Geometric parameters of 4D printed bilayer structure determine its deformation to a great extent. This paper proposed a geometric design method of 4D printed bilayer structures for accurate folding deformation. To precisely calculate the deformation, a folding deformation model of 4D printed bilayer structure is constructed considering thickness ratio and elastic modulus ratio. Then, for a target folding deformation, an adaptive surrogate-based optimization method is employed to obtain the geometric parameters of a given 4D printed bilayer structure. The numerical and physical experimental results show that the geometric parameters of 4D printed bilayer structure can be well designed by the proposed method.
AnBBenbernouNDemaineED, et al. (2011) Planning to fold multiple objects from a single self-folding sheet. Robotica29(1): 87–102.
2.
BartelsSBonitoAMulianaAH, et al. (2018) Modeling and simulation of thermally actuated bilayer plates. Journal of Computational Physics354: 512–528.
3.
CuiJAdamsJGMZhuY (2018) Controlled bending and folding of a bilayer structure consisting of a thin stiff film and a heat shrinkable polymer sheet. Smart Materials and Structures27(5): 055009.
4.
DengDChenY (2015) Origami-based self-folding structure design and fabrication using projection based stereolithography. Journal of Mechanical Design137(2): 1–12.
5.
FeltonSTolleyMDemaineE, et al. (2014) Applied origami. A method for building self-folding machines. Science345(6197): 644–646.
6.
FernandesRGraciasDH (2012) Self-folding polymeric containers for encapsulation and delivery of drugs. Advanced Drug Delivery Reviews64(14): 1579–1589.
7.
ForresterAIJKeaneAJ (2009) Recent advances in surrogate-based optimization. Progress in Aerospace Sciences45(1–3): 50–79.
8.
GeQDunnCKQiHJ, et al. (2014) Active origami by 4D printing. Smart Materials and Structures23(9): 094007.
9.
GeQQiHJDunnML (2013) Active materials by four-dimension printing. Applied Physics Letters103(13): 131901.
10.
GuanJHeHLeeLJ, et al.; HeH (2007) Fabrication of particulate reservoir-containing, capsule like, and self-folding polymer microstructures for drug delivery. Small3(3): 412–418.
11.
GuoXLiHAhnBY, et al. (2009) Two- and three-dimensional folding of thin film single-crystalline silicon for photovoltaic power applications. Proceedings of the National Academy of Sciences of the United States of America106(48): 20149–20154.
12.
KowalewskiJMahlerTReichardtL, et al. (2013) Shape memory alloy (SMA)-based pattern-reconfigurable antenna. IEEE Antennas and Wireless Propagation Letters12: 1598–1601.
13.
LiuZLiuHDuanG, et al. (2020) Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio. Mathematics and Mechanics of Solids25(2): 348–361.
14.
MiyashitaSGuitronSLudersdorferM, et al. (2015) An untethered miniature origami robot that self-folds, walks, swims, and degrades. In: Proceedings of the IEEE international conference on robotics and automation, Seattle, WA, 26–30 May 2015, pp.1490–1496. New York: IEEE.
15.
MomeniFMehdi HassaniNLiuS, et al. (2017) A review of 4D printing. Materials & Design122: 42–79.
ParkJS (1994) Optimal Latin-hypercube designs for computer experiments. Journal of Statistical Planning and Inference39(1): 95–111.
18.
Peraza-HernandezEAHartlDJMalakRJJr, et al. (2014) Origami-inspired active structures: A synthesis and review. Smart Materials and Structures23(9): 094001.
SuJWTaoXDengH, et al. (2018) 4D printing of a self-morphing polymer driven by a swellable guest medium. Soft Matter14: 765–772.
21.
SunXFeltonSMNiiyamaR, et al. (2015) Self-folding and self-actuating robots: A pneumatic approach. In: Proceedings of the IEEE international conference on robotics and automation, Seattle, WA, 26–30 May 2015, pp.3160–3165. New York: IEEE.
TimoshenkoS (1925) Analysis of bi-metal thermostats. Journal of the Optical Society of America11(3): 233–255.
24.
WangDLiLZhangB, et al. (2020) Effect of temperature on the programmable helical deformation of a reconfigurable anisotropic soft actuator. International Journal of Solids and Structures199: 169–180.
25.
WuJYuanCDingZ, et al. (2016) Multi-shape active composites by 3D printing of digital shape memory polymers. Scientific Reports6: 1–11.
26.
YuanCDingZWangTJ, et al. (2017) Shape forming by thermal expansion mismatch and shape memory locking in polymer/elastomer laminates. Smart Materials and Structures26(10): 105027.
27.
ZhouYHuangWMKangSF, et al. (2015) From 3D to 4D printing: Approaches and typical applications. Journal of Mechanical Science and Technology29(10): 4281–4288.
