title: Towards a quantitative understanding of period-doubling wrinkling patterns occurring in film/substrate bilayer systems.
abstract: Compression of a stiff film on a soft substrate may lead to surface wrinkling when the compressive strain reaches a critical value. Further compression may cause a wrinkling-folding transition, and the sinusoidal wrinkling mode can then give way to a period-doubling bifurcation. The onset of the primary bifurcation has been well understood, but a quantitative understanding of the secondary bifurcation remains elusive. Our theoretical analysis of the branching of surface patterns reveals that the wrinkling-folding transition depends on the wrinkling strain and the prestrain in the substrate. A characteristic strain in the substrate is adopted to determine the correlation among the critical strain of the period-doubling mode, the wrinkling strain and the prestrain in an explicit form. A careful examination of the total potential energy of the system reveals that beyond the critical strain of period-doubling, the sinusoidal wrinkling mode has a higher potential energy in comparison with the period-doubling mode. The critical strain of the period-doubling mode strongly depends on the deformation state of the hyperelastic solid, indicating that the nonlinear deformation behaviour of the substrate plays a key role here. The results reported here on the one hand provide a quantitative understanding of the wrinkling-folding transition observed in natural and synthetic material systems and on the other hand pave the way to control the wrinkling mode transition by regulating the strain state in the substrate.
authors.affiliation: AML and CNMM , Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University , Beijing 100084 , People's Republic of China.
authors.forename: Yan
authors.initials: Y
authors.lastname: Zhao
authors.affiliation: AML and CNMM , Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University , Beijing 100084 , People's Republic of China.
authors.forename: Yanping
authors.initials: Y
authors.lastname: Cao
authors.affiliation: Department of Aerospace Engineering , Iowa State University , Ames, IA 50011 , USA.
authors.forename: Wei
authors.initials: W
authors.lastname: Hong
authors.affiliation: College of Engineering, Mathematics and Physical Sciences , University of Exeter , North Park Road, Devon EX4 4QF , UK.
authors.forename: M Khurram
authors.initials: MK
authors.lastname: Wadee
authors.affiliation: AML and CNMM , Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University , Beijing 100084 , People's Republic of China.
authors.forename: Xi-Qiao
authors.initials: XQ
authors.lastname: Feng
keywords: nonlinear finite-element analysis; period-doubling wrinkling pattern; post-buckling analysis; prestrain; wrinkling pattern transition