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3D layerwise impact investigation of sandwich plates with multi-directional phase transformation SMA face sheets and nearly incompressible compliant hyperelastic cores

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Abstract

In the present article, the finite element (FE) simulation of the low-velocity impact of a sandwich plate with a nearly incompressible compliant hyperelastic core and SMA face sheets is accomplished for the first time, using a 3D pseudoelasticity phase transformation model and a semi-3D layerwise sandwich plate theory. The changes in the thickness and the time/load-dependence of the stiffness of the contact region are taken into account and various (neo-Hookean, Mooney-Rivlin, and Yeoh) hyperelasticity models and clamped and simply supported boundary conditions are examined. The resulting nonlinear coupled governing finite element equations of the damped impact response of the hyperelastic and pseudoelastic plate are solved by an iterative updating algorithm that is capable of tracing the impact and complete/incomplete direct and converse 3D phase transformation events. The modeling procedure, formulation, and solution algorithm feature apparent superiorities, even on the well-known commercial finite element analysis codes, due to employing higher scientific and mathematical accuracies. It is found that while the Mooney-Rivlin model induces larger compliance in comparison with the neo-Hookean and Yeoh hyperelasticity models, the SMA face sheets significantly reduce the resulting lateral deflections but increase the global stiffness of the contact region and the contact force, and that simply supported plates feature larger recovery strains and hysteresis loops that lead to higher damping and smoother time histories.

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References

  1. Cong, P.H., Cong, P.T., Nhat, N.V., Duc, N.D.: Geometrically nonlinear dynamic response of eccentrically stiffened circular cylindrical shells with negative Poisson’s ratio in auxetic honeycombs core layer. Int. J. Mech. Sci. 152, 443–453 (2019)

    Article  Google Scholar 

  2. Duc, N.D., Tuan, N.D., Tran, P., Quan, T.Q.: Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads. J. Mech. Adv. Mater. Struct. 24, 318–329 (2017)

    Article  Google Scholar 

  3. Phuc, P.M., Duc, N.D.: The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory. J. Compos. Part B Eng. 175, 107086 (2019)

    Article  Google Scholar 

  4. Cong, P.H., Duc, N.D.: New approach to investigate nonlinear dynamic response and vibration of functionally graded multilayer graphene nanocomposite plate on viscoelastic Pasternak medium in thermal environment. Acta Mech. 229, 3651–3670 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  5. Quan, T.Q., Ha, D.T.T., Duc, N.D.: Analytical solutions for nonlinear vibration of porous functionally graded sandwich plate subjected to blast loading. Thin-Walled Struct. 170, 108606 (2022)

    Article  Google Scholar 

  6. Nassiri-Monfared, A., Baghani, M., Zakerzadeh, M.R., Fahimi, P.: Developing a semi-analytical model for thermomechanical response of SMA laminated beams, considering SMA asymmetric behavior. Meccanica 53, 957–971 (2018)

    Article  Google Scholar 

  7. Lester, B.T., Baxevanis, T., Chemisky, Y., Lagoudas, D.C.: Review and perspectives: shape memory alloy composite systems. Acta Mech. 226, 3907–3960 (2015)

    Article  Google Scholar 

  8. Karimi Mahabadi, R., Danesh Pazhooh, M., Shakeri, M.: On the free vibration and design optimization of a shape memory alloy hybrid laminated composite plate. Acta Mech. 232, 323–343 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  9. Shariyat, M., Ghaznavi, A., Hosseini, S.H.: On inefficiency of the shape memory alloys in dynamically loaded sandwich plates with structural damping: New 3D zigzag-viscoelasticity theory and asymmetric transformations. Thin-Walled Struct. 155, 106879 (2020)

    Article  Google Scholar 

  10. Gupta, A.K., Velmurugan, R., Joshi, M., Gupta, N.K.: Studies on shape memory alloy-embedded GFRP composites for improved post-impact damage strength. Int. J. Crashworthiness 24, 363–379 (2019)

    Article  Google Scholar 

  11. Chang, M., Wang, Z., Liang, W., Sun, M.: A novel failure analysis of SMA reinforced composite plate based on a strain-rate-dependent model: low-high velocity impact. J. Mater. Res. Technol. 8, 812–826 (2019)

    Article  Google Scholar 

  12. Shariyat, M., Niknami, A.: Impact analysis of strain-rate-dependent composite plates with SMA wires in thermal environments: Proposing refined coupled thermoelasticity, constitutive, and contact models. Compos. Struct. 136, 191–203 (2016)

    Article  Google Scholar 

  13. Niknami, A., Shariyat, M.: Refined constitutive, bridging, and contact laws for including effects of the impact-induced temperature rise in impact responses of composite plates with embedded SMA wires. Thin-Walled Struct. 106, 166–178 (2016)

    Article  Google Scholar 

  14. Wang, J., Ren, X., Xu, Y., Zhang, W., Zhu, J., Li, B.: Thermodynamic behavior of NiTi shape memory alloy against low-velocity impact: experiment and simulation. Int. J. Impact Eng. 139, 103532 (2020)

    Article  Google Scholar 

  15. Chuanliang, S.H., Xiaodong, X.U., Xiaoyu, M.A., Yibo, H.U., Zhang, S., Yingchen, D.U., Zhenhai, G.A.: Shape memory alloy hybrid composites for improving impact properties. Mater. Sci. 27, 386–394 (2021)

    Google Scholar 

  16. Wang, W., Zhao, Y., Chen, S., Jin, X., Fan, X., Lu, C., Yang, C.: Low-velocity impact behaviors of glass fiber-reinforced polymer laminates embedded with shape memory alloy. Compos. Struct. 272, 114194 (2021)

    Article  Google Scholar 

  17. Popov, P., Lagoudas, D.C.: A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite. Int. J. Plast. 23, 1679–1720 (2007)

    Article  MATH  Google Scholar 

  18. Stebner, A.P., Brinson, L.C.: Explicit finite element implementation of an improved three dimensional constitutive model for shape memory alloys. Comput. Methods Appl. Mech. Eng. 257, 17–35 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Auricchio, F., Bonetti, E., Scalet, G., Ubertini, F.: Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation. Int. J. Plast. 59, 30–54 (2014)

    Article  Google Scholar 

  20. Breslavsky, I.D., Amabili, M., Legrand, M.: Nonlinear vibrations of thin hyperelastic plates. J. Sound Vib. 333, 4668–4681 (2014)

    Article  Google Scholar 

  21. Breslavsky, I.D., Amabili, M., Legrand, M.: Physically and geometrically non-linear vibrations of thin rectangular plates. Int. J. Non-Linear Mech. 58, 30–40 (2014)

    Article  Google Scholar 

  22. Xu, Q., Liu, J., Qu, L.: A higher-order plate element formulation for dynamic analysis of hyperelastic silicone plate. J. Mech. 35, 795–808 (2019)

    Article  Google Scholar 

  23. Ansari, R., Hassani, R., Oskouie, M.F., Rouhi, H.: Nonlinear bending analysis of hyperelastic Mindlin plates: a numerical approach. Acta Mech. 232, 741–760 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  24. Lezgy-Nazargah, M., Etemadi, E.: Reduced modal state-space approach for low-velocity impact analysis of sandwich beams. Compos. Struct. 206, 762–773 (2018)

    Article  Google Scholar 

  25. Lezgy-Nazargah, M., Etemadi, E., Hosseinian, S.R.: Assessment of four-variable refined shear deformation theory for low-velocity impact analysis of curved sandwich beams. Eur. J. Mech. A/Solids 94, 104604 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  26. Shariyat, M., Mozaffari, A., Pachenari, M.H.: Damping sources interactions in impact of viscoelastic composite plates with damping treated SMA wires, using a hyperbolic plate theory. Appl. Math. Model. 43, 421–440 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  27. Lagoudas, D., Hartl, D., Chemisky, Y., Machado, L., Popov, P.: Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. Int. J. Plast. 32, 155–183 (2012)

    Article  Google Scholar 

  28. Selvadurai, A.P.: Deflections of a rubber membrane. J. Mech. Phys. Solids 54, 1093–1119 (2006)

    Article  MATH  Google Scholar 

  29. Bergstrom, J.S.: Mechanics of Solid Polymers: Theory and Computational Modeling. William Andrew, Norwich (2015)

    Google Scholar 

  30. Piegl, L.A., Tiller, W.: The NURBS Book (Monographs in Visual Communication), 2nd edn. Springer, Berlin (1996)

    MATH  Google Scholar 

  31. Ren, J., Liew, K.M., Meguid, S.A.: Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method. Int. J. Mech. Sci. 44, 2393–2413 (2002)

    Article  MATH  Google Scholar 

  32. Shariyat, M., Jahanshahi, S., Rahimi, H.: Nonlinear Hermitian generalized hygrothermoelastic stress and wave propagation analyses of thick FGM spheres exhibiting temperature, moisture, and strain-rate material dependencies. Compos. Struct. 229, 111364 (2019)

    Article  Google Scholar 

  33. Shariyat, M., Khosravi, M., Yazdani Ariatapeh, M., Najafipour, M.: Nonlinear stress and deformation analysis of pressurized thick-walled hyperelastic cylinders with experimental verifications and material identifications. Int. J. Pressure Vessels Pip. 188, 104211 (2020)

    Article  Google Scholar 

  34. Mao, Y., Li, Y., Chen, Y., Miao, Y., Deng, Q., Niu, W.: Hyperelastic behavior of two rubber materials under quasistatic and dynamic compressive loadings- testing, modeling and application. Polimery 60, 516–522 (2015)

    Article  Google Scholar 

  35. Tejasri, P., Basak, A.: Comparative study of computational material models. Int. J. Appl. Eng. Res. 13, 8588–8595 (2018)

    Google Scholar 

  36. Brinson, L.C.: One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J. Intell. Mater. Syst. Struct. 4, 229–242 (1993)

    Article  Google Scholar 

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  1. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, 19991-43344, Iran

    M. Shariyat & S. H. Hosseini

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  1. M. Shariyat
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Shariyat, M., Hosseini, S.H. 3D layerwise impact investigation of sandwich plates with multi-directional phase transformation SMA face sheets and nearly incompressible compliant hyperelastic cores. Acta Mech 233, 4385–4406 (2022). https://doi.org/10.1007/s00707-022-03337-w

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  • DOI: https://doi.org/10.1007/s00707-022-03337-w

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