Geometric Stiffening and Softening of an Indented Floating Thin Film

Thin sheets can behave nonlinearly while the local material response is purely linear. We separate two distinct mechanisms for geometric nonlinearities by studying the normal-force response of an indented polymer film on a liquid bath, using experiments, simulations, and theory. First, we show that the force reaches a plateau at large indentation, causing the effective spring constant of the system to soften, and we use a simple geometric model to capture this behavior at large slopes [1]. Then, we map out the full phase diagram at small slopes, supporting recent predictions [2] that the system stiffens out of the typical linear response for small deflections. Our results provide a prototypical example of how multiple distinct geometric nonlinearities may arise under monotonic driving.
[1] Ripp et. al., arXiv:1804.02421 (2018)
[2] Vella et al., Phys. Rev. E 98, 013003 (2018)