Using a combination of theory and experiments we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane background. The tilt at the inter-domain edge forces splay, which in turn manifests as a spontaneous edge curvature whose energetics are controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at inter-domain edges explains a number of experimental observations, including a non-monotonic dependence of the edge twist on the domain radius, and annularly shaped domains of long rods. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids give rise to complex shapes and thermodynamics of domains, analogous to shape transitions in 3D fluid vesicles.
more »
« less
Numerical Method for Direct Solution to Form-Finding Problem in Convex Gridshell
Abstract Elastic gridshell is a class of net-like structure formed by an ensemble of elastically deforming rods coupled through joints, such that the structure can cover large areas with low self-weight and allow for a variety of aesthetic configurations. Gridshells, also known as X-shells or Cosserat Nets, are a planar grid of elastic rods in its undeformed configuration. The end points of the rods are constrained and positioned on a closed curve—the final boundary—to actuate the structure into a 3D shape. Here, we report a discrete differential geometry-based numerical framework to study the geometrically nonlinear deformation of gridshell structures, accounting for non-trivial bending-twisting coupling at the joints. The form-finding problem of obtaining the undeformed planar configuration given the target convex 3D topology is then investigated. For the forward (2D to 3D) physically based simulation, we decompose the gridshell structure into multiple one-dimensional elastic rods and simulate their deformation by the well-established discrete elastic rods (DER) algorithm. A simple penalty energy between rods and linkages is used to simulate the coupling between two rods at the joints. For the inverse problem associated with form-finding (3D to 2D), we introduce a contact-based algorithm between the elastic gridshell and a rigid 3D surface, where the rigid surface describes the target shape of the gridshell upon actuation. This technique removes the need of several forward simulations associated with conventional optimization algorithms and provides a direct solution to the inverse problem. Several examples—hemispherical cap, paraboloid, and hemi-ellipsoid—are used to show the effectiveness of the inverse design process.
more »
« less
- Award ID(s):
- 1925360
- NSF-PAR ID:
- 10292339
- Date Published:
- Journal Name:
- Journal of Applied Mechanics
- Volume:
- 88
- Issue:
- 2
- ISSN:
- 0021-8936
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract A new class of thin flexible structures is introduced that morph from flat into prescribed 3D shapes through strain mismatch between layers of a composite plate. To achieve control over the target shape, two different concepts are coupled. First, motivated by biological growth, strain mismatch is applied between the flat composite layers to transform it into a 3D shape. Depending on the amount of the applied strain mismatch, the transformation involves buckling into one of the available finite number of deformation modes. Second, inspired by kirigami, portions of the material are removed from one of the layers according to a specific pattern. This dramatically increases the number of possible 3D shapes and allows us to attain specific topologies. An experimental apparatus that allows precise control of the strain mismatch is devised. An inverse problem is posed, where starting from a given target shape, the physical parameters that make these shapes possible are determined. To show how the concept works, it focuses on circular composite plates and designs a kirigami pattern that yields a hemispherical structure. The analysis combines a theoretical approach with numerical simulations and physical experiments to understand and predict the shape transition from 2D to 3D. The tools developed here can be extended to attain arbitrary 3D shapes. The initially flat shape suggests that conventional additive manufacturing techniques can be used to functionalize the soft kirigami composite to fabricate, for example, deployable 3D structures, smart skins, and soft electromagnetic metasurfaces.
-
Abstract This paper introduces a new computational approach for the articulated joint/deformation actuation and motion control of robot manipulators with flexible components. Oscillations due to small deformations of relatively stiff robot components which cannot be ignored, are modeled in this study using the finite element (FE) floating frame of reference (FFR) formulation which employs two coupled sets of coordinates: the reference and elastic coordinates. The inverse dynamics, based on the FFR formulation, leads to driving forces associated with the deformation degrees of freedom. Because of the link flexibility, two approaches can be considered to determine the actuation forces required to achieve the desired motion trajectories. These two approaches are the partially constrained inverse dynamics (PCID) and the fully constrained inverse dynamics (FCID). The FCID approach, which will be considered in future investigations and allows for motion and shape control, can be used to achieve the desired motion trajectories and suppress undesirable oscillations. The new small-deformation PCID approach introduced in this study, on the other hand, allows for achieving the desired motion trajectories, determining systematically the actuation forces and moments associated with the robot joint and elastic degrees of freedom, and avoiding deteriorations in the vibration characteristics as measured by the differences between the inverse- and forward-dynamics solutions. A procedure for determining the actuation forces associated with the deformation degrees of freedom is proposed and is exemplified using piezoelectric actuators. The PCID solution is used to define a new set of algebraic equations that can be solved for the piezoelectric actuation voltages required to maintain the forward-dynamics oscillations within their inverse-dynamics limits. A planar two-link flexible-robot manipulator is presented to demonstrate the implementation of the joint/deformation actuation approach. The results obtained show deterioration in the robot precision if the deformation actuation is not considered.more » « less
-
more » « less
Abstract Numerous animals adapt their stiffness during natural motions to increase efficiency or environmental adaptability. For example, octopuses stiffen their tentacles to increase efficiency during reaching, and several species adjust their leg stiffness to maintain stability when running across varied terrain. Inspired by nature, variable‐stiffness machines can switch between rigid and soft states. However, existing variable‐stiffness systems are usually purpose‐built for a particular application and lack universal adaptability. Here, reconfigurable stiffness‐changing skins that can stretch and fold to create 3D structures or attach to the surface of objects to influence their rigidity are presented. These “jamming skins” employ vacuum‐powered jamming of interleaved, discrete planar elements, enabling 2D stretchability of the skin in its soft state. Stretching allows jamming skins to be reversibly shaped into load‐bearing, functional tools on‐demand. Additionally, they can be attached to host structures with complex curvatures, such as robot arms and portions of the human body, to provide support or create a mold. We also show how multiple skins can work together to modify the workspace of a continuum robot by creating instantaneous joints. Jamming skins thus serve as a reconfigurable approach to creating tools and adapting structural rigidity on‐demand.
-
more » « less
Abstract Soft deployable structures – unlike conventional piecewise rigid deployables based on hinges and springs – can assume intricate 3‐D shapes, thereby enabling transformative soft robotic and manufacturing technologies. Their virtually infinite degrees of freedom allow precise control over the final shape. The same enabling high dimensionality, however, poses a challenge for solving the inverse problem: fabrication of desired 3D structures requires manufacturing technologies with extensive local actuation and control, and a trial‐and‐error search over a large design space. Both of these shortcomings are addressed by first developing a simplified planar fabrication approach that combines two ingredients: strain mismatch between two layers of a composite shell and kirigami cuts that relieves localized stress. In principle, it is possible to generate targeted 3‐D shapes by designing the appropriate kirigami cuts and the amount of prestretch (without any local control). Second, a data‐driven physics‐guided framework is formulated that reduces the dimensionality of the inverse design problem using autoencoders and efficiently searches through the “latent” parameter space in an active learning approach. The rapid design procedure is demonstrated via a range of target shapes, such as peanuts, pringles, flowers, and pyramids. Experiments and our numerical predictions are found to be in good agreement.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4048849
