Now showing 1 - 3 of 3
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    Publication
    Lattice modes of periodic origami tessellations with voids
    (01-10-2023)
    Lahiri, Anandaroop
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    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.
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    Publication
    Folding-Angle Framework for Structural Modeling of Rigid Triangulated Miura-ori Lattices
    (01-10-2023)
    Lahiri, Anandaroop
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    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.
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    Publication
    Inhomogeneous folding modes in infinite lattices of rigid triangulated miura-ori
    (01-01-2021)
    Lahiri, Anandaroop
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    Infinite two-dimensional tessellations of triangulated Miura-ori with rigid panels are known to exhibit only homogeneous modes of folding, thereby limiting their usefulness in engineering applications. In this work, we show that the corresponding one-dimensional lattices are less restricted and can exhibit inhomogeneous folding modes of deformation. We demonstrate this by looking at the modes in the null space of Bloch-reduced compatibility matrix in a nodal-displacement-based formulation, that is typically employed in the context of origami structural analysis. We compute the deformation modes that vary non-uniformly across the lattice depending on their wavelength, and identify the minimal number of modes that can represent such deformations. We then present a more efficient formulation based on folding-angles to study the deformation modes of infinite one-dimensional rigid triangulated origami lattices. We derive the degrees of freedom of the tessellations in terms of the minimal number of folding-angles that are required to capture the periodic inhomogeneous deformations of the infinite lattices. Within this formulation, we provide the framework to analytically derive the stiffness matrix of the lattice. Finally, we verify the new formulation by comparing the results with the bar-and-hinge model that is based on nodal-displacements. The observations from our work could have implications for the use of rigid panel origami lattices as acoustic metamaterials.