Localization in an idealized heterogeneous elastic sheet

Swelling and Evaporation Determine Surface Morphology of Grafted Hydrogel Thin Films

We experimentally study the formation of surface patterns in grafted hydrogel films of nanometer-to-micrometer thickness during imbibition-driven swelling followed by evaporation-driven shrinking. Creases are known to form at the hydrogel surface during swelling; the wavelength of the creasing pattern is proportional to the initial thickness of the hydrogel film with a logarithmic correction that depends on microscopic properties of the hydrogel. We find that, although the characteristic wavelength of the pattern is determined during swelling, the surface morphology can be significantly influenced by evaporation-induced shrinking. We observe that the elastocapillary length based on swollen mechanical properties gives a threshold thickness for a surface pattern formation and consequently an important change in morphology.

Wrinkled Interfaces: Taking Advantage of Anisotropic Wrinkling to Periodically Pattern Polymer Surfaces

Periodically patterned surfaces can cause special surface properties and are employed as functional building blocks in many devices, yet remaining challenges in fabrication. Advancements in fabricating structured polymer surfaces for obtaining periodic patterns are accomplished by adopting "top-down" strategies based on self-assembly or physico-chemical growth of atoms, molecules, or particles or "bottom-up" strategies ranging from traditional micromolding (embossing) or micro/nanoimprinting to novel laser-induced periodic surface structure, soft lithography, or direct laser interference patterning among others. Thus, technological advances directly promote higher resolution capabilities. Contrasted with the above techniques requiring highly sophisticated tools, surface instabilities taking advantage of the intrinsic properties of polymers induce surface wrinkling in order to fabricate periodically oriented wrinkled patterns. Such abundant and elaborate patterns are obtained as a result of self-organizing processes that are rather difficult if not impossible to fabricate through conventional patterning techniques. Focusing on oriented wrinkles, this review thoroughly describes the formation mechanisms and fabrication approaches for oriented wrinkles, as well as their fine-tuning in the wavelength, amplitude, and orientation control. Finally, the major applications in which oriented wrinkled interfaces are already in use or may be prospective in the near future are overviewed.

On local intrinsic dimensionality of deformation in complex materials

We propose a new metric called s-LID based on the concept of Local Intrinsic Dimensionality to identify and quantify hierarchies of kinematic patterns in heterogeneous media. s-LID measures how outlying a grain's motion is relative to its s nearest neighbors in displacement state space. To demonstrate the merits of s-LID over the conventional measure of strain, we apply it to data on individual grain motions in a set of deforming granular materials. Several new insights into the evolution of failure are uncovered. First, s-LID reveals a hierarchy of concurrent deformation bands that prevails throughout loading history. These structures vary not only in relative dominance but also spatial and kinematic scales. Second, in the nascent stages of the pre-failure regime, s-LID uncovers a set of system-spanning, criss-crossing bands: microbands for small s and embryonic-shearbands at large s, with the former being dominant. At the opposite extreme, in the failure regime, fully formed shearbands at large s dominate over the microbands. The novel patterns uncovered from s-LID contradict the common belief of a causal sequence where a subset of microbands coalesce and/or grow to form shearbands. Instead, s-LID suggests that the deformation of the sample in the lead-up to failure is governed by a complex symbiosis among these different coexisting structures, which amplifies and promotes the progressive dominance of the embryonic-shearbands over microbands. Third, we probed this transition from the microband-dominated regime to the shearband-dominated regime by systematically suppressing grain rotations. We found particle rotation to be an essential enabler of the transition to the shearband-dominated regime. When grain rotations are completely suppressed, this transition is prevented: microbands and shearbands coexist in relative parity.

Controlled Wrinkling Patterns in Periodic Thickness-Gradient Films on Polydimethylsiloxane Substrates

Surface wrinkles in homogeneous and heterogeneous film-substrate systems have received intense attention in both science and engineering. Understanding the wrinkling phenomena of heterogeneous systems with continuously variable features is still a challenge. In this work, we propose an unconventional strategy to prepare periodic thickness-gradient metal films on polydimethylsiloxane (PDMS) substrates by masking of copper grids which are weaved by orthometric copper wires. It is found that a periodic thickness-gradient film spontaneously forms during the sputtering process because of the specific structures of the copper grids. Surface wrinkles are strongly modulated by the copper grid structures and are position-dependent within a period. A phase diagram has been established to correlate the wrinkle morphology with the mesh size and film thickness. The film surfaces at mesh centers are evolved from labyrinth wrinkling to herringbone wrinkling and then to stripe wrinkling and finally to wrinkling-free state when the mesh size decreases and/or the film thickness increases. The morphological characteristics, evolutional behaviors, and underlying mechanisms of such wrinkling are discussed in detail based on the stress theory and numerical simulation.

Hierarchical wrinkles and oscillatory cracks in metal films deposited on liquid stripes

Fascinating crack and wrinkle patterns driven by stresses are ubiquitous in natural and artificial systems. It is of great interest to control the morphologies of stress-driven patterns by using facile techniques. Here we report on the spontaneous formation of hierarchical wrinkles and oscillatory cracks in metal films deposited on liquid (or soft polymer) stripes. It is found that the metal film is under a tensile stress during deposition owing to the thermal expansion of the liquid substrate. As the film thickness is beyond a critical value, oscillatory cracks with sawtoothlike shapes form on the liquid stripes. The ratio of crack oscillation period to amplitude is independent of the stripe width and film material, which can be well explained by the "brittle adhesive joints" model. After deposition, the metal film is under a compressive stress, which is relieved by formation of various wrinkle patterns. Hierarchical wrinkles with changing wavelengths form near the stripe edge while labyrinth or wavy wrinkles form at the center. Energy analysis was adopted to explain the formation and evolution of the wrinkle patterns. This study could promote better understanding of the formations of crack and wrinkle patterns in constrained film structures and controllable fabrication of stress-driven patterns by prefabricating liquid (or soft polymer) interlayer arrays.

Harnessing fold-to-wrinkle transition and hierarchical wrinkling on soft material surfaces by regulating substrate stiffness and sputtering flux

Strain-induced complex surface patterns such as wrinkles, folds and hierarchical structures are quite useful in a wide range of practical applications. Although various surface patterns have been extensively investigated, precisely controlling the coexistence and transition of multimodal structures is still a challenge. In this work, we report on a facile technique to harness fold-to-wrinkle transition and hierarchical wrinkling on soft material surfaces by regulating substrate stiffness and sputtering flux. It is found that as the substrate stiffness or sputtering flux increases, the surface patterns successively evolve from networked folds to isolated folds (coexistence of folds and wrinkles) and finally to labyrinth-like wrinkles. For larger sputtering flux, two distinct wrinkling patterns (i.e., G1 wrinkling due to surface instability during sputtering and G2 wrinkling due to thermal compression after deposition) can coexist on the sample surfaces, resulting in the spontaneous formation of hierarchical wrinkles. The report in this work could promote better understanding of the sputtering effect on the spontaneous pattern formation for soft materials and controllable fabrication of multiple complex patterns by simply regulating substrate stiffness and sputtering flux.

Effects of Stiff Film Pattern Geometry on Surface Buckling Instabilities of Elastic Bilayers

Buckling instabilities-such as wrinkling and creasing-of micropatterned elastic surfaces play important roles in applications, including flexible electronics and microfluidics. In many cases, the spatial dimensions associated with the imposed pattern can compete with the natural length scale of the surface instabilities (e.g., the wrinkle wavelength), leading to a rich array of surface buckling behaviors. In this paper, we consider elastic bilayers consisting of a spatially patterned stiff film supported on a continuous and planar soft substrate. Through a combination of experimental and computational analyses, we find that three surface instability modes-wrinkling, Euler buckling, and rigid rotation-are observed for the stiff material patterns, depending on the in-plane dimensions of the film compared to the natural wrinkle wavelength, while the intervening soft regions undergo a creasing instability. The interplay between these instabilities leads to a variety of surface structures as a function of the pattern geometry and applied compressive strain, in many cases yielding contact between neighboring stiff material elements because of the formation of creases in the gaps between them.