4D printed tunable mechanical metamaterials with shape memory operations

The aim of this paper is to introduce tunable continuous-stable metamaterials with reversible thermomechanical memory operations by four-dimensional (4D) printing technology. They are developed based on an understanding on glassy-rubbery behaviors of shape memory polymers and hot/cold programming derived from experiments and theory. Fused decomposition modeling as a well-known 3D printing technology is implemented to fabricate mechanical metamaterials. They are experimentally tested revealing elastic-plastic and hyper-elastic behaviors in low and high temperatures at a large deformation range. A computational design tool is developed by implementing a 3D phenomenological constitutive model coupled with a geometrically non-linear finite element method. Governing equations are then solved by an elastic-predictor plastic-corrector return map procedure along with the Newton-Raphson and Riks techniques to trace non-linear equilibrium path. A tunable reversible mechanical metamaterial unit with bistable memory operations is printed and tested experimentally and numerically. By a combination of cold and hot programming, the unit shows potential applications in mimicking electronic memory devices like tactile displays and designing surface adaptive structures. Another design of the unit shows potentials to serve in designing self-deployable bio-medical stents. Experiments are also conducted to demonstrate potential applications of cold programming for introducing recoverable rolling-up chiral metamaterials and load-resistance supportive auxetics

Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors

In this work, we construct an effective continuum model for architected sheets that are composed of bulky tiles connected by slender elastic joints. Due to their mesostructure, these sheets feature quasi-mechanisms -- low-energy local kinematic modes that are strongly favored over other deformations. In sheets with non-uniform mesostructure, kinematic incompatibilities arise between neighboring regions, causing out-of-plane buckling. The effective continuum model is based on a geometric analysis of the sheets' unit cells and their energetically favorable modes of deformation. Its major feature is the construction of a strain energy that penalizes deviations from these preferred modes of deformation. The effect of non-periodicity is entirely described through the use of spatially varying geometric parameters in the model. Our simulations capture the out-of-plane buckling that occurs in non-periodic specimens and show good agreement with experiments. While we only consider one class of quasi-mechanisms, our modeling approach could be applied to a diverse set of shape-morphing systems that are of interest to the mechanics community

Time-efficient geometrically non-linear finite element simulations of thin shell deployable structures

Isogeometric analysis of thin shells can provide higher continuity and exact geometric description. It is shown in the existing literature that isogeometric analysis converges with fewer degrees of freedom than C⁰-continuous finite elements that use Langrange polynomial shape functions, but the speed of the solutions has not been previously assessed. In this research, the geometrically nonlinear bending of a thin shell deployable structure, a tape spring is studied, using both NURBS-based and C⁰-continuous finite elements. The complex deformation of a tape spring makes it a perfect case study to compare the computational efficiency of the mentioned techniques. The simulations are carried out in the commercial software ABAQUS and LS-DYNA, and it is found that isogeometric analysis is at least three times slower than the C⁰-continuous finite element methods

Flexible mechanical metamaterials

Mechanical metamaterials exhibit properties and functionalities that cannot be realized in conventional materials. Originally, the field focused on achieving unusual (zero or negative) values for familiar mechanical parameters, such as density, Poisson's ratio or compressibility, but more recently, new classes of metamaterials — including shape-morphing, topological and nonlinear metamaterials — have emerged. These materials exhibit exotic functionalities, such as pattern and shape transformations in response to mechanical forces, unidirectional guiding of motion and waves, and reprogrammable stiffness or dissipation. In this Review, we identify the design principles leading to these properties and discuss, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami-based metamaterials), metamaterials harnessing instabilities and frustration, and topological metamaterials. We conclude by outlining future challenges for the design, creation and conceptualization of advanced mechanical metamaterials.J.C. acknowledges support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the Ministerio de Economía, Industria y Competitividad (MINECO) through a Ramon y Cajal grant (Grant No. RYC‑2015‑17156). M.vH. acknowledges funding from the Netherlands Organisation for Scientific Research through Grant VICI No. NWO‑680‑47‑609. V.V. acknowledges support from the University of Chicago Materials Research Science and Engineering Center, which is funded by the National Science Foundation through Grant No. DMR-1420709

Reversible energy absorbing meta-sandwiches by 4D FDM printing

The aim of this paper is to introduce dual-material auxetic meta-sandwiches by four-dimensional (4D) printing technology for reversible energy absorption applications. The meta-sandwiches are developed based on an understanding of hyper-elastic feature of soft polymers and elasto-plastic behaviors of shape memory polymers and cold programming derived from theory and experiments. Dual-material lattice-based meta-structures with different combinations of soft and hard components are fabricated by 4D printing fused deposition modelling technology. The feasibility and performance of reversible dual-material meta-structures are assessed experimentally and numerically. Computational models for the meta-structures are developed and verified by the experiments. Research trials show that the dual-material auxetic designs are capable of generating a range of non-linear stiffness as per the requirement of energy absorbing applications. It is found that the meta-structures with hyper-elastic and/or elasto-plastic features dissipate energy and exhibit mechanical hysteresis characterized by non-coincident compressive loading-unloading curves. Mechanical hysteresis can be achieved by leveraging elasto-plasticity and snap-through-like mechanical instability through compression. Experiments also reveal that the mechanically induced plastic deformation and dissipation processes are fully reversible by simply heating. The material-structural model, concepts and results provided in this paper are expected to be instrumental towards 4D printing tunable meta-sandwiches for reversible energy absorption applications

Compliant morphing structures from twisted bulk metallic glass ribbons

In this work, we investigate the use of pre-twisted metallic ribbons as building blocks for shape-changing structures. We manufacture these elements by twisting initially flat ribbons about their (lengthwise) centroidal axis into a helicoidal geometry, then thermoforming them to make this configuration a stress-free reference state. The helicoidal shape allows the ribbon to have preferred bending directions that vary throughout its length. These bending directions serve as compliant joints and enable several deployed and stowed configurations that are unachievable without pre-twist, provided that compaction does not induce material failure. We fabricate these ribbons using a bulk metallic glass (BMG), for its exceptional elasticity and thermoforming attributes. Combining numerical simulations, an analytical model based on shell theory and torsional experiments, we analyze the finite-twisting mechanics of various ribbon geometries. We find that, in ribbons with undulated edges, the twisting deformations can be better localized onto desired regions prior to thermoforming. Finally, we join together multiple ribbons to create deployable systems. Our work proposes a framework for creating fully metallic, yet compliant structures that may find application as elements for space structures and compliant robots

Continuum Mechanical Models for Design and Characterization of Soft Robots

The emergence of ``soft'' robots, whose bodies are made from stretchable materials, has fundamentally changed the way we design and construct robotic systems. Demonstrations and research show that soft robotic systems can be useful in rehabilitation, medical devices, agriculture, manufacturing and home assistance. Increasing need for collaborative, safe robotic devices have combined with technological advances to create a compelling development landscape for soft robots. However, soft robots are not yet present in medical and rehabilitative devices, agriculture, our homes, and many other human-collaborative and human-interactive applications. This gap between promise and practical implementation exists because foundational theories and techniques that exist in rigid robotics have not yet been developed for soft robots. Theories in traditional robotics rely on rigid body displacements via discrete joints and discrete actuators, while in soft robots, kinematic and actuation functions are blended, leading to nonlinear, continuous deformations rather than rigid body motion. This dissertation addresses the need for foundational techniques using continuum mechanics. Three core questions regarding the use of continuum mechanical models in soft robotics are explored: (1) whether or not continuum mechanical models can describe existing soft actuators, (2) which physical phenomena need to be incorporated into continuum mechanical models for their use in a soft robotics context, and (3) how understanding on continuum mechanical phenomena may form bases for novel soft robot architectures. Theoretical modeling, experimentation, and design prototyping tools are used to explore Fiber-Reinforced Elastomeric Enclosures (FREEs), an often-used soft actuator, and to develop novel soft robot architectures based on auxetic behavior. This dissertation develops a continuum mechanical model for end loading on FREEs. This model connects a FREE’s actuation pressure and kinematic configuration to its end loads by considering stiffness of its elastomer and fiber reinforcement. The model is validated against a large experimental data set and compared to other FREE models used by roboticists. It is shown that the model can describe the FREE’s loading in a generalizable manner, but that it is bounded in its peak performance. Such a model can provide the novel function of evaluating the performance of FREE designs under high loading without the costs of building and testing prototypes. This dissertation further explores the influence viscoelasticity, an inherent property of soft polymers, on end loading of FREEs. The viscoelastic model developed can inform soft roboticists wishing to exploit or avoid hysteresis and force reversal. The final section of the dissertations explores two contrasting styles of auxetic metamaterials for their uses in soft robotic actuation. The first metamaterial architecture is composed of beams with distributed compliance, which are placed antagonistic configurations on a variety of surfaces, giving ride to shape morphing behavior. The second metamaterial architecture studied is a ``kirigami’’ sheet with an orthogonal cut pattern, utilizing lumped compliance and strain hardening to permanently deploy from a compact shape to a functional one. This dissertation lays the foundation for design of soft robots by robust physical models, reducing the need for physical prototypes and trial-and-error approaches. The work presented provides tools for systematic exploration of FREEs under loading in a wide range of configurations. The work further develops new concepts for soft actuators based on continuum mechanical modeling of auxetic metamaterials. The work presented expands the available tools for design and development of soft robotic systems, and the available architectures for soft robot actuation.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163236/1/asedal_1.pd

Modeling and Programming Shape-Morphing Structured Media

Shape-morphing and self-propelled locomotion are examples of mechanical behaviors that can be "programmed" in structured media by designing geometric features at micro- and mesostructural length scales. This programmability is possible because the small-scale geometry often imposes local kinematic modes that are strongly favored over other deformations. In turn, global behaviors are influenced by local kinematic preferences over the extent of the structured medium and by the kinematic compatibility (or incompatibility) between neighboring regions of the domain. This considerably expands the design space for effective mechanical properties, since objects made of the same bulk material but with different internal geometry will generally display very different behaviors. This motivates pursuing a mechanistic understanding of the connection between small-scale geometry and global kinematic behaviors. This thesis addresses challenges pertaining to the modeling and design of structured media that undergo large deformations. The first part of the thesis focuses on the relation between micro- or mesoscale patterning and energetically favored modes of deformation. This is first discussed within the context of twisted bulk metallic glass ribbons whose edges display periodic undulations. The undulations cause twist concentrations in the narrower regions of the structural element, delaying the onset of material failure and permitting the design of structures whose deployment and compaction emerge from the ribbons' chirality. Following this discussion of a periodic system, we study sheets with non-uniform cut patterns that buckle out-of-plane. Motivated by computational challenges associated with the presence of geometric features at disparate length scales, we construct an effective continuum model for these non-periodic systems, allowing us to simulate their post-buckling behavior efficiently and with good accuracy. The second part of the thesis discusses ways to leverage the connection between micro/mesoscale geometry and energetically favorable local kinematics to create "programmable matter" that undergo prescribed shape changes or self-propelled locomotion when exposed to an environmental stimulus. We first demonstrate the capabilities of an inverse design method that automates the design of structured plates that morph into target 3D geometries over time-dependent actuation paths. Finally, we present devices made of 3D-printed liquid crystal elastomer (LCE) hinges that change shape and self-propel when heated.</p

Printing-on-Fabric Meta-Material for Self-Shaping Architectural Models

International audienceWe describe a new meta-material for fabricating lightweight architectural models, consisting of a tiled plastic star pattern layered over pre-stretched fabric, and an interactive system for computer-aided design of doubly-curved forms using this meta-material. 3D-printing plastic rods over pre-stretched fabric recently gained popularity as a low-cost fabrication technique for complex free-form shapes that automatically lift in space. Our key insight is to focus on rods arranged into repeating star patterns, with the dimensions (and hence physical properties) of the individual pattern elements varying over space. Our star-based meta-material on the one hand allows effective form-finding due to its low-dimensional design space, while on the other is flexible and powerful enough to express large-scale curvature variations. Users of our system design free-form shapes by adjusting the star pattern; our system then automatically simulates the complex physical coupling between the fabric and stars to translate the design edits into shape variations. We experimentally validate our system and demonstrate strong agreement between the simulated results and the final fabricated prototypes

Origami-inspired structures and materials: analysis and metamaterial properties and seismic design of hybrid masonry structural systems

This dissertation includes two major sections. The first section presents the research on creating and studying novel classes of origami-inspired metamaterials and structures. The second section deals with seismic design of hybrid masonry structural systems. 1) Origami-Inspired Structures and Materials Origami, the traditional Japanese art of paper folding, has been recognized to be a significant source of inspiration in science and engineering. Specifically, its principles have been used for innovative design of mechanical metamaterials for which material properties arise from their geometry and structural layout. Most research on origami-inspired materials relies on known patterns, especially on the Miura-ori, i.e., a classic origami pattern with outstanding properties and a wide range of applications. Motivated by outstanding properties and a broad range of applications of the Miura-ori, in this dissertation, inspired by the kinematics of a one-degree of freedom zigzag strip, we create a novel class of cellular folded sheet mechanical metamaterials. The class of the patterns combines origami folding techniques with kirigami cutting. Using both analytical and numerical models, we study the key mechanical properties of the folded materials. We show that they possess properties as remarkable as those of the Miura-ori on which there has been a surge of research interest. Consequently, the introduced patterns are single degree of freedom (DOF), developable, rigid-foldable and flat-foldable. Furthermore, we show that depending on the geometry, these materials exhibit both negative and positive in-plane Poisson’s ratio. By introducing a novel class of zigzag-base materials, the current study extends the properties of the Miura-ori to those of the class of one-DOF zigzag-base patterns, and our work shows that Miura-ori is only one pattern in this class with such properties. Hence, by expanding upon the design space of the Miura-ori, our patterns are appropriate for a wide range of applications, from mechanical metamaterials to light cellular foldcore sandwich panels and deployable structures at both small and large scales. Furthermore, this study unifies the concept of the in-plane Poisson’s ratio from the literature for similar materials and extends it to this novel class of zigzag-base folded sheet metamaterials. Moreover, in this dissertation, by dislocating the zigzag strips of a Miura-ori pattern along the joining ridges, we create a class of one-degree of freedom (DOF) cellular mechanical metamaterials. We further show that dislocating zigzag strips of the Miura-ori along the joining ridges, preserves and/or tunes the outstanding properties of the Miura-ori. The introduced materials are lighter than their corresponding Miura-ori patterns due to the presence of holes in the patterns. They are also amenable to similar modifications available for Miura-ori which make them appropriate for a wide range of applications across the length scales. Additionally, we study the Eggbox pattern. Similarly to Miura-ori, a regular Eggbox folded sheet includes parallelogram facets which are connected along fold lines. However, Eggbox sheets cannot be folded from a flat sheet of material, and contrary to Miura-ori which has received considerable interest in the literature, there are fewer studies available on Eggbox folded sheet material. By employing both analytical and numerical models, we review and study the key in-plane mechanical properties of the Eggbox folded sheet, and we present cellular folded metamaterials containing Miura-ori and Eggbox cells. The entire structure of the folded materials is a one-DOF mechanism system and, similarly to Eggbox sheets, the materials composed of layers of Eggbox folded sheets are bi-directionally flat-foldable, resulting in a material flexible in those directions, but stiff in the third direction. 2) Seismic Design of Hybrid Masonry Structural Systems Hybrid masonry is an innovative seismic lateral-load resisting system. The system comprises reinforced masonry panels within a steel-framed structure as well as steel connector plates which attach the surrounding steel frame to the masonry panel. Depending on the interfacial conditions between a masonry panel and the steel frame, the system is categorized into three major groups: Types I, II and III. The first part of the research on hybrid masonry systems, in this dissertation, includes a series of exploratory studies aimed at understanding the global behavior of various types of hybrid masonry panels and setting the stage for the study on seismic design of the systems. In this regard, computational analyses were carried out to study the distribution of lateral forces between a masonry panel and a frame in various types of hybrid masonry structural systems. The results are used to demonstrate differences in lateral-force distributions in hybrid masonry systems with different boundary conditions and with various panel aspect ratios as well as with different stiffness of the wall to that of the frame. Furthermore, this study presents the general methodology for seismic design of Type I hybrid masonry systems as well as the steps of a capacity design process in which two favorable ductile modes of behavior are considered: steel connector plates behaving as fuses or flexural yielding of the masonry panels. Moreover, using the proposed approaches we design several prototype buildings located in a high seismic region and investigate viability of hybrid masonry as a new seismic lateral-load resisting system. According to this design framework and the exploratory studies, both approaches are shown to be feasible for developing realistic system configurations. Finally, in this study, an integrated approach for performance-based seismic analysis and design of hybrid masonry Type I systems with fuse connector plates is presented. The procedure used in this study is based on the Capacity Spectrum Method. The proposed method includes an iterative process through which a hybrid masonry structural system with fuse connector plates is designed depending on its energy dissipation capacity. In this regard, the value of the system R factor is regulated in the process. In this study, application of the method for design of a sample hybrid masonry building system is presented