Effects of pre-stretch, compressibility and material constitution on the period-doubling secondary bifurcation of a film/substrate bilayer

Abstract

We refine a previously proposed semi-analytical method, and use it to study the effects of pre-stretch, compressibility and material constitution on the period-doubling secondary bifurcation of a uni-axially compressed film/substrate bilayer structure. It is found that compared with the case of incompressible neo-Hookean materials for which the critical strain is approximately 0.17 when the thin layer is much stiffer than the substrate, the critical strain when the Gent materials are used is a monotonically increasing function of the constant J m that characterizes material extensibility, becoming as small as 0.12 when J m is equal to 1, whereas for compressible neo-Hookean materials the critical strain is a monotonically decreasing function of Poisson's ratio; the period-doubling secondary bifurcation seems to become impossible when Poisson's ratio is approximately equal to 0.307. The latter result may indicate that when Poisson's ratio is small enough there are other preferred secondary bifurcations -an example is given where a secondary bifurcation mode with 7/4 times the original period occurs at a lower strain value. The effect of a pre-stretch (compression or extension) in the substrate is not monotonic, giving rise to a critical strain that varies between 0.15 and 0.22.

Wrinkling to crinkling transitions and curvature localization in a magnetoelastic film bonded to a non-magnetic substrate

“…In addition, one can think of disposing of the pre-compression device by pre-stretching the underlying substrate and then depositing the film. Such an approach, however, would at one hand necessitate to introduce an anisotropic response of the substrate (Cai and Fu, 2019), while at the same time would negate the advantage of using a single active device to create different patterns by adjusting in real time both the magnetic field and the pre-compression.…”

Post-buckling of an elastic half-space coated by double layers

“…A major result arising from a weakly nonlinear analysis [6,21,28] is that there exists a critical stiffness ratio that marks the transition from sub-critical bifurcation to super-critical bifurcation. It can then be expected, and indeed confirmed by many recent numerical and experimental studies, that in the sub-critical regime localization is the norm [38] whereas in the super-critical regime stable periodic patterns and further secondary bifurcations are the norm [18,[39][40][41][42][43][44][45][46][47].…”

“…Pattern formation is also known to play an important role in many biological processes where the main driving mechanism is growth [16]. Motivated by these newly found applications, further linear and nonlinear analyses have been conducted by Cai and Fu [17,18], Steigmann and Ogden [19], Sun et al [20], Hutchinson [21], Ciarletta [22], Fu and Ciarletta [23], Ciarletta and Fu [24], Zhang [25], Holland et al [26], Alawiye et al [27,28] and Rambausek and Danas [29]. There also exists a large body of literature that employs approximate plate theories and simplified interfacial conditions in order to provide qualitative understanding of the phenomena observed; see, e.g., Chen and Hutchinson [30], Huang et al [31], Audoly and Boudaoud [32] and Song et al [33].…”

An experimental study of morphological formation in bilayered tubular structures driven by swelling/growth

“…It is well understood that the ratio of the shear modulus of the film to that of the substrate in planar and curved film-substrate structures is critical in determining the bifurcation nature [34,57,58], wrinkled pattern [33,59,60], and morphological evolution [61][62][63][64]. Specifically, The mechanical properties of PDMS are known to vary with the cross-linked temperature as well as the associated duration time [65].…”