Edwin A. Peraza Hernandez

SMI 2013: Towards building smart self-folding structures

We report our initial progress on synthesizing complex structures from programmable self-folding active materials, which we call Smart Multi-Use Reconfigurable Forms. We have developed a method to unfold a given convex polygonal mesh into a one-piece planar surface. We analyze the behavior of this surface as if it were constructed from realistic active materials such as shape memory alloys (SMAs), in which sharp creases and folds are not feasible. These active materials can change their shapes when they are heated and have been applied to medical, aerospace, and automotive applications in the engineering realm. We demonstrate via material constitutive modeling and utilization of finite element analysis (FEA) that by appropriately heating the unfolded planar surface it is possible to recover the 3D shape of the original polygonal mesh. We have simulated the process and our finite element analysis simulations demonstrate that these active materials can be raised against gravity, formed, and reconfigured automatically in three dimensions with appropriate heating in a manner that extends previous work in the area of programmable matter. Based on our results, we believe that it is possible to use active materials to develop reprogrammable self-folding complex structures.

Kinematics of Origami Structures With Smooth Folds

A kinematic model for origami with creased folds was presented in Chap. 2 and most existing models for origami also assume that folds are straight creases. However, such previous models are not intended for origami structures having non-negligible fold thickness or maximum fold curvature constraints based on material or structural limitations. In this chapter, we develop a model that captures the kinematic response of sheets having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, referred to as smooth folds. The geometry of smooth folds and the constraints on their associated kinematic variables are presented. We also address the implementation of the model in a computational environment and provide various representative examples.

Modeling and analysis of origami structures with smooth folds

Origami has the potential to impact numerous areas of design and manufacturing. Modeling and analysis of origami structures allow for the understanding of their behavior and the development of computational tools for their design. Most available origami models are limited to the idealization of folds as creases of zeroth-order geometric continuity, which is not proper for origami structures having non-negligible fold thickness or with maximum curvature at the folds restricted by material limitations. Structural analysis of origami sheets having creased folds requires further idealizations of the fold mechanical response such as the representation of the folds as torsional springs. In view of this, a novel model analogous to that for rigid origami is presented in this work for origami structures having folds of non-zero surface area that exhibit higher-order geometric continuity (termed smooth folds). This origami model allows for a proper structural analysis of origami sheets using plate or shell representations for the folds. The shape formulation of the smooth folds and the kinematic constraints on their associated shape variables are presented. Modeling of origami structures with smooth folds exhibiting elastic behavior is performed by determining the configuration of the structure that minimizes its total potential energy subject to the derived kinematic constraints. The presented results show that the structural response determined using the proposed model is in good agreement with both experiments and higher-fidelity finite element analyses. A model for origami with smooth folds including kinematics and kinetics is proposed.A model implementation for analysis of arbitrary fold patterns is presented.Arbitrarily complex fold patterns considering real materials can be modeled.The results obtained with the model are in good agreement with experiments and FEA.

Design and Optimization of an SMA-Based Self-Folding Structural Sheet With Sparse Insulating Layers

Origami inspired structures possess attractive characteristics such as the potential to be reconfigurable and the capability to be folded into compact forms for storage. Self-folding structures, which are systems able to perform folding operations without external mechanical input, are desirable in certain circumstances such as remote applications (e.g., space applications, underwater robotics). A self-folding structural sheet consisting of two outer layers of shape memory alloy (SMA) orthogonal wire meshes separated by an inner insulating layer is considered in this work. The inner layer consists of ABS plastic columns that connect the SMA wire mesh intersections of the top and bottom layers, which are co-located and co-oriented (denoted sparse middle layer/aligned meshes design). Significant reduction on the heat transfer between the SMA layers is expected in this design compared to previously considered designs with continuous or perforated elastomeric middle layers. The geometric and power input parameters of the sparse middle layer/aligned meshes design are optimized under mechanical and thermal constraints considering finite element and reduced order analytical models. The optimal folding performance of the sparse middle layer/aligned meshes design is compared to that of the previous designs. The results show that the sparse middle layer/aligned meshes design has promising characteristics as a self-folding structural sheet and provides for tighter folds compared to the designs with elastomeric middle layers.Copyright

Connectivity of Shape Memory Alloy-based Self-Folding Structures

Structures inspired by origami have attractive characteristics such as the potential to be reconfigurable, reduced manufacturing complexity, and the capability to be folded into compact forms for storage. In some circumstances, it may be impractical to apply external manipulations to generate the desired folds in origami-inspired structures (e.g., as in remote applications such as deployable satellite members, solar arrays, etc.). In such cases, self-folding capabilities may be necessary. The self-folding system considered herein consists of a laminate with outer layers of thermally actuated shape memory alloy (SMA) separated by a compliant and insulating layer. Localized actuation of the SMA layers allows for control of the laminate curvature anywhere in the sheet, allowing the initially planar sheet to reconfigure into a 3D structure. For self-folding structures created with this laminate, it is inefficient to hold permanent heating at the actuated regions to maintain the shape of the folded structure. Connectivity systems are proposed to avoid such permanent heating. Different ideas for connectivity systems are studied in this work via finite element analysis (FEA). The connections are compared in different aspects such as the capability of maintaining the folded structure upon cooling, the capability of disconnecting after connection is achieved, the complexity of the maneuver needed to connect the structure, and the complexity of adding multiple connections in a sheet for any general complex structure.

Numerically validated reduced-order model for laminates containing shape memory alloy wire meshes

The incorporation of active materials into composites is an active area of research. However, the design and optimization of such composites is challenging because detailed analysis using finite element analysis (FEA) is computationally intensive. This work presents a new reduced-order model for laminates containing shape memory alloy (SMA) wire meshes that significantly reduces the computational burden on design analysis while maintaining good accuracy. The approach is based on a foundation of classical laminated plate theory (CLPT). It considers fully non-linear stress distributions and incorporates a detailed phenomenological model of the hysteretic SMA constitutive behavior. The reduced-order CLPT-based model and its numerical implementation are fully described and unique laminate responses are presented. The model is validated against a corresponding high-fidelity FEA model of an SMA-based laminate. The reduced-order model produces accurate predictions at significantly less expense than the high-fidelity FEA approach, with normalized root-mean-squared error below 10% for most design cases.

Modeling size effects on the transformation behavior of shape memory alloy micropillars

The size dependence of the thermomechanical response of shape memory alloys (SMAs) at the micro and nano-scales has gained increasing attention in the engineering community due to existing and potential uses of SMAs as solid-state actuators and components for energy dissipation in small scale devices. Particularly, their recent uses in microelectromechanical systems (MEMS) have made SMAs attractive options as active materials in small scale devices. One factor limiting further application, however, is the inability to effectively and efficiently model the observed size dependence of the SMA behavior for engineering applications. Therefore, in this work, a constitutive model for the size-dependent behavior of SMAs is proposed. Experimental observations are used to motivate the extension of an existing thermomechanical constitutive model for SMAs to account for the scale effects. It is proposed that such effects can be captured via characteristic length dependent material parameters in a power-law manner. The size dependence of the transformation behavior of NiFeGa micropillars is investigated in detail and used as model prediction cases. The constitutive model is implemented in a finite element framework and used to simulate and predict the response of SMA micropillars with different sizes. The results show a good agreement with experimental data. A parametric study performed using the calibrated model shows that the influence of micropillar aspect ratio and taper angle on the compression response is significantly smaller than that of the micropillar average diameter. It is concluded that the model is able to capture the size dependent transformation response of the SMA micropillars. In addition, the simplicity of the calibration and implementation of the proposed model make it practical for the design and numerical analysis of small scale SMA components that exhibit size dependent responses.

Analysis and Optimization of a Shape Memory Alloy-Based Self-Folding Sheet Considering Material Uncertainties

Origami-inspired active structures have important characteristics such as reconfigurability and the ability to adopt compact flat forms for storage. A self-folding shape memory alloy (SMA)-based laminated sheet is considered in this work wherein SMA wire meshes comprise the top and bottom layers and a thermally insulating compliant elastomer comprises the middle layer. Uncertainty in various parameters (e.g. material properties) may affect the performance of the sheet, which is explored here. Different modeling approaches are studied in order to compare their accuracy and computational cost. A numerical approach based on the Euler-Bernoulli beam theory is selected due to its accuracy when compared to higher fidelity finite element simulations and its low computational cost, necessary to perform a large number of design evaluations as required for uncertainty analysis. Optimization is performed considering uncertainty in the material properties. Failure probabilities under mechanical constraints and expected values of fold curvature and blocking moment are considered during optimization of the self-folding sheet. The multiobjective genetic algorithm for technology characterization P3GA is used to obtain the Pareto dominant designs. Most designs forming the Pareto frontier have the same values for certain design parameters such as the distance between the wires in the SMA meshes non-dimensionalized by SMA wire thickness, elastomer layer thickness non-dimensionalized by SMA wire thickness, and applied temperature. The design parameter deciding the trade-off between fold curvature and blocking moment is found to be the SMA wire thickness.Copyright

An Experimental and Numerical Study of Shape Memory Alloy-Based Tensegrity/Origami Structures

This paper presents an initial experimental and numerical study on a novel concept of integrated tensegrity/origami morphing structures. Both tensegrity and origami are known for their potential transformative roles in applications in fields which exist at the interplay of shape, size, and function. Their integration, proposed here for the first time, is based on the interest in uniting the strengths of origami (membrane integration and folding capabilities) with the strengths of tensegrity (minimal mass and controllable rigidity). In order to achieve morphing capabilities while retaining low mass, the considered structures possess intrinsic material actuation provided by shape memory alloy (SMA) members. Two different representative structures of the proposed concept are studied. The first corresponds to a tensegrity/origami cylinder based on the double-helix tensegrity topology. Shape memory alloy wires play the role of the tensile members of the tensegrity structure while foldable surface components play the role of compressive members. The second structure corresponds to a tensegrity plate, which although not having a continuous dense surface, can be morphed in novel ways using origami principles. Fabrication of experimental prototypes and evaluation of the observed structural transformation are presented. Finite element analysis is performed to numerically evaluate the characteristics of the novel proposed structures. This initial study shows that the integration of tensegrity and origami results in a powerful combination that provides structural stability, flexibility in design and lightweight actuation mechanisms while allowing for significant deflections during morphing.Copyright

Introduction to Active Origami Structures

Origami, the ancient art of paper folding, has inspired the design and functionality of engineering structures for decades. The underlying principles of origami are very general, it takes two-dimensional components that are easy to manufacture (sheets, plates, etc.) into three-dimensional structures. More recently, researchers have become interested in the use of active materials that convert various forms of energy into mechanical work to produce the desired folding behavior in origami structures. Such structures are termed active origami structures and are capable of folding and/or unfolding without the application of external mechanical loads but rather by the stimulus provided by a non-mechanical field (thermal, chemical, electromagnetic). This is advantageous for many areas including aerospace systems, underwater robotics, and small scale devices. In this chapter, we introduce the basic concepts and applications of origami structures in general and then focus on the description and classification of active origami structures. We finalize this chapter by reviewing existing design and simulation efforts applicable to origami structures for engineering applications.