Dynamic compression of soft layered materials yields tunable and spatiotemporally evolving surface patterns

Soft layered systems buckling to form surface patterns has been widely studied under quasistatic loading. Here, we study the dynamic formation of wrinkles in a stiff-film-on-viscoelastic-substrate system as a function of impact velocity. We observe a spatiotemporally varying range of wavelengths, which display impactor velocity dependence and exceed the range exhibited under quasistatic loading. Simulations suggest the importance of both inertial and viscoelastic effects. Film damage is also examined, and we find that it can tailor dynamic buckling behavior. We expect our work to have applications to soft elastoelectronic and optic systems and open routes for nanofabrication.

Figure 1

(a) Pre-impact-test quasistatic compression of sample 1 yields period-doubling behavior. (b) The dynamic test setup. (c) Measured (open circles) and predicted (dashed curves) quasistatic wrinkle amplitude vs strain, corresponding to the test shown in (a). After the critical strain (vertical thick dashed line), the period-doubled mode (blue, top branch) grows, and the original mode (red, bottom branch) fades. (d) Snapshots from a test at 7.1 m/s impactor velocity on a “pristine” sample, displaying multiple-wavelength surface patterns. (e) A normalized spatiotemporal diagram of the experiment shown in (d), with color representing the $y$-direction surface displacement, $U_y$. The line visible at the right edge is an artifact of the camera frame edge and should be disregarded. (f) A normalized spatiotemporal diagram of the simulation [7.6 m/s impact velocity, same color scheme as in (e)].

Figure 2

(a) FFT of the sample 1 quasistatic compression test. FFT of a dynamic test (b) and FEM simulation (c), with impact speeds of 2.5 and 1.9 m/s, respectively. Wave number $\sim 263{\mathrm{m}}^{-1}$ corresponds to ${\lambda }_{0,\mathrm{av}}$ and is shown as the dashed vertical yellow lines in (a)–(c). The horizontal red dashed lines in (b) (lower horizontal dashed line) and (c) (sole horizontal dashed line) represent the time at which the striker hits the stop blocks and comes to a stop, while the white (upper) horizontal dashed line in (b) represents the time of arrival at the right edge of the peak of the bulk compression wave. This same bulk wave arrival time in (c) and (d) is the upper limit of the times shown. (d) Spatiotemporal evolution of strain obtained from the FEM simulation in (c), averaged over a depth of ${\lambda }_{0,1}$ (compression shown as positive).

Figure 3

(a) The maximum spectral centroid (in time) of the dynamically tested samples. Shown are results from pristine sample experiments (black circles), predamaged sample experiments (green squares), flat film simulations (blue stars), and substitution of measured $\omega$ into Eq. (1) (red triangles). (b) Wave-number spectral centroids for flat film simulations (blue stars) and prewrinkle film simulations (green squares), with the average and the range between minimum and maximum values indicated by the error bars. Sim., simulation.

Figure 4

(a) Wave-number maximum spectral centroid as a function of maximum local strain averaged over a depth of ${\lambda }_{0,1}$ for purely hyperelastic substrate simulations, showing that even without viscoelasticity the combination of nonlinearity and inertial effects present in dynamic cases (red, upper line) can induce wave numbers significantly exceeding quasistatic compression (blue, lower line). (b) Dimensionless parameters estimating inertial ($\rho \lambda a$), viscous ($f\eta$), and elastic ($E_0$) forces, where $a$ is the maximum acceleration of the striker, $\lambda$ is the wave-number maximum spectral centroid, and $\rho$ is the material density, showing that as impact speed is increased, both inertial and viscous forces increase with respect to elastic forces, with inertial forces increasing at a faster rate than viscous ones.