Session B14: Morphing Matter: From Soft Robotics to 4D Printing I

Modeling shape transformations in liquid crystal elastomers: a machine learning approach to inverse design

Liquid Crystal Elastomers (LCE) are stimuli-responsive, programmable actuators that undergo shape-morphing in response to a change of temperature, illumination, or other environmental cues. The resulting actuation trajectory is programmed by patterning the nematic director field, for instance by forming the material between two glass substrates with prescribed surface anchoring patterns which may be identical or entirely different. Removing one of the substrates leaves behind an LCE coating, while removing both produces a freestanding thin LCE film. Using a GPU-based finite element simulation developed in-house, we explore mechanisms by which arrays of topological defects in the microstructure of LCE thin coatings give rise to complex transformations in surface topography. A key challenge in LCE device engineering is the inverse design problem: find the nematic director field that morphs a sample to a desired target shape e.g. when heated uniformly. Inspired by recent collaboration with the Lavrentovich group [1], we investigate the inverse design problem for LCE surface coatings that morph to form complex topographies. We present a machine learning approach to address this inverse design challenge. First, we solve 1500 “forward” problems using our fast finite element approach [2] for different director configurations to form a training dataset. Next, we train a stacked ensemble regression model using the Autogluon framework [3]. Here 80% of the dataset was used to train the models including tree-based and deep learning algorithms. The prediction of the parameters defining the director field on the remaining test dataset was evaluated. The ensemble model outperformed any individual model and could also predict configurations that departed from the initial geometry by adding noise. As an example we model the design of morphing LCE suction cups to mimic the gripping capabilities of octopus suckers. We discuss plans to extend this approach to a broader class of LCE device geometries. 

[1] G. Babakhanova et al, Journal of Applied Physics 128, 184702 (2020)

[2] A. H. Gelebart et al,  Nature v. 546, 632 (2017)

[3] auto.gluon.ai   

Modeling self-folding of large-scale structures

We study the morphing of large-scale origami-inspired active structures made from strong and lightweight biodegradable polymer composites. Such morphable structures in response to external stimuli could form the basis for sustainable architecture and be an alternative to traditional construction processes with reduced cost, waste, and energy consumption. Though the basic design principles of small-scale self-morphing origami are well understood, it is unclear how these designs need to be adapted when gravitational loads become relevant. To investigate the role of gravity and material/structural properties, we created a two-part computational model to guide the design of self-morphing large-scale origami structures. The first part, based on finite-strain theory, models individual origami folds that curve because of differential swelling/contraction across the multi-layered material. This analysis helps identify parameter regimes that lead to foldability of the activated hinges in the presence of gravity. These results form the basis for the second part which is a coarse-grained discrete bar-hinge model with active torsion and elastic springs, and vertex loads. Both parts work together to relate local material/structural properties of activated folds to the global structure deployed on the ground.   

Traveling kinks in viscoelastic kirigami

Mechanical waves without inertia are functional mechanisms often found in nature yet remain rare in synthetic materials—so far, they only exist in active or stimuli-responsive materials. Here, we demonstrate the presence of traveling kinks in purely dissipative metamaterials, and we show that they can be used for sensing applications, dynamic pattern morphing, and transport of objects. To do this, we use multitexture kirigami with suitably patterned viscoelastic properties that buckle in different styles depending on the loading rate. At long timescales, viscoelastic relaxation triggers a snapping instability governed by geometrical nonlinearities and viscoelastic properties of kirigami unit cells. When multiple unit cells are connected into a 1D strip, the snapping instability occurs in sequence, and a traveling overdamped kink emerges. Our 1D model explains such a wave as a reaction-diffusion process similar to overdamped waves in many biological systems. We further demonstrate that such a kink underpins dynamic shape morphing in 2D kirigami and can be used to transport objects. Our results expand the span of nonlinear waves of metamaterials by appending an overdamped regime and open avenues for using highly viscoelastic materials in soft robotics and biomimicry.

    

Harnessing magneto-mechanical coupling to tailor structural transformations in soft composites

Materials with shape-shifting and morphing capabilities are crucial for applications such as soft robotics and deployable devices. Here, we focus on the structural transformations associated with the onset of instability in soft composites. This strategy of reversibly transforming the structural layout has been employed for designing materials with switchable properties and functionalities, for example, tunable Poisson’s ratio, phononic and photonic switches, and color displays. In all these designs, notably, the behavior of the material in the post-transformation regime is dictated by instability-induced patterns. However, in a purely mechanical setting, the range of admissible patterns is highly restricted. In our work, we address this issue by designing soft multiphase composites with magnetoactive constituents. We show that the utilization of the magneto-mechanical coupling provides new ways to expand the design space for soft tunable materials.

    

Manipulating energy flows in non-periodic mechanical metamaterials

Energy focusing, mechanical signal processing, cloaking and guiding of nonlinear elastic waves are all examples of complex dynamic tasks requiring effective control of the energy flow in a material domain. As no single periodic architecture can perform such tasks, a rational way to efficiently navigate non-periodic design spaces is necessary to discover optimal material structures. In the context of mechanical metamaterials, we present a design framework for the automated discovery of non-periodic architectures that are optimized for a single task as well as multiple concurrent tasks. Specifically, we show how dynamic material responses can be effectively tailored to achieve energy focusing, energy routing along arbitrary paths, dynamic protection, and shock absorption. The design framework is based on an inverse design approach powered by automatic differentiation of the forward solution to the nonlinear dynamical system. The versatility of the method paves the way for the development of metamaterial-based soft robotic systems endowed with energy harvesting and signal processing capabilities.   

Shaping with plasticity

Changes of in-plane dimensions lead to out-of-plane buckling and to non-zero Gaussian curvature of architected membranes. In this work, we fix a programmed buckled shape with the precise control of irreversible plastic deformations. A periodic membrane is deformed with simple uniaxial stretching. The periodic element is a cell parametrized to produce local changes of metric. The global change of properties results from the mechanical behavior of the cell assembly. We present a two-level validating approach. We validate our analytical and numerical models with a complete experimental characterization of periodic cells’ mechanics using 3d printed lattices. At the level of the assembly we show experimentally that precise curvatures can be realized at large scale to form structure that are structurally rigid. We create a new paradigm for programmable surfaces: they can both be mechanically functional and created using a simple actuation method.

    

Generalizing Deformable System Dynamics beyond Euclidean Geometry

The study of motion is one of the fundamental concepts in classical physics. While it has been a subject of study for centuries, it was developed for euclidean geometry, which is our everyday experience. We investigate how the mechanics of extended body systems is affected by the presence of curvature. Although we are initially interested in the dynamics of systems in curved space, we plan to apply our framework to other systems with internal degrees of freedom. This framework can span self-propulsion of microorganisms to deformable soft robotic systems both of which can locomote and interact with their environment. Our goal is to develop a physics engine for deformable bodies in curved space which can handle internal degrees of freedom, rigidity constraints, and collisions between objects. The physics engine is used to probe and visualize how the presence of curvature affects the dynamics of deformable systems. Through the simulation of these nonintuitive deformable systems, we hope to gain deeper insight in dynamical deformable systems in flat space and systems with controls.   

Electrochemical Actuators for Microrobots

We show progress towards the design and fabrication of microrobots with electrochemical actuators. The proof-of-concept robot consists of a simple photovoltaic connected to two electrodes, allowing it to use optical power to drive electrochemical reactions. We show that the robots exhibit a variety of behaviors, including electrokinetic propulsion, electroplating, and active assembly. In hydrogen peroxide, the robots can propel at speeds over 300 microns/s and navigate microfluidic structures. In nickel electrolyte, swarms of robots can form metallic bonds between each other, assembling into macroscopic metallic structures with adaptable strength and conductivity. Notably, these behaviors can be powered and controlled with patterned laser light or onboard CMOS electronics, clearing a path towards a new class of controllable and programmable active microscopic matter.   

Production of Metric Jammed Structures with Morpho

Sam Hocking, Chaitanya Joshi, Tim Atherton

Metric jamming is a process whereby particles embedded on a moving interface can become rigid and arrest further evolution of the interface. It can occur, for example, in emulsion droplets, bacterial colonies and the formation of bijels. The metric jammed state may be thought of as the ultimate limit of a sequence of arrest, unjamming, relaxing and subsequent arrest events, whereby the system ultimately becomes rigid both with respect to particle and shape degrees of freedom. In this talk, we explore such configurations with *morpho*, a program for shape optimization and where the surface is directly discretized as a simplicial complex. Mechanical and vibrational properties of these structures are also discussed.   

Direct 3D printing of baromorph structures

Wrapping a three-dimensional object with a sheet is a generally difficult task: if the object locally exhibits more than one curvature, the sheet has to locally change its metric in order to reproduce the target shape. In baromorph structures the local metric of a soft plate can be changed by inflating embedded channels. In the present work we show that it is possible to build efficiently these channels from a 3D printing technique refered to as direct ink writing. In addition to being able to print structures that produce in-plane stresses, this versitile printing technique allows us to preselect the direction of the curvature produced by the changes in local metric and not only to program the change in metric, but also the direction of the local curvature.

    

Deep Spring: Inverse Design of Suspended Elastic Rods using Physics-Informed Neural Networks

Accurately predicting the geometrically nonlinear deformation of slender structures has been extensively studied across different scientific disciplines, such as mechanics and computer graphics. Our structure of interest is rods, which are unique structures that are prone to large deformation even under small loading, e.g., its own weight. The forward problem of predicting the deformation of rods can be readily addressed with efficient frameworks such as Discrete Elastic Rods (DER). However, the inverse problem of finding the initial geometry that deforms into the target shape is a highly nonlinear optimization problem. Previously, by capitalizing on the availability of inexpensive data generated through DER, we have introduced the concept of Deep Spring methodology to tackle the inverse problem for beams. Here, we extend our methodology to three-dimensional rods, which contain a higher level of complexity in their geometry due to the concept of twisting. Moreover, we implement a physics-informed structure to our neural network, which imposes satisfaction of the work-energy theorem to the predicted geometry.   

Electromechanical actuation and control of active, living epithelia

Biological tissues are extraordinary active materials, with each type possessing unique properties emerging from collective cell interactions and evolved to suit specific tasks. Active matter physics can help to explain these behaviors, enabling development of biophysical engineering approaches to harness them. Here, we discuss our work on engineering and controlling epithelial tissue behavior using electrical cues. Epithelia are complex cellular surfaces that provide mechanical protection (skin/cornea) and mass transport control (gut/kidney/blood-brain-barrier). Epithelial ‘superpowers’ include self-healing, conformal mapping to complex topographies, and hydraulic pumping across the tissue. Moreover, all epithelia are intrinsically electroactive, and naturally-occurring direct-current (DC) ion gradients (non-neuromuscular) help to direct both epithelial migration (healing) and fluid transport (kidney). We have previously mimicked these electric fields to allow us to accelerate epithelial self-healing, and here we will discuss a new experimental approach and theoretical modeling strategy allowing us to use these same fields to turn epithelial sheets and organoids (kidney and intestinal) into actuatable and responsive fluid pumping systems for control of 3D morphogenetic processes and scalable active hydraulic interfaces. 

    

Nonlinear topological solitons in mirror-symmetric triangle chains

Topologically polarized structures support an excess of zero-modes at one boundary, thereby softening the edge where they are localized. This leads to a variety of rich phenomena underpinned by the structure's specific geometry. Here we present the mirror-symmetric triangle chain, analytically characterize its polarization phase space, and manufacture an idealized prototype through FDM to show that it can be actively reconfigured between bistable states via the propagation of a soliton. Through the introduction of additional elastic bonds, we create more realistic physical prototypes that allow for elastic wave propagation and mechano-chemical interactions. Using experiments on these prototypes in addition to molecular dynamic simulations, we explore potential applications in energy release and trapping via the programmed soliton.