Micromechanical Modeling of Two-Way Shape Memory Response of Semi-Crystalline Polymers Based on Equivalent Inclusion Method

[1] Vaziri, S., & Narooei, K. (2024). Investigation of post-buckling, energy harvesting, and relaxation of shape memory auxetic structure with thermo-visco-hyperelastic modeling. Iranian Journal of Materials Forming, 11(3), 28-39. https://doi.org/10.22099/ijmf.2024.51080.1302

[2] Ghorbanoghli, A., & Narooei, K. (2019). A new hyper-viscoelastic model for investigating rate dependent mechanical behavior of dual cross link self-healing hydrogel. International Journal of Mechanical Sciences, 159, 278-286. https://doi.org/10.1016/j.ijmecsci.2019.06.019

[3] Fang-Fang, L., & Guo-Liang, L. (2025). Rational molecular Design: Advances in stimuli-responsive shape memory polymers and composites. European Polymer Journal, 223, 113642. https://doi.org/10.1016/j.eurpolymj.2024.113642

[4] Hosseinzadeh, M., Ghoreishi, M., & Narooei, K. (2023). 4D printing of shape memory polylactic acid beams: An experimental investigation into FDM additive manufacturing process parameters, mathematical modeling, and optimization. Journal of Manufacturing Processes, 85, 774-782. https://doi.org/10.1016/j.jmapro.2022.12.006

[5] He, Q., Zhao, Z., Zhong, Q., Liu, S., Deng, K., Liu, Y., Zhang, N., Zhao, Z., Zhan, F., & Zhao, J. (2024). Switchable shape memory polymer bio-inspired adhesive and its application for unmanned aerial vehicle landing. Chinese Journal of Aeronautics, 37(3), 380-390. https://doi.org/10.1016/j.cja.2023.09.032

[6] Hosseinzadeh, M., Ghoreishi, M., & Narooei, K. (2021). An investigation into the effect of thermal variables on the 3D printed shape memory polymer structures with different geometries. Journal of Intelligent Material Systems and Structures, 33(5), 715-726. https://doi.org/10.1177/1045389X211028286

[7] Prem Kumar, C., N., S., D., L., Naga, M. R. G., & Vakkalagadda, M. R. K. Shape memory polymers, blends, and composites: processing, properties, and applications. Polymer-Plastics Technology and Materials, 1-29. https://doi.org/10.1080/25740881.2025.2460063

[8] Ke, D., Chen, Z., Momo, Z. Y., Jiani, W., Xuan, C., Xiaojie, Y., & Xueliang, X. (2020). Recent advances of two-way shape memory polymers and four-dimensional printing under stress-free conditions. Smart Materials and Structures, 29(2), 023001. https://doi.org/10.1088/1361-665X/ab5e6d

[9] Basak, S., & Bandyopadhyay, A. (2022). Two-way semicrystalline shape memory elastomers: development and current research trends. Advanced Engineering Materials, 24(10), 2200257. https://doi.org/10.1002/adem.202200257

[10] Scalet, G. (2020). Two-way and multiple-way shape memory polymers for soft robotics: An overview. Actuators, 9(1), 10. https://doi.org/10.3390/act9010010

[11] Zeng, H., Sun, H., & Gu, J. (2021). Modeling the one-way and two-way shape memory effects of semi-crystalline polymers. Smart Materials and Structures, 30(9), 095020. https://doi.org/10.1088/1361-665X/ac179e

[12] Rashidi, M., & Narooei, K. (2020). Structural mechanics approach to investigate the hyperelastic mechanical behavior of single and multi-wall carbon nanotubes. Iranian Journal of Materials Forming, 7(2), 88-103. https://doi.org/10.22099/ijmf.2020.37930.1163

[13] Dolynchuk, O., Kolesov, I., & Radusch, H. J. (2014). Theoretical description of an anomalous elongation during two-way shape-memory effect in crosslinked semicrystalline polymers. Macromolecular Symposia, 346(1), 48-58. https://doi.org/10.1002/masy.201400065

[14] Yan, C., Yang, Q., & Li, G. (2020). A phenomenological constitutive model for semicrystalline two-way shape memory polymers. International Journal of Mechanical Sciences, 177, 105552. https://doi.org/10.1016/j.ijmecsci.2020.105552

[15] Janbaz, S., Narooei, K., van Manen, T., & Zadpoor, A. A. (2020). Strain rate–dependent mechanical metamaterials. Science Advances, 6(25), eaba0616. https://doi.org/10.1126/sciadv.aba0616

[16] Liang, Z., Li, J., Zhang, X., & Kan, Q. (2023). A viscoelastic-viscoplastic constitutive model and its finite element implementation of amorphous polymers. Polymer Testing, 117, 107831. https://doi.org/10.1016/j.polymertesting.2022.107831

[17] Liu, Y., Gall, K., Dunn, M. L., Greenberg, A. R., & Diani, J. (2006). Thermomechanics of shape memory polymers: Uniaxial experiments and constitutive modeling. International Journal of Plasticity, 22(2), 279-313. https://doi.org/10.1016/j.ijplas.2005.03.004

[18] Srivastava, V., Chester, S. A., & Anand, L. (2010). Thermally actuated shape-memory polymers: Experiments, theory, and numerical simulations. Journal of the Mechanics and Physics of Solids, 58(8), 1100-1124. https://doi.org/10.1016/j.jmps.2010.04.004

[19] Bakhtiari, M., & Narooei, K. (2025). A micromechanical model to predict the effective thermomechanical behavior of one-way shape memory polymers. Mechanics of Materials, 201, 105230. https://doi.org/10.1016/j.mechmat.2024.105230

[20] Nemat-Nasser, S., & Hori, M., (2013). Micromechanics: overall properties of heterogeneous materials. Elsevier.

[21] Voigt, W. (1928). Crystal physics textbook. Journal of Modern Physics, 9(4), 80-85.

[22] Reuss, A. (1929). Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals. Zeitschrift für Angewandte Mathematik und Mechanik, 9(1), 49-58. https://doi.org/10.1002/zamm.19290090104

[23] Mori, T., & Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3

[24] Nemat-Nasser, S., Su, Y., Guo, W. G., & Isaacs, J. (2005). Experimental characterization and micromechanical modeling of superelastic response of a porous NiTi shape-memory alloy. Journal of the Mechanics and Physics of Solids, 53(10), 2320-2346. https://doi.org/10.1016/j.jmps.2005.03.009

[25] Kachanov, M., & Sevostianov, I., (2018). Micromechanics of materials, with applications. Springer.

[26] Poluektov, M., Freidin, A. B., & Figiel, Ł. (2019). Micromechanical modelling of mechanochemical processes in heterogeneous materials. Modelling and Simulation in Materials Science and Engineering, 27(8), 084005. https://doi.org/10.1088/1361-651X/ab3b3a

[27] Baniassadi, M., Baghani, M., & Rémond, Y., (2023). Applied micromechanics of complex microstructures: Computational modeling and numerical characterization. Elsevier.

[28] Umer, U., Abidi, M. H., Almutairi, Z., & El-Meligy, M. A. (2024). Micromechanics evaluation of equivalent temperature-dependent stiffness of graphene-reinforced shape memory polymer nanocomposites. Results in Engineering, 24, 102978. https://doi.org/10.1016/j.rineng.2024.102978

[29] Tang, T., & Felicelli, S. D. (2015). Micromechanical investigations of polymer matrix composites with shape memory alloy reinforcement. International Journal of Engineering Science, 94, 181-194. https://doi.org/10.1016/j.ijengsci.2015.05.008

[30] Guo, Q., & Zaïri, F. (2021). A micromechanics-based model for deformation-induced damage and failure in elastomeric media. International Journal of Plasticity, 140, 102976. https://doi.org/10.1016/j.ijplas.2021.102976

[31] Yang, Q., & Li, G. (2016). Temperature and rate dependent thermomechanical modeling of shape memory polymers with physics based phase evolution law. International Journal of Plasticity, 80, 168-186. https://doi.org/10.1016/j.ijplas.2015.09.005

[32] Fulati, A., Uto, K., & Ebara, M. (2022). Influences of crystallinity and crosslinking density on the shape recovery force in poly(ε-caprolactone)-based shape-memory polymer blends. Polymers, 14(21), 4740. https://doi.org/10.3390/polym14214740

[33] Westbrook, K. K., Mather, P. T., Parakh, V., Dunn, M. L., Ge, Q., Lee, B. M., & Qi, H. J. (2011). Two-way reversible shape memory effects in a free-standing polymer composite. Smart Materials and Structures, 20(6), 065010. https://doi.org/10.1088/0964-1726/20/6/065010

[34] Scalet, G., Pandini, S., Messori, M., Toselli, M., & Auricchio, F. (2018). A one-dimensional phenomenological model for the two-way shape-memory effect in semi-crystalline networks. Polymer, 158, 130-148. https://doi.org/10.1016/j.polymer.2018.10.027

[35] Gu, J., Wang, C., Zeng, H., Duan, H., Wan, M., & Sun, H. (2024). A thermo-mechanical constitutive model for triple-shape and two-way shape memory polymers. Smart Materials and Structures, 33(6), 065034. https://doi.org/10.1088/1361-665X/ad4cc2

[36] Kim, J. H., Kang, T. J., & Yu, W. R. (2010). Thermo-mechanical constitutive modeling of shape memory polyurethanes using a phenomenological approach. International Journal of Plasticity, 26(2), 204-218. https://doi.org/10.1016/j.ijplas.2009.06.006

[37] Gilormini, P., & Diani, J. (2012). On modeling shape memory polymers as thermoelastic two-phase composite materials. Comptes Rendus Mécanique, 340(4), 338-348. https://doi.org/10.1016/j.crme.2012.02.016

[38] Chen, Y. C., & Lagoudas, D. C. (2008). A constitutive theory for shape memory polymers. Part I: Large deformations. Journal of the Mechanics and Physics of Solids, 56(5), 1752-1765. https://doi.org/10.1016/j.jmps.2007.12.005

[39] Smith Jr, K. J. (1983). Crystallization under stress: A theory of fibrillar crystallization. Journal of Polymer Science: Polymer Physics Edition, 21(1), 55-63. https://doi.org/10.1002/pol.1983.180210105

[40] Abdul-Hameed, H., Messager, T., Ayoub, G., Zaïri, F., Naït-Abdelaziz, M., Qu, Z., & Zaïri, F. (2014). A two-phase hyperelastic-viscoplastic constitutive model for semi-crystalline polymers: Application to polyethylene materials with a variable range of crystal fractions. Journal of the Mechanical Behavior of Biomedical Materials, 37, 323-332. https://doi.org/10.1016/j.jmbbm.2014.04.016

[41] Nguyen, T. L., Bédoui, F., Mazeran, P. E., & Guigon, M. (2015). Mechanical investigation of confined amorphous phase in semicrystalline polymers: Case of PET and PLA. Polymer Engineering & Science, 55(2), 397-405. https://doi.org/10.1002/pen.23896

[42] Chen, J. (2021). Advanced electron microscopy of nanophased synthetic polymers and soft complexes for energy and medicine applications. Nanomaterials, 11(9), 2405. https://doi.org/10.3390/nano11092405

[43] Brusselle-Dupend, N., & Cangémi, L. (2008). A two-phase model for the mechanical behaviour of semicrystalline polymers. Part I: Large strains multiaxial validation on HDPE. Mechanics of Materials, 40(9), 743-760. https://doi.org/10.1016/j.mechmat.2008.03.011

[44] Bédoui, F., Diani, J., Régnier, G., & Seiler, W. (2006). Micromechanical modeling of isotropic elastic behavior of semicrystalline polymers. Acta Materialia, 54(6), 1513-1523. https://doi.org/10.1016/j.actamat.2005.11.028

[45] Mura, T., (2013). Micromechanics of defects in solids. Springer Science & Business Media.

[46] Baghani, M., Naghdabadi, R., Arghavani, J., & Sohrabpour, S. (2012). A constitutive model for shape memory polymers with application to torsion of prismatic bars. Journal of Intelligent Material Systems and Structures, 23(2), 107-116. https://doi.org/10.1177/1045389X11431745

[47] Pandini, S., Baldi, F., Paderni, K., Messori, M., Toselli, M., Pilati, F., Gianoncelli, A., Brisotto, M., Bontempi, E., & Riccò, T. (2013). One-way and two-way shape memory behaviour of semi-crystalline networks based on sol–gel cross-linked poly(ε-caprolactone). Polymer, 54(16), 4253-4265. https://doi.org/10.1016/j.polymer.2013.06.016

[48] Wurm, A., Lellinger, D., Minakov, A. A., Skipa, T., Pötschke, P., Nicula, R., Alig, I., & Schick, C. (2014). Crystallization of poly(ε-caprolactone)/MWCNT composites: A combined SAXS/WAXS, electrical and thermal conductivity study. Polymer, 55(9), 2220-2232. https://doi.org/10.1016/j.polymer.2014.02.069

[49] Tencé-Girault, S., Woehling, V., Oikonomou, E. K., Karpati, S., & Norvez, S. (2018). About the art and science of visualizing polymer morphology using transmission electron microscopy. Macromolecular Chemistry and Physics, 219(3), 1700483. https://doi.org/10.1002/macp.201700483