Phanisri Pradeep Pratapa

Geometrical-frustration-induced anisotropy and inhomogeneity are explored to achieve unique properties of metamaterials that set them apart from conventional materials. According to Neumann's principle, to achieve anisotropic responses, the material unit cell should possess less symmetry. Based on such guidelines, a triclinic metamaterial system of minimal symmetry is presented, which originates from a Trimorph origami pattern with a simple and insightful geometry: a basic unit cell with four tilted panels and four corresponding creases. The intrinsic geometry of the Trimorph origami, with its changing tilting angles, dictates a folding motion that varies the primitive vectors of the unit cell, couples the shear and normal strains of its extrinsic bulk, and leads to an unusual Poisson effect. Such an effect, associated with reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant mathematical formulae. The nonlinearities of the folding motions allow the unit cell to display three robust stable states, connected through snapping instabilities. When the tristable unit cells are tessellated, phenomena that resemble linear and point defects emerge as a result of geometric frustration. The frustration is reprogrammable into distinct stable and inhomogeneous states by arbitrarily selecting the location of a single or multiple point defects. The Trimorph origami demonstrates the possibility of creating origami metamaterials with symmetries that are hitherto nonexistent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant microrobots.

Origami-based deployable structures are of great interest as they can be manufactured and folded from thin flat sheets of material. However, the thin nature of origami panels results in a weak structural form at configurations close to unfolded or developed geometries. It, therefore, limits the functionality of such structures in applications involving load-bearing and full-unfolding. In this work, we show that by using the thick panel versions of the origami structures, one could obtain better load-bearing characteristics, especially at configurations close to the fully-unfolded geometries obtained through deployment. Specifically, we compare and contrast the geometry and structural behavior of a Yoshimura origami structure made from thin and thick panels. We present and implement a geometric framework to calculate the nodal coordinates of tessellated thick Yoshimura structures with arbitrarily specified panel dimensions and folded states. We discuss the structural modeling of a three-cell Yoshimura at a meter length scale and perform structural analysis at various folded configurations. We demonstrate the suitability of the thick panel structure over the thin panel version for resisting applied loads at configurations close to the fully-deployed state. The results indicate that employing thick panel geometries could enable the use of origami-based deployable structures at large length scales, especially for applications involving load-bearing.

The generation of wind fields is of interest in the study of the structural performance of wind turbines in critical events, such as thunderstorm downbursts. Various methods ranging from the use of empirical data to employing computational simulations are typically adopted to study the response of wind turbines in downburst flow fields. While the former approach is limited in the ability to account for accurate and spatially resolved details of the flow field, the latter is expensive and, therefore, has limitations in its use. As an alternative, in this work, we propose a paused downburst model in which a snapshot of a time-dependent computational fluid dynamics (CFD) simulation is used to generate “mean” wind fields during thunderstorm downbursts. The developed model for the mean wind field is validated against recorded downburst data in the literature. The turbulent component of the wind field is generated using computationally inexpensive techniques based on Fourier-based power spectral density functions and coherence functions. In an illustrative example, the combined mean and turbulence wind fields are generated and applied on a utility-scale wind turbine to study structural load characteristics during a downburst event.

Tensegrity structures resemble biological tissues: A structural system that holds an internal balance of prestress. Owing to the presence of prestress, biological tissues can dramatically change their properties, making tensegrity a promising platform for tunable and functional metamaterials. However, tensegrity metamaterials require harmony between form and force in an infinitely–periodic scale, which makes the design of such systems challenging. In order to explore the full potential of tensegrity metamaterials, a systematic design approach is required. In this work, we propose an automated design framework that provides access to unlimited tensegrity metamaterial designs. The framework generates tensegrity metamaterials by tessellating blocks with designated geometries that are aware of the system periodicity. In particular, our formulation allows creation of Class-1 (i.e., floating struts) tensegrity metamaterials. We show that tensegrity metamaterials offer tunable effective elastic moduli, Poisson's ratio, and phononic bandgaps by properly changing their prestress levels, which provide a new dimension of programmability beyond geometry.

Elastic modes of origami lattices are of scientific value in the context of metamaterial applications. Miura-ori is a well-studied origami pattern, especially in engineering. A deeper understanding of spatially homogeneous deformations can be useful to homogenization-based material characterization. Miura-ori with rigid parallelogram panels deforms exclusively through crease-folding as a single degree of freedom (DOF) system. Substituting parallelograms with rigid triangular panels introduces two additional DOFs per vertex and could admit a rich space of lattice deformations. In this paper, we investigate the lattice modes of rigid triangulated Miura-ori (RTM) with enclosed voided regions within the tessellations. We use two widely adopted approaches — the bar and hinge framework (BHF) and a folding-angle framework (FAF), that are typically used for the analysis of origami lattices. Unlike the 2D RTM lattice without voids, we find that for the origami lattices with voids, the compatibility constraints based on the crease folding-angles alone are insufficient to capture the admissible deformation modes. Additional loop-closure constraints, based on Denavit–Hartenberg analysis of spatial linkages, must be imposed on creases around each enclosed void. We observe that the homogeneous modes with accumulation of deformations across the lattice are exclusive to the space of Bloch-wave modes within the FAF approach and are not straightforwardly obtained using BHF approach of modeling origami lattices. The 2D RTM lattices with voids, irrespective of the size and aspect ratio of enclosed voids, are found to exhibit exactly six such exclusive FAF modes which can be further characterized using intuitively defined relations between crease angle perturbations.

We analyze the folding kinematics of a recently proposed origami-based tessellated structure called the Morph pattern, using thin, rigid panel assumptions. We discuss the geometry of the Morph unit cell that can exist in two characteristic modes differing in the mountain/valley assignment of a degree-four vertex and explain how a single tessellation of the Morph structure can undergo morphing through rigid origami kinematics resulting in multiple hybrid states. We describe the kinematics of the tessellated Morph pattern through multiple branches, each path leading to different sets of hybrid states. We study the kinematics of the tessellated structure through local and global Poisson's ratios and derive an analytical condition for which the global ratio switches between negative and positive values. We show that the interplay between the local and global kinematics results in folding deformations in which the hybrid states are either locked in their current modes or are transformable to other modes of the kinematic branches, leading to a reprogrammable morphing behavior of the system. Finally, using a bar-and-hinge model-based numerical framework, we simulate the nonlinear folding behavior of the hybrid systems and verify the deformation characteristics that are predicted analytically.

Periodic structures are found to exhibit band gaps which are frequency bandwidths where structural vibrations are absorbed. In this paper, meta-structures are built by dynamically linking oscillators in a periodic pattern, which are referred to as dynamically linked element grade oscillators or D-LEGOs. The location of the band gaps is numerically determined for a one-dimensional D-LEGO. The unit cell for the D-LEGO structure is considered to be made up of two longitudinal bar elements of different properties. For such a structure, the frequency response functions (FRFs) of a single unit cell are used to estimate the band gaps of a periodic-lattice structure by adapting the Bloch wave theory. Alternatively, the FRF of the multi-unit cell is determined using FRF-based substructuring (FBS) approach. The band gaps resulting from these two approaches are compared and verified.

Origami-based structures have gained interest in recent years due to their potential to develop lattice materials, called metamaterials, the mechanics of which are primarily driven by the unit cell geometry. The folding deformations of typical origami metamaterials result in stretch-dependent Poisson's ratios, and therefore in Poisson functions with significant variability across finite deformation. This limits their applicability, because the desired response is retained only for a narrow strain range. To overcome this limitation, a class of composite origami metamaterials with a nearly a constant Poisson function, specifically in the range -0.5 to 1.2 over a finite stretch of up to 3.0 with a minimum of 1.1, is presented. Drawing from the recently proposed Morph pattern, the composite system is built as a compatible combination of two sets of cells with contrasting Poisson effects. The number and dimensions of the cells were optimized for a stretch-independent Poisson function. The effects of various strain measures in defining the Poisson function were discussed. The results of the study were validated using a bar-and-hinge-based numerical framework capable of simulating the finite deformation behavior of the proposed designs.

Origami is rapidly gaining prominence in the research of metamaterials as it allows for tuning the properties of interest by change in the folded state. Origami-based lattices that allow low-frequency wave-propagation can potentially find use as acoustic metamaterials. Rigid-panel origami tessellations have lattice modes which are exclusively due to the low-energy folding deformations at creases and hence will be suitable for low-frequency wave-propagation applications. Modeling frameworks like bar-and-hinge that are typically used to study origami lattice mechanics allow for panel stretching behavior which is forbidden and redundant in rigid-panel origami lattices. This drives the necessity for an efficient analysis framework dealing exclusively with folding-angles for the study of origami lattices with rigid panels. As a first step in this direction, in this paper, we propose a folding-angle-based analytical framework for structural modeling of infinite lattices of triangulated Miura-ori (an origami pattern studied widely for its metamaterial applications) with rigid panels. We assign rotational stiffness to the creases and analytically derive the stiffness matrix for the lattices based on a minimal number of folding-angle degrees of freedom. Finally, we study the influence of the equilibrium state of folding and the relative crease stiffness on the modal energies, to demonstrate the tunable and programmable nature of the structure. The framework proposed in our work could enable the study of wave dynamics in rigid-panel Miura-ori-based lattices and our findings show significant promise for the future use of 1D origami with rigid panels as acoustic metamaterials.

Origami metamaterials are known to display highly tunable Poisson's ratio depending on their folded state. Most studies on the Poisson effects in deployable origami tessellations are restricted to theory and simulation. Experimental realization of the desired Poisson effects in origami metamaterials requires special attention to the boundary conditions to enable nonlinear deformations that give rise to tunability. In this work, we present a novel experimental setup suitable to study the Poisson effects in 2D origami tessellations that undergo simultaneous deformations in both the applied and transverse directions. The setup comprises a gripping mechanism, which we call a Saint-Venant fixture, to eliminate Saint-Venant end effects during uniaxial testing. Using this setup, we conduct Poisson's ratio measurements of the Morph origami pattern whose configuration space combines features of the Miura-ori and Eggbox parent patterns. We experimentally observe the Poisson's ratio sign switching capability of the Morph pattern, along with its ability to display either completely positive or negative values of Poisson's ratio by virtue of topological transformations. To demonstrate the versatility of the novel setup we also perform experiments on the standard Miura-ori and the standard Eggbox patterns. Our results demonstrate the agreement between the theory, the simulations, and the experiments on the Poisson's ratio measurement and its tunability in origami metamaterials. The proposed experimental technique can be adopted for investigating other tunable properties of origami metamaterials in static and in dynamic regimes, such as elastic thermal expansion, and wave propagation control.