Abstract
The four-dimensional (4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties. The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures, in particular to the bilayer structures based on temperature-driven shape-memory polymers (SMPs) and fabricated using the fused deposition modeling (FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency, as the three-dimensional (3D) problem is converted to a two-dimensional (2D) problem. The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.
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CHUNG, S., SONG, S. E., and CHO, Y. T. Effective software solutions for 4D printing: a review and proposal. International Journal of Precision Engineering and Manufacturing-Green Technology, 4(3), 359–371 (2017)
KUANG, X., ROACH, D. J., WU, J. T., HAMEL, C. M., DING, Z., WANG, T. J., DUNN, M. L., and QI, H. J. Advances in 4D printing: materials and applications. Advanced Functional Materials, 29(2), 1805290 (2019)
WU, J. J., HUANG, L. M., ZHAO, Q., and XIE, T. 4D printing: history and recent progress. Chinese Journal of Polymer Science, 36(5), 563–575 (2018)
MOMENI, F., LIU, X., and NI, J. A review of 4D printing. Materials & Design, 122, 42–79 (2017)
KUKSENOK, O. and BALAZS, A. C. Stimuli-responsive behavior of composites integrating thermo-responsive gels with photo-responsive fibers. Materials Horizons, 3(1), 53–62 (2016)
RYU, J., JUNG, B. S., KIM, M. S., KONG, J. P., CHO, M. H., and AHN, S. H. Numerical simulation of hybrid composite shape-memory alloy wire-embedded structures. Journal of Intelligent Material Systems and Structures, 22(17), 1941–1948 (2011)
AKBARI, S., SAKHAEI, A. H., KOWSARI, K., YANG, B., SERJOUEI, A., ZHANG, Y. F., and GE, Q. Enhanced multimaterial 4D printing with active hinges. Smart Materials and Structures, 27(6), 065027 (2018)
GE, Q., SAKHAEI, A. H., LEE, H., DUNN, C. K., FANG, N. X., and DUNN, M. L. Multimaterial 4D printing with tailorable shape memory polymers. Scientific Reports, 6(1), 1–11 (2016)
SONG, Z. Y., REN, L. Q., ZHAO, C., LIU, H. L., YU, Z. L., LIU, Q. P., and REN, L. Biomimetic nonuniform, dual-stimuli self-morphing enabled by gradient four-dimensional printing. ACS Applied Materials & Interfaces, 12(5), 6351–6361 (2020)
WANG, G. Y., TAO, Y., CAPUNAMAN, O. B., YANG, H., and YAO, L. N. A-line: 4D printing morphing linear composite structures. Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems, Association for Computing Machinery, New York, 1–12 (2019)
SOSSOU, G., DEMOLY, F., BELKEBIR, H., QI, H., GOMES, S., and MONTAVON, G. Design for 4D printing: a voxel-based modeling and simulation of smart materials. Materials & Design, 175, 107798 (2019)
SOSSOU, G., DEMOLY, F., BELKEBIR, H., QI, H., GOMES, S., and MONTAVON, G. Design for 4D printing: modeling and computation of smart materials distributions. Materials & Design, 181, 108074 (2019)
ZHANG, Z. and GU, G. X. Finite-element-based deep-learning model for deformation behavior of digital materials. Advanced Theory and Simulations, 3(7), 2000031 (2020)
QIU, H., FENG, Y. X., GAO, Y. C., ZENG, S. Y., and TAN, J. R. The origami inspired design of polyhedral cells of truss core panel. Thin-Walled Structures, 163, 107725 (2021)
DENG, D. and CHEN, Y. Origami-based self-folding structure design and fabrication using projection based stereolithography. Journal of Mechanical Design, 137(2), 021701 (2015)
DENG, D. and CHEN, Y. 4D printing: design and fabrication of 3D shell structures with curved surfaces using controlled self-folding. ASME 2015 International Manufacturing Science and Engineering Conference, American Society of Mechanical Engineers Digital Collection, North Carolina (2015)
MAO, Y., YU, K., ISAKOV, M. S., WU, J. T., DUNN, M. L., and QI, H. J. Sequential self-folding structures by 3D printed digital shape memory polymers. Scientific Reports, 5(1), 1–12 (2015)
ZENG, S. Y., FENG, Y. X., GAO, Y. C., ZHENG, H., and TAN, J. R. Layout design and application of 4D-printing bio-inspired structures with programmable actuators. Bio-Design and Manufacturing (2021) https://doi.org/10.1007/s42242-021-00146-3
GE, Q., DUNN, C. K., QI, H. J., and DUNN, M. L. Active origami by 4D printing. Smart Materials and Structures, 23(9), 094007 (2014)
YUAN, C., DING, Z., WANG, T. J., DUNN, M. L., and QI, H. J. Shape forming by thermal expansion mismatch and shape memory locking in polymer/elastomer laminates. Smart Materials and Structures, 26(10), 105027 (2017)
SU, J. W., TAO, X., DENG, H., ZHANG, C., JIANG, S., LIN, Y. Y., and LIN, J. 4D printing of a self-morphing polymer driven by a swellable guest medium. Soft Matter, 14(5), 765–772 (2018)
CUI, J., ADAMS, J. G. M., and ZHU, Y. Controlled bending and folding of a bilayer structure consisting of a thin stiff film and a heat shrinkable polymer sheet. Smart Materials and Structures, 27(5), 055009 (2018)
NAFICY, S., GATELY, R., GORKIN, R., XIN, H., and SPINKS, G. M. 4D printing of reversible shape morphing hydrogel structures. Macromolecular Materials and Engineering, 302(1), 1600212 (2017)
GLADMAN, A. S., MATSUMOTO, E. A., NUZZO, R. G., MAHADEVAN, L., and LEWIS, J. A. Biomimetic 4D printing. Nature Materials, 15(4), 413–418 (2016)
WU, Y., HAO, X. P., XIAO, R., LIN, J., WU, Z. L., YIN, J., and QIAN, J. Controllable bending of bi-hydrogel strips with differential swelling. Acta Mechanica Solida Sinica, 32(5), 652–662 (2019)
VAN REES, W. M., VOUGA, E., and MAHADEVAN, L. Growth patterns for shape-shifting elastic bilayers. Proceedings of the National Academy of Sciences, 114(44), 11597–11602 (2017)
VAN REES, W. M., MATSUMOTO, E. A., GLADMAN, A. S., LEWIS, J. A., and MAHADEVAN, L. Mechanics of biomimetic 4D printed structures. Soft Matter, 14(43), 8771–8779 (2018)
BARTELS, S., BONITO, A., and NOCHETTO, R. H. Bilayer plates: model reduction, Γ-convergent finite element approximation, and discrete gradient flow. Communications on Pure and Applied Mathematics, 70(3), 547–589 (2017)
BARTELS, S., BONITO, A., MULIANA, A. H., and NOCHETTO, R. H. Modeling and simulation of thermally actuated bilayer plates. Journal of Computational Physics, 354, 512–528 (2018)
LIU, Z. Y., LIU, H., DUAN, G. F., and TAN, J. R. Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio. Mathematics and Mechanics of Solids, 25(2), 348–361 (2020)
VAN MANEN, T., JANBAZ, S., and ZADPOOR, A. A. Programming 2D/3D shape-shifting with hobbyist 3D printers. Materials Horizons, 4(6), 1064–1069 (2017)
ZHENG, S. Y., SHEN, Y. Y., ZHU, F. B., YIN, J., QIAN, J., FU, J. Z., WU, Z. L., and ZHENG, Q. Programmed deformations of 3D-printed tough physical hydrogels with high response speed and large output force. Advanced Functional Materials, 28(37), 1803366 (2018)
WANG, Y. and LI, X. An accurate finite element approach for programming 4D-printed self-morphing structures produced by fused deposition modeling. Mechanics of Materials, 151, 103628 (2020)
YU, Y. X., LIU, H. L., QIAN, K. R., YANG, H., MCGEHEE, M., GU, J. Z., LUO, D. L., YAO, L. N., and ZHANG, Y. J. Material characterization and precise finite element analysis of fiber reinforced thermoplastic composites for 4D printing. Computer-Aided Design, 122, 102817 (2020)
NOROOZI, R., BODAGHI, M., JAFARI, H., ZOLFAGHARIAN, A., and FOTOUHI, M. Shape-adaptive metastructures with variable bandgap regions by 4D printing. Polymers, 12(3), 519 (2020)
ANG, K. J., RILEY, K. S., FABER, J., and ARRIETA, A. F. Switchable bistability in 3D printed shells with bio-inspired architectures and spatially distributed pre-stress. ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, American Society of Mechanical Engineers Digital Collection, Texas (2018)
ZENG, S. Y., GAO, Y. C., FENG, Y. X., ZHENG, H., QIU, H., and TAN, J. R. Programming the deformation of a temperature-driven bilayer structure in 4D printing. Smart Materials and Structures, 28(10), 105031 (2019)
FENG, Y. X., XU, J. J., ZENG, S. Y., GAO, Y. C., and TAN, J. R. Controlled helical deformation of programmable bilayer structures: design and fabrication. Smart Materials and Structures, 29(8), 085042 (2020)
TIMOSHENKO, S. Analysis of bi-metal thermostats. Journal of the Optical Society of America, 11(3), 233–255 (1925)
BARTELS, S. Numerical Methods for Nonlinear Partial Differential Equations, Springer, Berlin, 217–257 (2015)
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Citation: SONG, J. J., FENG, Y. X., WANG, Y., ZENG, S. Y., HONG, Z. X., QIU, H., and TAN, J. R. Complicated deformation simulating on temperature-driven 4D printed bilayer structures based on reduced bilayer plate model. Applied Mathematics and Mechanics (English Edition), 42(11), 1619–1632 (2021) https://doi.org/10.1007/s10483-021-2788-9
Project supported by the National Natural Science Foundation of China (Nos. 52130501 and 52075479) and the National Key R&D Program of China (No. 2018YFB1700804)
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Song, J., Feng, Y., Wang, Y. et al. Complicated deformation simulating on temperature-driven 4D printed bilayer structures based on reduced bilayer plate model. Appl. Math. Mech.-Engl. Ed. 42, 1619–1632 (2021). https://doi.org/10.1007/s10483-021-2788-9
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DOI: https://doi.org/10.1007/s10483-021-2788-9
Key words
- reduced bilayer plate model
- four-dimensional (4D) printing
- temperature-driven shape-memory polymer (SMP)
- bilayer structure
- complicated deformation simulating