Analytical and numerical solution for multiple shape memory effect of smart corrugated-core sandwich panels with different patterns. (English) Zbl 1516.74065
Summary: Shape memory polymers (SMPS) are a class of smart materials used in various industries due to their unique properties. On the other hand, sandwich structures have attracted the attention of many researchers and industries due to their low weight and high strength. Therefore, this study it is aimed to present a semi-analytical solution to describe the behavior of a sandwich plate made of temperature-sensitive SMPs with a corrugated structure, based on the Reissner-Mindlin plate theory together with the viscoelastic theory. The solution is implemented for both dual shape memory (shape and force recovery) and triple shape memory scenarios. Three types of structure, including rectangular, triangular and trapezoidal, have been studied. In addition, in order to examine the impact of the support type, simply supported and clamped boundary conditions have also been investigated for three different geometries. Also, this work examines the impact of thermal stress caused by expansion. In addition to the semi-analytical solution, finite element modeling has also been carried out in all problems. Comparing the results in different geometries and supports shows the proposed semi-analytical solution’s ability to predict the material’s behavior with great accuracy. Moreover, by examining different cores and supports, one may observe a significant difference in the amount and distribution of the force and deformation, which are key to the design. Therefore, the semi-analytical solution can be considered reliable and accurate for various problems. In addition, compared to the finite element solution, the analytical solution enjoys a much higher speed; thus, it can be used for optimization and design problems that require a huge number of simulations.
MSC:
| 74K20 | Plates |
| 74E30 | Composite and mixture properties |
| 74F05 | Thermal effects in solid mechanics |
| 74D05 | Linear constitutive equations for materials with memory |
| 74M05 | Control, switches and devices (“smart materials”) in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
Reissner-Mindlin plate theory; thermo-viscoelastic Weichert polymer model; double Fourier series solution; finite element methodReferences:
| [1] | Abbasi-Shirsavar, M.; Baghani, M.; Taghavimehr, M.; Golzar, M.; Nikzad, M.; Ansari, M.; George, D., An experimental-numerical study on shape memory behavior of PU/PCL/ZnO ternary blend, J. Intell. Mater. Syst. Struct., 30, 1, 116-126 (2019) |
| [2] | Akbari-Azar, S.; Baghani, M.; Zakerzadeh, M. R.; Shahsavari, H.; Sohrabpour, S., Analytical investigation of composite sandwich beams filled with shape memory polymer corrugated core, Meccanica, 54, 10, 1647-1661 (2019) · Zbl 1532.74068 |
| [3] | Arrieta, S.; Diani, J.; Gilormini, P., Experimental characterization and thermoviscoelastic modeling of strain and stress recoveries of an amorphous polymer network, Mech. Mater., 68, 95-103 (2014) |
| [4] | Bakhtiyari, A.; Baniasadi, M.; Baghani, M., Development of a large strain formulation for multiple shape-memory-effect of polymers under bending, Int. J. Mech. Sci., 204, Article 106560 pp. (2021) |
| [5] | Bakhtiyari, A.; Baniasadi, M.; Baghani, M., A modified constitutive model for shape memory polymers based on nonlinear thermo-visco-hyperelasticity with application to multi-physics problems, Int. J. Appl. Mech., Article 2350032 pp. (2023) |
| [6] | Bakhtiyari, A.; Baghani, M.; Sohrabpour, S., An investigation on multilayer shape memory polymers under finite bending through nonlinear thermo-visco-hyperelasticity, Appl. Math. Mech., 44, 1, 73-88 (2023) · Zbl 1514.74016 |
| [7] | Baniasadi, M.; Maleki-Bigdeli, M.-A.; Baghani, M., Force and multiple-shape-recovery in shape-memory-polymers under finite deformation torsion-extension, Smart Mater. Struct., 29, 5, 55011 (2020) |
| [8] | Baniasadi, M.; Yarali, E.; Foyouzat, A.; Baghani, M., Crack self-healing of thermo-responsive shape memory polymers with application to control valves, filtration, and drug delivery capsule, Eur. J. Mech. Solid., 85, 104093 (2021) · Zbl 1478.74061 |
| [9] | Bartolozzi, G.; Pierini, M.; Orrenius, U.; Baldanzini, N., An equivalent material formulation for sinusoidal corrugated cores of structural sandwich panels, Compos. Struct., 100, 173-185 (2013) |
| [10] | Brinson, H. F.; Brinson, L. C., Polymer engineering science and viscoelasticity, An introduction, 99-157 (2008) |
| [11] | Buckley, P. R.; McKinley, G. H.; Wilson, T. S.; Small, W.; Benett, W. J.; Bearinger, J. P.; McElfresh, M. W.; Maitland, D. J., Inductively heated shape memory polymer for the magnetic actuation of medical devices, IEEE Trans. Biomed. Eng., 53, 10, 2075-2083 (2006) |
| [12] | Chang, W.-S., Elasto-plastic Analysis of Corrugated Sandwich Steel Panels (2004), The Pennsylvania State University |
| [13] | Chang, W.-S.; Ventsel, E.; Krauthammer, T.; John, J., Bending behavior of corrugated-core sandwich plates, Compos. Struct., 70, 1, 81-89 (2005) |
| [14] | Chung, T.; Romo-Uribe, A.; Mather, P. T., Two-way reversible shape memory in a semicrystalline network, Macromolecules, 41, 1, 184-192 (2008) |
| [15] | Di Marzio, E. A.; Yang, A. J., Configurational entropy approach to the kinetics of glasses, Journal of research of the National Institute of Standards and Technology, 102, 2, 135 (1997) |
| [16] | Diani, J.; Liu, Y.; Gall, K., Finite strain 3D thermoviscoelastic constitutive model for shape memory polymers, Polym. Eng. Sci., 46, 4, 486-492 (2006) |
| [17] | El Kouri, M.; Bakkali, A.; Azrar, L., Mathematical modeling of the overall time-dependent behavior of non-ageing viscoelastic reinforced composites, Appl. Math. Model., 40, 7-8, 4302-4322 (2016) · Zbl 1459.74031 |
| [18] | Fan, P.; Chen, W.; Zhao, B.; Hu, J.; Gao, J.; Fang, G.; Peng, F., Formulation and numerical implementation of tensile shape memory process of shape memory polymers, Polymer, 148, 370-381 (2018) |
| [19] | Gharehnazifam, Z.; Dolatabadi, R.; Baniassadi, M.; Shahsavari, H.; Kajbafzadeh, A. M.; Abrinia, K.; Baghani, M., Computational analysis of vincristine loaded silk fibroin hydrogel for sustained drug delivery applications: multiphysics modeling and experiments, Int. J. Pharm., 609 (2021) |
| [20] | Gharehnazifam, Z.; Dolatabadi, R.; Baniassadi, M.; Shahsavari, H.; Kajbafzadeh, A.-M.; Abrinia, K.; Gharehnazifam, K.; Baghani, M., Multiphysics modeling and experiments on ultrasound-triggered drug delivery from silk fibroin hydrogel for Wilms tumor, Int. J. Pharm., 621, 121787 (2022) |
| [21] | Hager, M. D.; Bode, S.; Weber, C.; Schubert, U. S., Shape memory polymers: past, present and future developments, Prog. Polym. Sci., 49, 3-33 (2015) |
| [22] | Han, X. J.; Dong, Z. Q.; Fan, M. M.; Liu, Y.; li, J. H.; Wang, Y. F.; Yuan, Q. J.; Li, B. J.; Zhang, S., pH-induced shape-memory polymers, Macromol. Rapid Commun., 33, 12, 1055-1060 (2012) |
| [23] | Hardy, J. G.; Palma, M.; Wind, S. J.; Biggs, M. J., Responsive biomaterials: advances in materials based on shape-memory polymers, Adv. Mater., 28, 27, 5717-5724 (2016) |
| [24] | Herrmann, A. S.; Zahlen, P. C.; Zuardy, I., Sandwich structures technology in commercial aviation, Sandwich structures 7: Advancing with sandwich structures and materials, 13-26 (2005) |
| [25] | Isaksson, P.; Krusper, A.; Gradin, P. A., Shear correction factors for corrugated core structures, Compos. Struct., 80, 1, 123-130 (2007) |
| [26] | Ko, W. L., Elastic constants for superplastically formed/diffusion-bonded sandwich structures, AIAA J., 18, 8, 986-987 (1980) · Zbl 0466.73084 |
| [27] | Koudzari, M.; Zakerzadeh, M.-R.; Baghani, M., Corrugated structures reinforced by shape memory alloy sheets: analytical modeling and finite element modeling, Proc. IME G J. Aero. Eng., 233, 7, 2445-2454 (2019) |
| [28] | Kress, G.; Winkler, M., Corrugated laminate homogenization model, Compos. Struct., 92, 3, 795-810 (2010) |
| [29] | Lei, M.; Chen, Z.; Lu, H.; Yu, K., Recent progress in shape memory polymer composites: methods, properties, applications and prospects, Nanotechnol. Rev., 8, 1, 327-351 (2019) |
| [30] | Li, G.; Fei, G.; Xia, H.; Han, J.; Zhao, Y., Spatial and temporal control of shape memory polymers and simultaneous drug release using high intensity focused ultrasound, J. Mater. Chem., 22, 16, 7692-7696 (2012) |
| [31] | Libove, C.; Batdorf, S., A general small-deflection theory for flat sandwich plates, NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON DC. (1948) |
| [32] | Libove, C.; Hubka, R. E., Elastic Constants for Corrugated-Core Sandwich Plates (1951) |
| [33] | Libove, C.; Hubka, R. E., Elastic Constants for Corrugated-Core Sandwich Plates (1951) |
| [34] | Liew, K. M.; Peng, L.; Kitipornchai, S., Vibration analysis of corrugated Reissner-Mindlin plates using a mesh-free Galerkin method, Int. J. Mech. Sci., 51, 9-10, 642-652 (2009) |
| [35] | Lin, J.; Chen, L., Shape-memorized crosslinked ester-type polyurethane and its mechanical viscoelastic model, J. Appl. Polym. Sci., 73, 7, 1305-1319 (1999) |
| [36] | Liu, Y.; Gall, K.; Dunn, M. L.; Greenberg, A. R.; Diani, J., Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling, Int. J. Plast., 22, 2, 279-313 (2006) · Zbl 1330.74052 |
| [37] | Lu, H.; Liu, Y.; Leng, J.; Du, S., Qualitative separation of the effect of the solubility parameter on the recovery behavior of shape-memory polymer, Smart Mater. Struct., 18, 8, 85003 (2009) |
| [38] | Lu, H.; Huang, W. M.; Fu, Y. Q.; Leng, J., Quantitative separation of the influence of hydrogen bonding of ethanol/water mixture on the shape recovery behavior of polyurethane shape memory polymer, Smart Mater. Struct., 23, 12, 125041 (2014) |
| [39] | Lu, H.; Lei, M.; Zhao, C.; Xu, B.; Leng, J.; Fu, Y. Q., Structural design of flexible Au electrode to enable shape memory polymer for electrical actuation, Smart Mater. Struct., 24, 4, 45015 (2015) |
| [40] | Lu, H.; Liang, F.; Zhu, S.; Yang, Y.; Yao, Y.; Fu, Y. Q., Graphene oxide enabled polymeric shape memory composites for enhanced electro-actuation, Nanosci. Nanotechnol. Lett., 7, 3, 215-219 (2015) |
| [41] | Lu, H.; Lu, C.; Huang, W. M.; Leng, J., Quantitative separation of the influence of copper (II) chloride mass migration on the chemo-responsive shape memory effect in polyurethane shape memory polymer, Smart Mater. Struct., 25, 10, 105003 (2016) |
| [42] | Mackerle, J., Finite element analyses of sandwich structures: a bibliography, Eng. Comput., 19, 2, 206-245 (2002), 1980-2001 · Zbl 1038.74001 |
| [43] | Maleki-Bigdeli, M.-A.; Sheikhi, S.; Baghani, M., Development of an analytical framework for viscoelastic corrugated-core sandwich plates and validation against FEM, Meccanica, 56, 8, 2103-2120 (2021) · Zbl 1520.74057 |
| [44] | Nordstrand, T.; Carlsson, L. A.; Allen, H. G., Transverse shear stiffness of structural core sandwich, Compos. Struct., 27, 3, 317-329 (1994) |
| [45] | Prathumrat, P.; Nikzad, M.; Hajizadeh, E.; Arablouei, R.; Sbarski, I., Shape memory elastomers: a review of synthesis, design, advanced manufacturing, and emerging applications, Polym. Adv. Technol., 33, 6, 1782-1808 (2022) |
| [46] | Pydah, A.; Batra, R., Analytical solution for cylindrical bending of two-layered corrugated and webcore sandwich panels, Thin-Walled Struct., 123, 509-519 (2018) |
| [47] | Reissner, E., On bending of elastic plates. Quarterly of Applied Mathematics, 5, 1, 55-68 (1947) · Zbl 0030.04302 |
| [48] | Roudbarian, N.; Jebellat, E.; Famouri, S.; Baniasadi, M.; Hedayati, R.; Baghani, M., Shape-memory polymer metamaterials based on triply periodic minimal surfaces, Eur. J. Mech. Solid., 96, Article 104676 pp. (2022) · Zbl 1498.74009 |
| [49] | Samanta, A.; Mukhopadhyay, M., Finite element static and dynamic analyses of folded plates, Eng. Struct., 21, 3, 277-287 (1999) |
| [50] | Shaban, M.; Alibeigloo, A., Three-dimensional elasticity solution for sandwich panels with corrugated cores by using energy method, Thin-Walled Struct., 119, 404-411 (2017) |
| [51] | Shaban, M.; Mazaheri, H., Closed-form elasticity solution for smart curved sandwich panels with soft core, Appl. Math. Model., 76, 50-70 (2019) · Zbl 1481.74201 |
| [52] | Tobushi, H.; Hashimoto, T.; Hayashi, S.; Yamada, E., Thermomechanical constitutive modeling in shape memory polymer of polyurethane series, J. Intell. Mater. Syst. Struct., 8, 8, 711-718 (1997) |
| [53] | Valdevit, L.; Hutchinson, J. W.; Evans, A. G., Structurally optimized sandwich panels with prismatic cores, Int. J. Solid Struct., 41, 18-19, 5105-5124 (2004) · Zbl 1073.74043 |
| [54] | Valdevit, L.; Wei, Z.; Mercer, C.; Zok, F. W.; Evans, A. G., Structural performance of near-optimal sandwich panels with corrugated cores, Int. J. Solid Struct., 43, 16, 4888-4905 (2006) · Zbl 1120.74697 |
| [55] | Varkani, M. M.; Bidgoli, M. R.; Mazaheri, H., Mathematical modelling and dynamic response of concrete frames containing shape memory alloys under seismic loads, Appl. Math., 111, 590-609 (2022) · Zbl 1505.74023 |
| [56] | Wang, H.-X.; Chung, S. W., Equivalent elastic constants of truss core sandwich plates, J. Pressure Vessel Technol., 133, 4 (2011) |
| [57] | Wang, X.; Yuan, Z., Accurate stress analysis of sandwich panels by the differential quadrature method, Appl. Math. Model., 43, 548-565 (2017) · Zbl 1446.74063 |
| [58] | Wang, C. C.; Huang, W. M.; Ding, Z.; Zhao, Y.; Purnawali, H., Cooling-/water-responsive shape memory hybrids, Compos. Sci. Technol., 72, 10, 1178-1182 (2012) |
| [59] | Winkler, M.; Kress, G., Influence of corrugation geometry on the substitute stiffness matrix of corrugated laminates, Compos. Struct., 94, 9, 2827-2833 (2012) |
| [60] | Xia, Y.; Friswell, M.; Flores, E. S., Equivalent models of corrugated panels, Int. J. Solid Struct., 49, 13, 1453-1462 (2012) |
| [61] | Xia, Y.; He, Y.; Zhang, F.; Liu, Y.; Leng, J., A review of shape memory polymers and composites: mechanisms, materials, and applications, Adv. Mater., 33, 6, 2000713 (2021) |
| [62] | Xiao, R., Modeling solvent-activated shape-memory behaviors based on an analogy between solvent and temperature, RSC Adv., 6, 8, 6378-6383 (2016) |
| [63] | Yang, J.; Zheng, Y.; Sheng, L.; Chen, H.; Zhao, L.; Yu, W.; Zhao, K.-Q.; Hu, P., Water induced shape memory and healing effects by introducing carboxymethyl cellulose sodium into poly (vinyl alcohol), Ind. Eng. Chem. Res., 57, 44, 15046-15053 (2018) |
| [64] | Yarali, E.; Baniassadi, M.; Baghani, M., Numerical homogenization of coiled carbon nanotube reinforced shape memory polymer nanocomposites, Smart Mater. Struct., 28, 3 (2019) |
| [65] | Yokozeki, T.; Takeda, S.-i.; Ogasawara, T.; Ishikawa, T., Mechanical properties of corrugated composites for candidate materials of flexible wing structures, Compos. Appl. Sci. Manuf., 37, 10, 1578-1586 (2006) |
| [66] | Yuan, Z.; Muliana, A.; Rajagopal, K. R., Modeling the response of light-activated shape memory polymers, Math. Mech. Solid, 22, 5, 1116-1143 (2017) · Zbl 1371.74102 |
| [67] | Zhang, F.; Zhang, Z.; Luo, C.; Lin, I.-T.; Liu, Y.; Leng, J.; Smoukov, S. K., Remote, fast actuation of programmable multiple shape memory composites by magnetic fields, J. Mater. Chem. C, 3, 43, 11290-11293 (2015) |
| [68] | Zhi, Y.; Muliana, A.; Rajagopal, K., Quasi-linear viscoelastic modeling of light-activated shape memory polymers, J. Intell. Mater. Syst. Struct., 28, 18, 2500-2515 (2017) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
