Multimodal Surface Instabilities in Curved Film–Substrate Structures

Structures of thin films bonded on thick substrates are abundant in biological systems and engineering applications. Mismatch strains due to expansion of the films or shrinkage of the substrates can induce various modes of surface instabilities such as wrinkling, creasing, period doubling, folding, ridging, and delamination. In many cases, the film-substrate structures are not flat but curved. While it is known that the surface instabilities can be controlled by film-substrate mechanical properties, adhesion and mismatch strain, effects of the structures' curvature on multiple modes of instabilities have not been well understood. In this paper, we provide a systematic study on the formation of multimodal surface instabilities on film-substrate tubular structures with different curvatures through combined theoretical analysis and numerical simulation. We first introduce a method to quantitatively categorize various instability patterns by analyzing their wave frequencies using fast Fourier transform (FFT). We show that the curved film-substrate structures delay the critical mismatch strain for wrinkling when the system modulus ratio between the film and substrate is relatively large, compared with flat ones with otherwise the same properties. In addition, concave structures promote creasing and folding, and suppress ridging. On the contrary, convex structures promote ridging and suppress creasing and folding. A set of phase diagrams are calculated to guide future design and analysis of multimodal surface instabilities in curved structures. Keywords: instability, curvature, film–substrate structure, morphogenesisUnited States. Office of Naval Research (N00014-14-1-0528)Massachusetts Institute of Technology. Institute for Soldier NanotechnologiesNational Science Foundation (U.S.) (CMMI1253495

On the Elastic Stability of Folded Rings in Circular and Straight States

Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by experimental demonstrations. The analysis ascertains stability by exploring variations of the elastic energy of the rings for admissible deformations in the vicinity of the equilibrium state. The approach employed is the conventional stability analysis for elastic conservative systems which differs from most of the analyses that have been published on this class of problems, as will be illustrated by reproducing and elaborating on several problems in the literature. In addition to providing solutions to two basic problems, the paper analyses and demonstrates the stability of six-sided rings that fold into straight configurations

Multiple equilibrium states of a curved-sided hexagram:Part I-Stability of states

The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Each of the six segments is a rod having the same length and uniform natural curvature. These rods are bent uniformly in the plane of the hexagram into equal arcs of 120deg or 240deg and joined at a cusp where their ends meet to form a 1-loop planar ring. The 1-loop rings formed from 120deg or 240deg arcs are inversions of one another and they, in turn, can be folded into a 3-loop straight line configuration or a 3-loop ring with each loop in an "8" shape. Each of these four equilibrium states has a uniform bending moment. Two additional intriguing planar shapes, 6-circle hexagrams, with equilibrium states that are also uniform bending, are identified and analyzed for stability. Stability is lost when the natural curvature falls outside the upper and lower limits in the form of a bifurcation mode involving coupled out-of-plane deflection and torsion of the rod segments. Conditions for stability, or lack thereof, depend on the geometry of the rod cross-section as well as its natural curvature. Rods with circular and rectangular cross-sections will be analyzed using a specialized form of Kirchhoff rod theory, and properties will be detailed such that all four of the states of interest are mutually stable. Experimental demonstrations of the various states and their stability are presented. Part II presents numerical simulations of transitions between states using both rod theory and a three-dimensional finite element formulation, includes confirmation of the stability limits established in Part I, and presents additional experimental demonstrations and verifications

Stiffness Change for Reconfiguration of Inflated Beam Robots

Active control of the shape of soft robots is challenging. Despite having an infinite number of passive degrees of freedom (DOFs), soft robots typically only have a few actively controllable DOFs, limited by the number of degrees of actuation (DOAs). The complexity of actuators restricts the number of DOAs that can be incorporated into soft robots. Active shape control is further complicated by the buckling of soft robots under compressive forces; this is particularly challenging for compliant continuum robots due to their long aspect ratios. In this work, we show how variable stiffness can enable shape control of soft robots by addressing these challenges. Dynamically changing the stiffness of sections along a compliant continuum robot can selectively "activate" discrete joints. By changing which joints are activated, the output of a single actuator can be reconfigured to actively control many different joints, thus decoupling the number of controllable DOFs from the number of DOAs. We demonstrate embedded positive pressure layer jamming as a simple method for stiffness change in inflated beam robots, its compatibility with growing robots, and its use as an "activating" technology. We experimentally characterize the stiffness change in a growing inflated beam robot and present finite element models which serve as guides for robot design and fabrication. We fabricate a multi-segment everting inflated beam robot and demonstrate how stiffness change is compatible with growth through tip eversion, enables an increase in workspace, and achieves new actuation patterns not possible without stiffening

Multiple equilibrium states of a curved-sided hexagram: Part II-Transitions between states

Curved-sided hexagrams with multiple equilibrium states have great potential in engineering applications such as foldable architectures, deployable aerospace structures, and shape-morphing soft robots. In Part I, the classical stability criterion based on energy variation was used to study the elastic stability of the curved-sided hexagram and identify the natural curvature range for stability of each state for circular and rectangular rod cross-sections. Here, we combine a multi-segment Kirchhoff rod model, finite element simulations, and experiments to investigate the transitions between four basic equilibrium states of the curved-sided hexagram. The four equilibrium states, namely the star hexagram, the daisy hexagram, the 3-loop line, and the 3-loop "8", carry uniform bending moments in their initial states, and the magnitudes of these moments depend on the natural curvatures and their initial curvatures. Transitions between these equilibrium states are triggered by applying bending loads at their corners or edges. It is found that transitions between the stable equilibrium states of the curved-sided hexagram are influenced by both the natural curvature and the loading position. Within a specific natural curvature range, the star hexagram, the daisy hexagram, and the 3-loop "8" can transform among one another by bending at different positions. Based on these findings, we identify the natural curvature range and loading conditions to achieve transition among these three equilibrium states plus a folded 3-loop line state for one specific ring having a rectangular cross-section. The results obtained in this part also validate the elastic stability range of the four equilibrium states of the curved-sided hexagram in Part I. We envision that the present work could provide a new perspective for the design of multi-functional deployable and foldable structures

Genome-Wide Mapping of DNA Methylation in Chicken

Cytosine DNA methylation is an important epigenetic modification termed as the fifth base that functions in diverse processes. Till now, the genome-wide DNA methylation maps of many organisms has been reported, such as human, Arabidopsis, rice and silkworm, but the methylation pattern of bird remains rarely studied. Here we show the genome-wide DNA methylation map of bird, using the chicken as a model organism and an immunocapturing approach followed by high-throughput sequencing. In both of the red jungle fowl and the avian broiler, DNA methylation was described separately for the liver and muscle tissue. Generally, chicken displays analogous methylation pattern with that of animals and plants. DNA methylation is enriched in the gene body regions and the repetitive sequences, and depleted in the transcription start site (TSS) and the transcription termination site (TTS). Most of the CpG islands in the chicken genome are kept in unmethylated state. Promoter methylation is negatively correlated with the gene expression level, indicating its suppressive role in regulating gene transcription. This work contributes to our understanding of epigenetics in birds