Session L11: Focus Session: Extreme Mechanics II

Controlling Elastic Instabilities: From Complex Pattern Formation to Functionality

Exploiting elastic instability in thin films has proven a robust method for creating complex patterns and structures across a wide range of lengthscales. Even the simplest of systems, an elastic membrane with a lattice of pores, under stress, generates a plethora of complex patterns featuring long-range orientational order. Harnessing the underlying elastic instability allows for the rational design of materials with highly desirable properties: from a film with a switchable photonic bandgap to a material with a negative Poisson ratio. Within the framework of linear elasticity, we model the system as a lattice of interacting deformation elements, or ``dislocation dipoles,'' which captures the configuration and orientational order present in any conceivable deformation of the system. In addition, when we promote this system to a curved surface, a novel set of features, patterns and broken symmetries appears.   

Novel negative Poisson's ratio behavior induced by an elastic instability

When materials are compressed along a particular axis they are most commonly observed to expand in directions orthogonal to the applied load. The property that characterizes this behavior is the Poisson's ratio which is defined as the ratio between the negative transverse and longitudinal strains. Materials with a negative Poisson's ratio will contract in the transverse direction when compressed and demonstration of practical examples is relatively recent. A significant challenge in the fabrication of auxetic materials is that it usually involves embedding structures with intricate geometries within a host matrix. As such, the manufacturing process has been a bottleneck in the practical development towards applications. Here we exploit elastic instabilities to create novel effects within materials with periodic microstructure and we show that they may lead to negative Poisson's ratio behavior for the 2D periodic structures i.e. it only occurs under compression. The uncomplicated manufacturing process of the samples together with the robustness of the observed phenomena suggests that this may form the basis of a practical method for constructing planar auxetic materials over a wide range of length-scales.   

Tearing graphene sheets from adhesive substrates

Graphene, the first example of a truly two-dimensional atomic crystal, is the ultimate ``tinniest'' of all thin films and it exhibits exceptional electronic and mechanical properties. We perform a combination of experiments and molecular dynamics simulations to study the tearing of graphene sheets from adhesive substrates. Under tearing loading, we observe the formation of tapered ribbons whose geometry is controlled by the adhesion energy between graphene and the substrate, and by the number of layers of the torn graphene sample. We find good agreement between the predictions of the molecular modeling and experimental results. In particular, for the case of a single graphene layer, the analysis of the tearing angle as a function of the adhesion strength shows a drastic departure from conventional thin film tearing theory; the release of elastic stretching energy stored in the sheet becomes the driving force for the tapering of the torn ribbon. This behavior is attributed to the two-dimensional nature of graphene, which results in a bending modulus that is much lower than that predicted by continuum theory.   

Mechanics of Highly-Deformed Elastic Shells

Emergence of new technological applications, in addition to the constantly growing interest in biological materials has accentuated the importance of studying the mechanics of highly deformed shells. The key challenge is the intricate interplay of physics and geometry, which leads to a mechanical response much different from the response of solid objects. The quest to understand the underlying phenomena has spawned theoretical and experimental studies, which have helped in understanding the underlying mechanisms of deformation and response of shells. In this talk, I will discuss the mechanics of highly deformed elastic shells in several classical problems: indentation of elastic spherical caps by a flat rigid plate and a rigid sharp indenter and pure. These assays are used to highlight some of the key aspects of the mechanics of highly deformed elastic shells, while an overview of the current state-of-the-art and suggestions for future research on this subject will be also provided.   

Multiple lengthscales elastic instability via period-doubling bifurcations

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad distribution of energy. We have studied the energy distribution for highly confined membranes resting on an elastomer and showed the emergence of a new morphological instability triggered by a period-doubling bifurcation. A periodic self-organized focalization of the deformation energy is observed provided a symmetry breaking, induced by the elastic foundation, occurs. The period-doubling bifurcation is induced by a parametric resonance similar to those observed in nonlinear oscillators. The model developped may prove to be useful for understanding the morphology of various confined systems, such as coated materials or living tissues. Moreover, it opens the way to new kind of microfabrication design of multiperiodic or chaotic (aperiodic) surface topography via self-organization.   

Peeling of elastic thin films on heterogeneous solids

Thin film adhesives have become increasingly important in various applications such as packaging and coating, and we benefit daily of their adhesion properties by using various kinds of tape. Here, we study the effect of heterogeneities on their peeling properties. From the theoretical side, we show how perturbations of the peeling front induced by heterogeneities of fracture energy at the film-substrate interface result in additional bending and stretching of the thin film. The energetical cost associated with these deformations is balanced by the wandering of the peeling front that takes advantage of area of lower interfacial fracture energy. This leads to various peeling front geometries that are calculated as a function of the landscape of fracture energy. These predictions are confronted with experimental measurements performed on a model system where we follow in real time the adhesion front during the peeling of an elastic thin film on a rigid substrate with controlled heterogeneous properties. A PDMS thin film produced by spin coating is peeled from a rigid solid on which patterns are designed by using a regular printer, taking advantage of the high adhesion energy of the ink-PDMS interface. The measured peeling front geometry is compared with the theoretical predictions and the toughening effect induced by the heterogeneities is finally discussed.   

Wrinkled Membrane Morphology of Biological Cell

Membranes of many biological cells possess a wrinkled surface topology that, in some instance, serves as a reservoir for providing large surface area and membrane expansion during osmotic swelling. We consider and model the development of the wrinkled morphology to result from buckling instabilities which occur during the membrane growth. In particular, we examine the wrinkled membrane morphology of white blood cell experimentally and numerically. Our results show that the deformation mismatch between the membrane and the cytoskeleton during membrane growth triggers buckling of the membrane. This behavior of the wrinkled topology enables expansion of the cell during swelling and reveals interesting details on the role of the membrane topology.   

A curtain-type problem: pattern formation on uniaxially confined sheet with deformed edge

An elastic sheet subject to uniaxial compression will buckle out of plane. In order to minimize the bending energy, the wrinkled shape that is created will have as large a wavelength as possible. This behavior can be frustrated by constraining one edge of the sheet to smaller amplitude, as is often the case with curtains, which forces a shorter wavelength near the constrained edge. Narrow strips will adopt this shape across their width, while wider sheets exhibit a transition pattern between wrinkles of smaller and larger wavelengths. We will present simulations illustrating this behavior. We will discuss the mechanisms that govern the transition between the translationally-symmetric and -unsymmetric shapes and examine the characteristic features of the unsymmetric shape. Additionally, we will show how tension applied transverse to the compression direction affects the emergent pattern. We acknowledge support from the NSF-supported MRSEC on Polymers at UMass (DMR-0820506).   

Deformation of an asymmetric film

Recent experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [1,2], we represent the effect of chemical vapors by a change in the target metric tensor. In this problem, unlike Refs. [1,2], the target metric is asymmetric between the two sides of the film. Changing this metric induces a curvature of the film, which may be Gaussian curvature into a sphere or mean curvature into a cylinder. We calculate the elastic energy for each of these shapes, and show that the sphere is favored for films smaller than a critical size, which depends on the film thickness, while the cylinder is favored for larger films. We compare the formalism for asymmetric films with previous theoretical work on symmetric films, and compare the predictions with experimental results. \\[4pt] [1] Y. Klein, E. Efrati, and E. Sharon, Science 315, 1116 (2007).\\[0pt] [2] E. Efrati, E. Sharon, and R. Kupferman, J. Mech. Phys. Solids 57, 762 (2009).   

Multistability of spontaneously curved anisotropic strips

Multistable structures are elastic objects, typically composite plates or shells, with more than one stable conformation. The common tape measure or the steel band enclosed inside the bright fabric cover of a ``slap bracelet'', are classic examples of plates that exhibit two stable configurations: folded and unfolded. Multistable structures have many potential applications, from the simple construction of objects of adjustable size to the design of mechanical devices that switch between a discrete number of states. In this talk I will discuss multistability in a quasi-one-dimensional anisotropic strip. The reduced dimensionality allows an exact analytical treatment in terms of the classic F\"oppl - von K\'arm\'an theory of plates. In the conclusions I will comment on the possible occurrence of multistability in biological materials.   

Time resolved deformation of a thin polyimide film absorbing layer for laser-induced forward transfer printing

Laser-induced forward transfer (LIFT) is a versatile direct write technique capable of printing high resolution patterns from a variety of functional materials. In LIFT, the material to be printed is coated as a thin liquid or solid donor film onto the bottom surface of a glass substrate and held in close proximity above a receiver substrate. A pulsed laser is focused through the glass, into the donor film, initiating the transfer of a small amount of material onto the receiver. In order to shield sensitive donor materials from direct laser irradiation, sacrificial absorbing layers are often deposited before the donor is coated. Recently, we demonstrated the use of a thin polyimide film absorbing layer to provide damage free transfers of sensitive rheological donor materials. Transfer is initiated by the laser-induced formation of a rapidly expanding, sealed blister on the polyimide film which mechanically ejects the adjacent donor material without significant heating or contamination. In this talk, we present time resolved images of the blister deformation as well as the dynamics of an ejected liquid donor material.   

Geometric Stability and Elastic Response of a Supported Nanoparticle Membrane

We discuss the mechanical response to compression of a self-assembled gold nanoparticle monolayer and trilayer supported on water. Analysis of the film's buckling morphology under compression reveals an anomalously low bending rigidity for both the monolayer and the trilayer, which we attribute to the spherical geometry of the nanoparticles and poor coupling between layers, respectively. The elastic energy of the trilayers is first delocalized in wrinkles then localized into folds, as predicted by linear and non-linear elastic theory for an inextensible thin film supported on water.   

stress response of silver nanoparticle film on a water subphase

We examine the stress response of a film composed of dodecanethiol-ligated silver nanoparticles and supported on a water subphase, using optical microscopy and synchrotron x-ray techniques (x-ray reflectivity and grazing incidence x-ray diffraction). We observe a monolayer-to-bilayer transition, which is followed by wrinkling and folding of the nanoparticle film. The results are quantitatively different from a similar film of gold nanoparticles, which undergoes a monolayer-to-trilayer transition and wrinkles with a longer wavelength. The silver film is also less covered in wrinkles and folds than the gold film at similar compressive strains, and the wrinkles quickly relax when compression is stopped.