar stress continuity and C 0 plate bending element for cross-ply laminated composite plates, Computational Mechanics, Vol. 45, No. 5, pp. 387-400, 2010.
[43]      M. Shariyat, An accurate double-superposition global–local theory for vibration and bending analyses of cylindrical composite and sandwich shells subjected to thermo-mechanical loads, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 225, No. 8, pp. 1816-1832, 2011.
[44]      M. Shariyat, A. Ghaznavi, Influence analysis of phase transformation anisotropy of shape memory alloy wires embedded in sandwich plates with flexible cores by a third-order zigzag theory with dynamic three-dimensional elasticity corrections, Journal of Sandwich Structures & Materials, Vol. 22, No. 5, pp. 1450-1495, 2020.
[45]      F. Tornabene, N. Fantuzzi, M. Bacciocchi, J. Reddy, A posteriori stress and strain recovery procedure for the static analysis of laminated shells resting on nonlinear elastic foundation, Composites Part B: Engineering, Vol. 126, pp. 162-191, 2017.
[46]      L. Iurlaro, M. Gherlone, M. Di Sciuva, A. Tessler, Refined Zigzag Theory for laminated composite and sandwich plates derived from Reissner’s Mixed Variational Theorem, Composite Structures, Vol. 133, pp. 809-817, 2015.
[47]      K. E. Evans, A. Alderson, Auxetic materials: functional materials and structures from lateral thinking!, Advanced materials, Vol. 12, No. 9, pp. 617-628, 2000.
[48]      Y. Wang, T. Tsai, Static and dynamic analysis of a viscoelastic plate by the finite element method, Applied Acoustics, Vol. 25, No. 2, pp. 77-94, 1988.
[49]      A. Araújo, C. Mota Soares, C. Mota Soares, Finite element model for hybrid active-passive damping analysis of anisotropic laminated sandwich structures, Journal of Sandwich Structures & Materials, Vol. 12, No. 4, pp. 397-419, 2010.
[50]      Z. Huang, Z. Qin, F. Chu, Vibration and damping characteristics of sandwich plates with viscoelastic core, Journal of Vibration and Control, Vol. 22, No. 7, pp. 1876-1888, 2016.
[51]      G. Wang, S. Veeramani, N. M. Wereley, Analysis of sandwich plates with isotropic face plates and a viscoelastic core, J. Vib. Acoust., Vol. 122, No. 3, pp. 305-312, 2000.
[52]      A. Assie, M. Eltaher, F. Mahmoud, The response of viscoelastic-frictionless bodies under normal impact, International journal of mechanical sciences, Vol. 52, No. 3, pp. 446-454, 2010. 
Volume 52, Issue 1
March 2021
Pages 126-153
  • Receive Date: 09 December 2020
  • Revise Date: 13 January 2021
  • Accept Date: 15 January 2021