|
|
||
|
|
|
|
From:
Yanping Cao (1) and John W. Hutchinson (2)
(1) AML, Department of Engineering Mechanics, Tsinghua University, Beijing, P.R. China
(2) School of Engineering and Applied Sciences, Harvare University, Cambridge, MA USA
“From wrinkles to creases in elastomers: The instability and imperfection-sensitivity of wrinkling”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468(2137): 94-115, 2012,
DOI: 10.1098/rspa.2011.0384, Citable Link: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10169557
ABSTRACT: The stability of the wrinkling mode experienced by a compressed half-space of neo- Hookean material is investigated using analytical and numerical methods to study the post-bifurcation behavior of periodic solutions. It is shown that wrinkling is highly unstable due to the nonlinear interaction among the multiple modes associated with the critical compressive state. Concomitantly, wrinkling is sensitive to exceedingly small initial imperfections that significantly reduce the compressive strain at which the instability occurs. The study provides insight into the connection between wrinkling and an alternative surface mode, the finite amplitude crease, or sulcus. The shape of the critical combination of wrinkling modes has the form of an incipient crease, and a tiny initial imperfection can trigger a wrinkling instability that collapses into a crease.
Fig. 7 from that paper:
Details of the development of the wrinkle and the formation of the crease for a sinusoidal imperfection with xi(1)bar = 0.005 . The onset of instability (A) occurs when small
scale wrinkling occurs at the minimum point on the surface at the overall strain, epsilon*. With overall strain held constant, the crease develops in (B). The wrinkle becomes dynamically unstable when the overall strain attains epsilon* and would collapse dynamically into the crease. The pseudo-dynamic algorithm used in the numerical simulations enable the transition to occur in a controlled manner. In the inserts, (A) and (B), X denotes the horizontal distance measured in the deformed state.
Page 107 / 360