Localization in an idealized heterogeneous elastic sheet

Abstract

Localized deformation is ubiquitous in many natural and engineering materials as they approach failure, and a significant effort has been made to understand localization processes with simple continuum models. Real materials are much more commonly heterogeneous but it is unclear exactly how heterogeneity affects outcomes. In this work we study the response of an idealized heterogenous elastic sheet on a soft foundation as it is uniaxially compressed. The patterned surface layers are created by selective ultraviolet/ozone treatment of the top surface of a polydimethylsiloxane (PDMS) sample using a TEM grid as a mask. By controlling the exposure time of UV/O₃, samples ranging from continuous thin films to sets of isolated small plates were created. We find that patterned regions noticeably localize while bulk regions appear as uniform wrinkles, and that local and global strains depend on the pattern pitch, exposure levels and the treatment protocol. Remarkably, various responses can be modeled using well-understood theory that ignores pattern details aside from the small distance between the adjacent boundaries and the local value of strain.