Session F29: Morphing Matter I

Recent Advances in the Additive Manufacturing of Soft, Morphing Matter

The convergence of human creativity, bioinspiration, and advanced computational tools holds the potential to yield the most captivating — and efficient — designs for new engineering materials, structures, and systems. Yet, realizing these designs in the physical realm presents an ongoing challenge. Amidst this pursuit, Additive Manufacturing (AM), or 3D Printing, has emerged as a compelling alternative to conventional methodologies. However, it has yet to fully meet its lofty expectations, often faltering when confronted with the intricate demands of materials options, structural complexity, throughput speed, and repeatability. This is particularly limiting in soft matter fabrication where specific requirements apply, such as fluid impermeability and multifunctionality via integrated actuation and sensing. Consequently, these limitations have hampered advancements in morphing matter and related research domains where fabrication is the bottleneck. In this talk, I will present how we can design and physically realize novel materials with exceptional properties for applications in soft robotics and beyond. This includes overcoming mutual exclusivities, integrating multifunctionality, and surpassing properties found in natural materials. First, we will explore how specific design requirements can lead to new AM technologies, realizing designs that cannot be manufactured through other means. Second, we will see how these specialized AM processes can inspire unexpected designs outside the initial scope. Lastly, I will showcase examples of new fabrication techniques that address the general limitations of AM, expanding the available design space for soft matter fabrication.   

Bundling of a twisted thin tube

The twisted end of a candy may at first look simple, but it contains complex features such as the wrinkles and creases that form as the material is packed into a tight bundle. We present experiments where a thin flexible sheet is clamped on two ends and pulled taut, and then twisted to a large angle. We first summarize our recent results showing how the system exhibits an attractive mechanical response in the form of a "tunable locking material." Then we turn to study the deformations at larger twist. While twisting, the shell at first shows an ordered wrinkle pattern that gradually evolves into two cones. At larger twist angles, the material between the cones condenses into a tightly-packed helical structure – a "bundle.". We investigate how this bundle is affected by various geometric and mechanical parameters, such as the aspect ratio of the shell, the normal load, and the geometry of the clamping. Our results show how such tightly-packed structures evolve while twisted and stretched, and how they reflect conditions at larger length scales.   

A centerline-based energy model of elastic ribbons using implicit neural ODE

Ribbons are slender structures with length » width & width » thickness. We present a simulation framework based on implicit neural ordinary differential equation (iNODE) designed for modeling behavior of elastic ribbons. Our approach uses a 1D energy model based on physics-informed neural networks (PINNs) in the Discrete Elastic Rods (DER) algorithm, originally devised for 1D rods. Adapting DER for ribbons posed challenges in capturing bending and twisting interactions. While the Discrete Elastic Plates (DEP) captures ribbon mechanics precisely, it is computationally expensive compared to rod-based methods. To strike a balance between computational efficiency and physical accuracy, we employ a NN-based energy model of ribbon's central axis within a rod-like framework. Using DEP simulations, we collect time-series data of curvatures and twist of ribbon's central axis across various bending and twisting configurations. Next, we deploy our iNODE to train a PINN-based energy model. It employs implicit Euler integrator on top of NODE, enabling efficient simulation of quasi-static dynamic systems. It outperforms the standard NODE in capturing ribbon mechanics with reduced data and faster training. We perform ablation study on our energy model, comparing state-of-the-art ribbon analytical models. Our energy model stands as a potential benchmark for forthcoming analytical models in the ribbon domain. Furthermore, iNODE offers a powerful tool for non-linear dynamics of systems where analytical expressions proves challenging, enabling efficient training for quasi-static systems and improved generalization.   

Measuring the Transition from Wrinkles to Crumples in Stamped Thin Sheets

Wrapping a basketball with a sheet of wrapping paper is a frustrating exercise. The geometries of the planar sheet and the spherical surface are incompatible, resulting in a rough, crinkled appearance. These deformations can occur in any sufficiently thin sheet confined to a surface with a different metric, such as in the use of wearable sensors or synthetic skins. Recent studies have characterized a transition from smooth “wrinkles” to sharp “crumples” in thin polymer films placed on curved liquid surfaces. Their experiments established a threshold for this transition, which depends on the boundary tension, the imposed curvature, the length of the buckled region, and the stretching modulus of the material. But, how do the parameters governing the wrinkle to crumple transition change in the absence of surface tension pulling at the boundary of the film?

We report experiments using a pair of curved glass lenses to stamp a thin sheet placed between them. We find that the wrinkle to crumple transition depends on the sheet's thickness, the sheet's diameter, and the imposed curvature; and we identify an empirical threshold from wrinkles to crumples based on these parameters. Our work expands the range of environments in which the wrinkle to crumple transition can be predicted, which will lead to a more generic description of the transition.   

Unleashing snap-power through folded structures

Slender structures are integral components in soft robotics, commonly employed as actuators with applications in various fields, from aerospace engineering to microelectronics and fluidics. These actuators harness the snap mechanism to swiftly release stored bending energy, facilitating rapid transitions between two stable states. Our study delves into the potential for optimizing snap actuation by introducing folds into thin ribbons. Through a combination of experimental investigations and theoretical modeling, we reveal how the presence of a crease significantly impacts the stability of the snapping process and increases energy storage capabilities. Furthermore, it enables a faster transition between the two stable states, surpassing the performance of conventional flat thin sheets. This innovative approach offers promising avenues for developing next-generation fast soft actuators, with enhanced effectiveness through the fold properties.   

The stability of a tape loop.

If a thin sticky sheet is bent into a loop such that the two ends contact and overlap a small amount, will the loop remain closed?  On one hand, there is mechanical energy stored in the bending of the material.  On the other, there is interfacial energy created by the small amount of overlap (adhesion).  Clearly, if the adhesion is high the loop remains closed and if the adhesion is low the loop will open.  In order to find the limits of stability we employ Kirchhoff’s rod theory to model the planar equilibria of a closed loop of a strip obtained by overlapping its two terminal ends. The overlapping region is taken to be held together by an adhesive of constant strength. The reactive force density exerted by the adhesive to prevent detachment of the overlap is assumed to be purely normal to the centerlines of the inner and outer segments. Using appropriate jump conditions across the boundaries of the overlap, we compute the effective modulus of overlapping region, and reduce the entire system to a closed loop formed out of a strip with non-uniform thickness.  We verify our predictions with experiments utilizing various polydimethylsiloxane elastomers.  Ultimately, the technique could form the basis of a simple adhesion test for thin sticky films.   

Harnessing stiffness asymmetry in thin sheets inflatables for high deformation shape morphing

Inflatables are particularly popular in the field of shape morphing materials. Their simple, purely mechanical actuation allows for fast deployment and high reusability. Moreover, just as the structural stiffness of a party balloon is directly linked to its inside pressure, inflatable objects offer an elegant example of the coupling of elasticity and geometry.

In this presentation, we focus on the inflation of a network of tubes presenting two sides of distinct stiffness. The showcased objects are indeed made by welding two sheets of different mechanical properties. Upon inflation, a tube will overall bend towards its stiffer side similarly to the well-studied bilayer effect. Such deformations allow for enormous deformations across large networks. We present experimental results on the mechanics of inflation of either one or several connected tubes.

Afterwards we formulate and solve an inverse problem to design a wide variety of objects that can be described as a two-dimensional curve perpendicularly to the direction of the tubes. The question of the stiffness of such structures is discussed as well. We finally present several applications of asymmetric tubular inflatables to more complex geometries: axisymmetric surfaces, kirigami, and curved folding.   

A new design strategy for multistable structures

Multistable architected structures have been proposed as candidates for shock-absorbing, wave-guiding, and shape-transforming materials. However, current strategies rely on one-off unit cell designs stacked in periodic tesselations. Here, we present a novel design strategy for the creation of multistable kirigami metamaterials in 2 and 3 dimensions. We introduce a simple triangular building block along with a set of compatibility rules that can be used to create tesselations of arbitrary order, from periodic to quasicrystalline. This work presents a general design platform for highly multistable architectures that facilitate extreme mechanical deformations.   

Pneumatic Gaussian cells

In Nature, plants leaves or petals may develop into very complex shapes through differential growth. Such change of a surface into a well-defined 3D shape requires both distorting distance along the plane and bending curvature simultaneously. However, current mechanisms are usually limited to either bending or metric distortion with soft systems. Programming complete morphing in stiff structures are relevant for engineering applications remains a challenge.

 

Here, we present and rationalize a novel and versatile gaussian morphing approach inspired by pneumatic actuation in monocotyledon plant leaves (bulliform cells). Our method relies on two pieces of airtight fabric separated by a network of thin walls that define pneumatic Gaussian cells. Both in-plane contraction and angular deflection of the panels can be programmed simultaneously through the cross section of the walls and the width of the cell. In addition, the stiffness of the structure is proportional to the applied pressure, which paves the way for the development of large-scale objects. These surfaces with controlled stiffness and fast actuation are manufactured using consumer-grade materials and constitutes an important milestone towards large-scale shape-morphing robotics applications.

 

    

Deep Spring: A Neural Network that Learns Physics Through Differentiable Simulation for the Inverse Design of Suspended Elastic Rods

Predicting the geometrically nonlinear deformation of slender structures has been extensively studied in various scientific fields, including mechanics and computer graphics. We are interested in rods, which are unique structures that undergo large deformation even under minimal loads, such as their own weight. While the forward problem of predicting a rod's deformation can be easily addressed with efficient frameworks such as Discrete Elastic Rods (DER), the inverse problem of finding the initial geometry that deforms into the target shape is a challenging nonlinear optimization problem. Previously, we have proposed a propagative method to solve the inverse problem for an entire rod. Leveraging the DeepSpringNet, a neural network designed to determine the initial geometry based on the deformed shape of a rod segment, we decompose the problem into manageable subproblems, starting from the fixed end and progressing towards the free end. However, the iterative nature of this method makes it susceptible to error propagation, where the error at a later step reflects the cumulative error from all prior steps. In this work, we address this problem through two solutions: 1) We enforce DeepSpringNet to learn the underlying physics by including the forward simulation in the training loop, which increases the accuracy of the neural network, 2) We compute the loss after linking multiple segments together, and backpropagate through the propagated error. This work brings us one step closer to real-time prediction of undeformed shapes of rods given their deformed shapes under gravity.   

Viscoelasticity-driven dynamical shape shifting of soft bilayer strips

Elastic bilayers with different strain recoveries can be used for dynamical shape shifting through ambient stimuli, such as temperature, mass diffusion, and light. As a fundamentally different approach to designing temporal shape change, we leverage constituent polymer molecular features (rather than external fields), specifically the viscoelasticity of gelatin bilayers, to achieve dynamical three-dimensional (3D) curls and helical twists. After stretching and releasing, the acquired 3D shape recovers its original flat shape on a timescale set by polymer viscoelasticity. The time-dependent bilayer curvature can be predicted from hyperelastic and viscoelastic functions: In one incarnation, the time-dependent strain obtained from modified creep recovery experiments is used in the Timoshenko bilayer model to predict curvature. In another incarnation, viscoelastic parameters found by fitting the stress-strain and the stress relaxation data are used in finite-element analysis to predict the nonlinear shape dynamics in space and time in quantitative agreement with experiments. Our framework leverages material properties as opposed to external field variations for biomimetic shape change, bringing us one step closer to acquiring autonomous shape-shifting capabilities of living systems.   

Shape Morphing of Twisted Nematic Elastomer Shells

We study the geometry of Twisted Nematic Liquid Crystal Elastomers (TNLCEs) by modeling a layered TNLCE with a varying nematic director. We present a mathematical framework in terms of elasticity theory wherein we identify a novel term that results from the interplay between the orientational order and elasticity. This emergent term dominates the traditional bending contributions but is weaker than the stretching components. Additionally, we explore the shape morphing of these materials by adapting our theoretical framework from a continuous to a discrete setting.   

Kelp blade morphogenesis through wrinkling mechanical instabilities

Brown macroalgae, also known as kelp, form an important marine ecosystems and their varied morphology directly affects their function and survival. A kelp individual is composed of a holdfast that anchors it to the sea floor, a stipe that rises to the water surface, and leaf-like structures known as blades. A close inspection of the blades' surface reveals complex and diverse types of wrinkled patterns. The morphogenesis of these surfaces could be linked to the differential growth across the thickness of the blade. Indeed, the outer layers (i.e, the meristoderm) grow through cell proliferation while pulling on a passive inner core (i.e., the medulla and cortex). This incompatibility in growth eventually leads to a surface instability called wrinkling which has mostly been characterized in bi-layers systems. Here, we model the kelp blades as a tri-layer to study the influence of wrinkling instabilities. Using a combination of reduced-order models and finite element simulations, we characterize the influence of material and geometrical parameters (e.g., layers' modulus, thickness, boundary conditions) on the wrinkling onset and the post-instability deformation of the system. In light of numerical predictions, we experimentally reproduce and control wrinkled surfaces on pre-stretched polymers. Our results shed light onto the role of wrinkling in the morphogenesis of kelp blade and are used to induce wrinkles in artificial systems.