Originated from the art of paper cutting and folding, kirigami and origami have shown promising applications in a broad range of scientific and engineering fields. Developments of kirigami-inspired inverse design methods that map target three-dimensional (3D) geometries into two-dimensional (2D) patterns of cuts and creases are desired to serve as guidelines for practical applications. In this paper, using programed kirigami tessellations, we propose two design methods to approximate the geometries of developable surfaces and nonzero Gauss curvature surfaces with rotational symmetry. In the first method, a periodic array of kirigami pattern with spatially varying geometric parameters is obtained, allowing formation of developable surfaces of desired curvature distribution and thickness, through controlled shrinkage and bending deformations. In the second method, another type of kirigami tessellations, in combination with Miura origami, is proposed to approximate nondevelopable surfaces with rotational symmetry. Both methods are validated by experiments of folding patterned thin copper films into desired 3D structures. The mechanical behaviors of the kirigami designs are investigated using analytical modeling and finite element simulations. The proposed methods extend the design space of mechanical metamaterials and are expected to be useful for kirigami-inspired applications.
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June 2017
Research-Article
Patterning Curved Three-Dimensional Structures With Programmable Kirigami Designs
Fei Wang,
Fei Wang
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
Search for other works by this author on:
Xiaogang Guo,
Xiaogang Guo
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
Search for other works by this author on:
Jingxian Xu,
Jingxian Xu
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
Search for other works by this author on:
Yihui Zhang,
Yihui Zhang
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
Search for other works by this author on:
C. Q. Chen
C. Q. Chen
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
e-mail: chencq@tsinghua.edu.cn
CNMM & AML,
Tsinghua University,
Beijing 100084, China
e-mail: chencq@tsinghua.edu.cn
Search for other works by this author on:
Fei Wang
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
Xiaogang Guo
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
Jingxian Xu
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
Yihui Zhang
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
CNMM & AML,
Tsinghua University,
Beijing 100084, China
C. Q. Chen
Department of Engineering Mechanics,
CNMM & AML,
Tsinghua University,
Beijing 100084, China
e-mail: chencq@tsinghua.edu.cn
CNMM & AML,
Tsinghua University,
Beijing 100084, China
e-mail: chencq@tsinghua.edu.cn
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 17, 2017; final manuscript received April 11, 2017; published online April 24, 2017. Editor: Yonggang Huang.
J. Appl. Mech. Jun 2017, 84(6): 061007 (7 pages)
Published Online: April 24, 2017
Article history
Received:
March 17, 2017
Revised:
April 11, 2017
Citation
Wang, F., Guo, X., Xu, J., Zhang, Y., and Chen, C. Q. (April 24, 2017). "Patterning Curved Three-Dimensional Structures With Programmable Kirigami Designs." ASME. J. Appl. Mech. June 2017; 84(6): 061007. https://doi.org/10.1115/1.4036476
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