Spontaneous Buckling of Thin Films on Curved Compliant Substrates
It is very common to observe that after bathing or swimming, prominent wrinkles occur on the skin of our fingertips and toes. The underlying mechanics issues governing the wrinkled morphology are studied by using finite element method and analytical modeling. Through the wrinkling of a multilayered skin on soft tissues, it is found that the stiffness of the stratum corneum (SC) and the dermal layer in the skin has a larger effect on the wrinkling behavior. From a mechanical/material perspective, stiffening of the SC and the dermal layer can increase the critical wrinkle stress, which can be used for anti-aging, whereas increasing the dermal layer's modulus and decreasing the SC's stiffness may lead to finer wrinkles (i.e. smaller wrinkle wavelength) with lower wrinkle depth/amplitude, which can be used for wrinkle removal8.   The modeling and multilayered structure of a typical fingertip Effect of respective layers on wrinkling wavelength
The explanation of plants pattern formation is a long-lasting problem existing in science, which could "drive the sanest man mad" remarked by Charles Darwin1. In nature, some fruits distinguish themselves with intriguing groovy surface topologies from those with smooth shape, for example, the ten-ridged Korean melon (golden melon), pumpkin, silk gourds, wavy wax apple and so on. However, these fruits are not born with groovy skin. In mechanics, such a morphology transition can be viewed as a mechanical stability problem. The groovy features on fruits are analytically investigated and reproduced in FEM simulations through the elastic buckling of stiff skins resting on compliant spheroidal flesh, where mechanical buckling might act as a template for confining or interacting with biology processes during the morphology development2.
The typical growth process of a pumpkin fruits (top row) and corresponding simulated buckling shapes (bottom row)
Conventional fabrication techniques of microstructures and microcomponents are highly developed, however, these techniques are either high-cost or require complicated fabrication processes3, where the resulting features are limited by the designed patterning mold and etching processes. Here we present an alternative lithography-free fabrication method of microgears through the controllable spontaneous buckling of films on curved (e.g. cylindrical or coned) substrates, where the flexible pattern features (e.g. gear teeth number and height) can be manipulated by varying the geometrical and material parameters of the film/substrate system4. The mismatched deformation between film and substrates can be induced by thermal expansion, dehydration or swelling.   Gear teeth number Proof-of -concept mesoscale experiments
Simulated various gears
Geometry and Mechanics of Biomembranes and Membrane Tube Network (with Prof. Yajun Yin)
Lipid bilayer membrane can be mathematically considered as a 2D smooth curved surface. The shape equations and stability conditions under external force stimuli are one of the fundamental problems for the study of biomembranes mechanics. Two new gradient operators defined on the 2D Riemann surface are discovered in the study, which are related with the second fundamental form of the curved surface and correspond to the traditional gradient and Laplace operators in Euclidean space. Based on the integral theorem of these operators, the most generalized differential equilibrium equations for biomembranes with Helfrich potential energy functional are studied under a concise mathematical framework5. The integral theorems are further extended to the study of biomembrane nanotube network6 and the super carbon nanotubes7 (SCN).
References: 1. F. Darwin, The life and letters of Charles Darwin: including an autobiographical chapter (Appleton, New York) (1897)
2. J. Yin, Z. Cao, C. Li, I. Sheinman, X. Chen. PNAS, 105, 19132,(2008); J. Yin, I. Sheinman, X. Chen. JMPS, 57, 1470 (2009)
3. R.C. Jaeger, Prentice-Hall, Inc, New Jersey, (2002)
4. J. Yin, E. Bar-Kochba, X. Chen, Soft. Matter. doi: 10.1039/b904635f, (2009)
5. Y. Yin, J. Yin, D. Ni, J. Math. Biol. 51, 403, (2005); J. Yin, Y. Yin, C. Lv, Appl. Math. Sci. 1, 1439, (2007); Y. Yin, J. Yin, C. Lv, J. Geom. Phys. 58, 122, (2008).
8. J. Yin, G. J. Gerling, Y. Chen, Acta. Biomater. doi:10.1016/j.actbio.2009.10.025, (2009) |
