Numerical study to compare effective elastic, piezoelectric, and thermal properties of a gyroid triply periodic minimal surface and 0–3 piezoelectric composites with lead-free Ba(Ti_0.8Zr_0.2)O₃ - x(Ba_0.7Ca_0.3)TiO₃ reinforcement

References

• R. Fries and A.J. Moulson, Fabrication and properties of an anisotropic PZT/polymer 0–3 composite. J. Mater. Sci.: Mater. Electron. 5(4) (1994), pp. 238–243. doi:10.1007/BF00186193
   Web of Science ®Google Scholar
• N.W. Hagood and A.A. Bent. Development of piezoelectric fiber composites for structural actuation. (1993).
   Google Scholar
• S.R. Anton and H.A. Sodano, A review of power harvesting using piezoelectric materials (2003-2006). Smart Mater. Struct. 16(3) (2007), pp. R1–R1. doi:10.1088/0964-1726/16/3/R01
   Web of Science ®Google Scholar
• R.E. Newnham, D.P. Skinner, and L.E. Cross, Connectivity and piezoelectric-pyroelectric composites. Mater. Res. Bull. 13(5) (1978), pp. 525–536. doi:10.1016/0025-5408(78)90161-7
   Web of Science ®Google Scholar
• K.C. Cheng, H.L.W. Chan, C.L. Choy, Q. Yin, H. Luo, and Z. Yin, Single crystal PMN-0.33PT/epoxy 1-3 composites for ultrasonic transducer applications. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50(9) (2003), pp. 1177–1183. doi:10.1109/TUFFC.2003.1235328
   PubMed Web of Science ®Google Scholar
• A.V. Krivoruchko and V.Y. Topolov, On the remarkable performance of novel 2-2-type composites based on [0 1 1] poled 0.93Pb(Zn1/3Nb2/3)O3-0.07PbTiO 3 single crystals. J. Phys. D: Appl. Phys. 40(22) (2007), pp. 7113–7120. doi:10.1088/0022-3727/40/22/038
   Web of Science ®Google Scholar
• T. Ritter, Single crystal pzn/pt-polymer composites for ultrasound transducer applications. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(4) (2000), pp. 792–800. doi:10.1109/58.852060
   PubMed Web of Science ®Google Scholar
• V.Y. Topolov, C.R. Bowen, S.V. Glushanin, and A.E. Panich, Electromechanical coupling in the novel 2-2 parallel-connected PMN-0.33PT single-domain crystal/polymer composite. Ferroelectr 393(1) (2009), pp. 27–37. doi:10.1080/00150190903412689
   Web of Science ®Google Scholar
• F. Wang, F. Wang, C. He, Y. Tang, X. Zhao, and H. Luo, Single-crystal 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3/epoxy 1-3 piezoelectric composites prepared by the lamination technique. Mater. Chem. Phys. 105(2-3) (2007), pp. 273–277. doi:10.1016/j.matchemphys.2007.04.060
   Web of Science ®Google Scholar
• A. Safari, Development of piezoelectric composites for transducers. J. Phys. III France 4(7) (1994), pp. 1129–1149.
   Google Scholar
• N. Jayasundere and B.V. Smith, Dielectric constant for binary piezoelectric 0-3 composites. J. Appl. Phys. 73(5) (1993), pp. 2462–2466. doi:10.1063/1.354057
   Web of Science ®Google Scholar
• J.A. Mitchell and J.N. Reddy, A study of embedded piezoelectric layers in composite cylinders. J. Appl. Mech. 62(1) (1995), pp. 166–173. doi:10.1115/1.2895898
   Web of Science ®Google Scholar
• E.C. Nelli Silva, J.S. Ono Fonseca, and N. Kikuchi, Optimal design of periodic piezo-composites. Comput. Methods. Appl. Mech. Eng. 159(1-2) (1998), pp. 49–77. doi:10.1016/S0045-7825(98)80103-5
   Web of Science ®Google Scholar
• M. Wilm, S. Ballandras, V. Laude, and T. Pastureaud, A full 3D plane-wave-expansion model for 1-3 piezoelectric composite structures. J. Acoust. Soc. Am. 112(3) (2002), pp. 943–952. doi:10.1121/1.1496081
   PubMed Web of Science ®Google Scholar
• V.J. Challis, A.P. Roberts, and A.H. Wilkins, Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. Int. J. Solids Struct. 45(14-15) (2008), pp. 4130–4146. doi:10.1016/j.ijsolstr.2008.02.025
   Web of Science ®Google Scholar
• W.T. Góźdź and R. Hołyst, Triply periodic surfaces and multiply continuous structures from the Landau model of microemulsions. Physical Review E – Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 54(5) (1996), pp. 5012–5027. doi:10.1103/PhysRevE.54.5012
   PubMed Web of Science ®Google Scholar
• L. Han and S. Che, An overview of materials with triply periodic minimal surfaces and related geometry: From biological structures to self-assembled systems. Adv. Mater. 30(17) (2018), pp. 1705708–1705708. doi:10.1002/adma.201705708
   PubMed Web of Science ®Google Scholar
• S. Torquato and A. Donev, Minimal surfaces and multifunctionality. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 460(2047) (2004), pp. 1849–1856. doi:10.1098/rspa.2003.1269
   Web of Science ®Google Scholar
• S. Torquato, S. Hyun, and A. Donev, Multifunctional composites: optimizing microstructures for simultaneous transport of heat and electricity. Phys. Rev. Lett. 89(26) (2002), pp. 266601–266601. doi:10.1103/PhysRevLett.89.266601
   PubMed Web of Science ®Google Scholar
• O. Al-Ketan and R.K. Abu Al-Rub, Multifunctional mechanical metamaterials based on triply periodic minimal surface lattices. Adv. Eng. Mater. 21(10) (2019), pp. 1900524–1900524. doi:10.1002/adem.201900524
   Web of Science ®Google Scholar
• O. Al-Ketan and R.K. Abu Al-Rub, MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces. Mater. Des. Process. Commun. 3(6) (2021), pp. e205–e205. doi:10.1002/mdp2.205
   Google Scholar
• D.W. Abueidda, R.K. Abu Al-Rub, A. S. Dalaq, D-W. Lee, K.A. Khan, and I. Jasiuk, Effective conductivities and elastic moduli of novel foams with triply periodic minimal surfaces. Mech. Mater. 95 (2016), pp. 102–115. doi:10.1016/j.mechmat.2016.01.004
   Web of Science ®Google Scholar
• Z. Chen, Y.M. Xie, X. Wu, Z. Wang, Q. Li, and S. Zhou, On hybrid cellular materials based on triply periodic minimal surfaces with extreme mechanical properties. Mater. Des. 183 (2019), pp. 108109–108109. doi:10.1016/j.matdes.2019.108109
   Web of Science ®Google Scholar
• A.S. Dalaq, D.W. Abueidda, R.K. Abu Al-Rub, and I.M. Jasiuk, Finite element prediction of effective elastic properties of interpenetrating phase composites with architectured 3D sheet reinforcements. Int. J. Solids Struct. 83 (2016), pp. 169–182. doi:10.1016/j.ijsolstr.2016.01.011
   Web of Science ®Google Scholar
• S.C. Kapfer, S.T. Hyde, K. Mecke, C.H. Arns, and G.E. Schröder-Turk, Minimal surface scaffold designs for tissue engineering. Biomaterials 32(29) (2011), pp. 6875–6882. doi:10.1016/j.biomaterials.2011.06.012
   PubMed Web of Science ®Google Scholar
• H. Xu, Y.M. Xie, R. Chan, and S. Zhou, Piezoelectric properties of triply periodic minimum surface structures. Compos. Sci. Technol. 200 (2020), pp. 108417. doi:10.1016/j.compscitech.2020.108417
   Web of Science ®Google Scholar
• R. Vaish, Piezoelectric and pyroelectric materials selection. Int. J. Appl. Ceram. Technol. 10(4) (2013), pp. 682–689. doi:10.1111/j.1744-7402.2012.02765.x
   Web of Science ®Google Scholar
• G. Vats and R. Vaish, Piezoelectric material selection for transducers under fuzzy environment. J. Adv. Ceram. 2(2) (2013), pp. 141–148. doi:10.1007/s40145-013-0053-1
   Web of Science ®Google Scholar
• G. Vats and R. Vaish, Selection of lead-free piezoelectric ceramics. Int. J. Appl. Ceram. Technol. 11(5) (2014), pp. 883–893. doi:10.1111/ijac.12063
   Web of Science ®Google Scholar
• S. Priya, H-C. Song, Y. Zhou, R. Varghese, A. Chopra, S-G. Kim, I. Kanno, L. Wu, D.S. Ha, and J. Ryu, et al., A review on piezoelectric energy harvesting: materials, methods, and circuits. Energy Harvesting and Systems 4(1) (2017), pp. 3–39. doi:10.1515/ehs-2016-0028
   Google Scholar
• P.K. Panda and B. Sahoo, PZT to lead free piezo ceramics: A review. Ferroelectrics 474(1) (2015), pp. 128–143. doi:10.1080/00150193.2015.997146
   Web of Science ®Google Scholar
• W. Liu and X. Ren, Large piezoelectric effect in Pb-free ceramics. Phys. Rev. Lett. 103(25) (2009), pp. 257602. doi:10.1103/PhysRevLett.103.257602
   PubMed Web of Science ®Google Scholar
• Y. Zhang, M. Xie, J. Roscow, and C. Bowen, Dielectric and piezoelectric properties of porous lead-free 0.5Ba(Ca0.8Zr0.2)O3-0.5(Ba0.7Ca 0.3)TiO3 ceramics. Mater. Res. Bull. 112 (2019), pp. 426–431. doi:10.1016/j.materresbull.2018.08.031
   Web of Science ®Google Scholar
• K.K. Sappati and S. Bhadra, Piezoelectric polymer and paper substrates: A review. Sensors 18(11) (2018. doi:10.3390/s18113605
   PubMed Web of Science ®Google Scholar
• R.W. Whatmore, Pyroelectric devices and materials. Rep. Prog. Phys. 49(12) (1986), pp. 1335–1386. doi:10.1088/0034-4885/49/12/002
   Web of Science ®Google Scholar
• F.-C. Chiu and Y.-J. Chen, Evaluation of thermal, mechanical, and electrical properties of PVDF/GNP binary and PVDF/PMMA/GNP ternary nanocomposites. Compos. – A: Appl. Sci. Manuf. 68 (2015), pp. 62–71. doi:10.1016/j.compositesa.2014.09.019
   Web of Science ®Google Scholar
• W. Zhou, J. Zuo, and W. Ren, Thermal conductivity and dielectric properties of Al/PVDF composites. Compos. – A: Appl. Sci. Manuf. 43(4) (2012), pp. 658–664. doi:10.1016/j.compositesa.2011.11.024
   Web of Science ®Google Scholar
• C. Multiphysics. COMSOL Material Library®. Material Library User’s Guide, V5.3, 1998–2017. Version 5.3.
   Google Scholar
• Y. Tian, S. Li, Y. Li, Y. Gong, X. Ji, S. Sun, and Q. Jing, Diversiform electrical and thermal expansion properties of (1 − x)Ba0.95Ca0.05Ti0.94Zr0.06O3–(x)Dy lead-free piezoelectric ceramics influenced by defect complexes. J. Mater. Sci. 53(16) (2018), pp. 11228–11241. doi:10.1007/s10853-018-2428-8
   Web of Science ®Google Scholar
• Y. He, Heat capacity, thermal conductivity, and thermal expansion of barium titanate-based ceramics. Thermochim. Acta 419(1) (2004), pp. 135–141. doi:10.1016/j.tca.2004.02.008
   Web of Science ®Google Scholar
• K.S. Srikanth, S. Patel, and R. Vaish, Functional cementitious composites for pyroelectric applications. J. Electron. Mater. 47(4) (2018), pp. 2378–2385. doi:10.1007/s11664-018-6071-6
   Web of Science ®Google Scholar
• S. Nemat-Nasser, M. Lori, and S.K. Datta, Micromechanics: overall properties of heterogeneous materials. J. Appl. Mech. 63(2) (1996), pp. 561–561. doi:10.1115/1.2788912
   Google Scholar
• K.A. Brakke, The surface evolver. Exp. Math. 1(2) (1992), pp. 141–165. doi:10.1080/10586458.1992.10504253
   Google Scholar
• N. Yang, Z. Quan, D. Zhang, and Y. Tian, Multi-morphology transition hybridization CAD design of minimal surface porous structures for use in tissue engineering. CAD Comput. Aided Des. 56 (2014), pp. 11–21. doi:10.1016/j.cad.2014.06.006
   Web of Science ®Google Scholar
• D.-J. Yoo, Computer-aided porous scaffold design for tissue engineering using triply periodic minimal surfaces. Int. J. Prec. Eng. Manuf. 12(1) (2011), pp. 61–71. doi:10.1007/s12541-011-0008-9
   Web of Science ®Google Scholar
• O. Al-Ketan and R.K. Abu Al-Rub, MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces. Mater. Des. Process. Commun. 3(6) (2021), pp. e205.
   Google Scholar
• P. Gaudenzi, On the electromechanical response of active composite materials with piezoelectric inclusions. Computers and Structures 65(2) (1997), pp. 157–168. doi:10.1016/S0045-7949(96)00375-6
   Google Scholar
• M. Melnykowycz, X. Kornmann, C. Huber, M. Barbezat, and A J. Brunner, Performance of integrated active fiber composites in fiber reinforced epoxy laminates. Smart Mater. Struct. 15(1) (2006), pp. 204–212. doi:10.1088/0964-1726/15/1/050
   Google Scholar
• C. Poizat and M. Sester, Effective properties of composites with embedded piezoelectric fibres. Comput. Mater. Sci. 16(1-4) (1999), pp. 89–97. doi:10.1016/S0927-0256(99)00050-6
   Web of Science ®Google Scholar
• R. Guinovart-Díaz, J. Bravo-Castillero, R. Rodrıguez-Ramos, and F.J. Sabina, Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: elastic and hexagonal symmetry. J. Mech. Phys. Solids 49(7) (2001), pp. 1445–1462. doi:10.1016/S0022-5096(01)00005-9
   Web of Science ®Google Scholar
• F.J. Sabina, R. Rodrıguez-Ramos, J. Bravo-Castillero, and R. Guinovart-Dıaz, Closed-form expressions for the effective coefficients of a fibre-reinforced composite with transversely isotropic constituents. II: Piezoelectric and hexagonal symmetry. J. Mech. Phys. Solids 49(7) (2001), pp. 1463–1479. doi:10.1016/S0022-5096(01)00006-0
   Web of Science ®Google Scholar
• H. Berger, S. Kari, U. Gabbert, R. Rodriguez-Ramos, J. Bravo-Castillero, R. Guinovart-Diaz, F.J. Sabina, and G.A. Maugin, Unit cell models of piezoelectric fiber composites for numerical and analytical calculation of effective properties. Smart Mater. Struct. 15(2) (2006), pp. 451–458. doi:10.1088/0964-1726/15/2/026
   Web of Science ®Google Scholar
• S. Karmakar, R. Kiran, V. Singh Chauhan, and R. Vaish, Effect of porosity on energy harvesting performance of 0.5Ba(Ca0.8Zr0.2)O3 − 0.5(Ba0.7Ca0.3)TiO3 ceramics: A numerical study. Energy Technology 8(5) (2020), pp. 1901302. doi:10.1002/ente.201901302
   Web of Science ®Google Scholar
• R. Kiran, A. Kumar, V.S. Chauhan, R. Kumar, and R. Vaish, Finite element study on performance of piezoelectric bimorph cantilevers using porous/ceramic 0–3 polymer composites. J. Electron. Mater. 47(1) (2018), pp. 233–241. doi:10.1007/s11664-017-5751-y
   Web of Science ®Google Scholar
• N. Magouh, M. Dietze, H. Bakhti, C-H. Solterbeck, L. Azrar, and M. Es-Souni, Finite element analysis and EMA predictions of the dielectric and pyroelectric properties of 0-3 Pz59/PVDF-TrFE composites with experimental validation. Sens. Actuators, A 310 (2020), pp. 112073. doi:10.1016/j.sna.2020.112073
   Google Scholar
• H.S. Tzou and R. Ye, Piezothermoelasticity and precision control of piezoelectric systems: Theory and finite element analysis. J. Vib. Acoust. 116(4) (1994), pp. 489–495. doi:10.1115/1.2930454
   Web of Science ®Google Scholar
• D. Singh, S. Sharma, S. Karmakar, R. Kumar, V.S. Chauhan, and R. Vaish, A finite element computational framework for enhanced photostrictive performance in 0–3 composites. Int. J. Mech. Mater. Des. 17(3) (2021), pp. 609–632. doi:10.1007/s10999-021-09550-0
   Web of Science ®Google Scholar
• P.M. Suquet, Elements of homogenization for inelastic solid mechanics, homogenization techniques for composite media. Lect. Notes Phys. 272(November) (1987), pp. 193–278. doi:10.1007/3-540-17616-0_15
   Google Scholar
• Z. Xia, Y. Zhang, and F. Ellyin, A unified periodical boundary conditions for representative volume elements of composites and applications. Int. J. Solids Struct. 40(8) (2003), pp. 1907–1921. doi:10.1016/S0020-7683(03)00024-6
   Web of Science ®Google Scholar
• D.W. Abueidda, M. Bakir, R.K. Abu Al-Rub, J.S. Bergström, N.A. Sobh, and I. Jasiuk, Mechanical properties of 3D printed polymeric cellular materials with triply periodic minimal surface architectures. Mater. Des. 122 (2017), pp. 255–267. doi:10.1016/j.matdes.2017.03.018
   Web of Science ®Google Scholar
• T. Gao, K. Liu, X. Wang, Z. Li, and Z. Wang, Elastic mechanical property hybridization of configuration-varying TPMS with geometric continuity. Mater. Des. 221 (2022), pp. 110995. doi:10.1016/j.matdes.2022.110995
   Web of Science ®Google Scholar
• Y. Zhang, M.-T. Hsieh, and L. Valdevit, Mechanical performance of 3D printed interpenetrating phase composites with spinodal topologies. Compos. Struct. 263 (2021), pp. 113693. doi:10.1016/j.compstruct.2021.113693
   Web of Science ®Google Scholar
• C. Bonatti and D. Mohr, Mechanical performance of additively-manufactured anisotropic and isotropic smooth shell-lattice materials: Simulations & experiments. J. Mech. Phys. Solids 122 (2019), pp. 1–26. doi:10.1016/j.jmps.2018.08.022
   Web of Science ®Google Scholar
• R. Liu, G. Yao, L. Sha, Z. Yu, P. Liang, C. Han, K. Zhu, L. Dong, Z. Xu, and J. Zhang, et al., Study on mechanical properties of polyurethane-enhanced triply periodic minimal composite structures inspired by rachis microstructure. Compos. Sci. Technol. 242 (2023), pp. 110197. doi:10.1016/j.compscitech.2023.110197
   Web of Science ®Google Scholar
• S. Yu, J. Sun, and J. Bai, Investigation of functionally graded TPMS structures fabricated by additive manufacturing. Mater. Des. 182 (2019), pp. 108021. doi:10.1016/j.matdes.2019.108021
   Web of Science ®Google Scholar
• S. Khaleghi, F.N. Dehnavi, M. Baghani, M. Safdari, K. Wang, and M. Baniassadi, On the directional elastic modulus of the TPMS structures and a novel hybridization method to control anisotropy. Mater. Des. 210 (2021), pp. 110074. doi:10.1016/j.matdes.2021.110074
   Web of Science ®Google Scholar
• N. Yang, M. Zhao, and H. Wei, Self-rotation-symmetry transformation for tuning anisotropy of single type lattice structures with minimal surfaces. Additive Manufacturing 78 (2023), pp. 103865. doi:10.1016/j.addma.2023.103865
   Web of Science ®Google Scholar
• D.W. Abueidda, A.S. Dalaq, R.K. Abu Al-Rub, and I. Jasiuk, Micromechanical finite element predictions of a reduced coefficient of thermal expansion for 3D periodic architectured interpenetrating phase composites. Compos. Struct. 133 (2015), pp. 85–97. doi:10.1016/j.compstruct.2015.06.082
   Web of Science ®Google Scholar
• O. Sigmund and S. Torquato, Composites with extremal thermal expansion coefficients. Appl. Phys. Lett. 69(21) (1996), pp. 3203–3205. doi:10.1063/1.117961
   Web of Science ®Google Scholar
• A.H. Muliana, A micromechanical model for predicting thermal properties and thermo-viscoelastic responses of functionally graded materials. Int. J. Solids Struct. 46(9) (2009), pp. 1911–1924. doi:10.1016/j.ijsolstr.2009.01.008
   Web of Science ®Google Scholar
• C.-X. Hu, H-J. Li, S-Y. Zhang, Y-S. Song, Numerical simulation on thermal expansion coefficient of 3D braided C/C composites. Rare Met. 33(1) (2014), pp. 99–106. doi:10.1007/s12598-013-0083-4
   Web of Science ®Google Scholar
• D.W. Abueidda, A.S. Dalaq, R.K. Abu Al-Rub, and H.A. Younes, Finite element predictions of effective multifunctional properties of interpenetrating phase composites with novel triply periodic solid shell architectured reinforcements. Int. J. Mech. Sci. 92 (2015), pp. 80–89. doi:10.1016/j.ijmecsci.2014.12.004
   Web of Science ®Google Scholar
• S. Li, D. Xiong, M. Liu, S. Bai, and X. Zhao, Thermophysical properties of SiC/Al composites with three dimensional interpenetrating network structure. Ceram. Int. 40(5) (2014), pp. 7539–7544. doi:10.1016/j.ceramint.2013.12.105
   Web of Science ®Google Scholar