Self-folding origami, structures that are engineered flat to fold into targeted, three-dimensional shapes, have many potential engineering applications. Though significant effort in recent years has been devoted to designing fold patterns that can achieve a variety of target shapes, recent work has also made clear that many origami structures exhibit multiple folding pathways, with a proliferation of geometric folding pathways as the origami structure becomes complex. The competition between these pathways can lead to structures that are programmed for one shape, yet fold incorrectly. To disentangle the features that lead to misfolding, we introduce a model of self-folding origami that accounts for the finite stretching rigidity of the origami faces and allows the computation of energy landscapes that lead to misfolding. We find that, in addition to the geometrical features of the origami, the finite elasticity of the nearly-flat origami configurations regulates the proliferation of potential misfolded states through a series of saddle-node bifurcations. We apply our model to one of the most common origami motifs, the symmetric “bird's foot,” a single vertex with four folds. We show that though even a small error in programmed fold angles induces metastability in rigid origami, elasticity allows one to tune resilience to misfolding. In a more complex design, the “Randlett flapping bird,” which has thousands of potential competing states, we further show that the number of actual observed minima is strongly determined by the structure's elasticity. In general, we show that elastic origami with both stiffer folds and less bendable faces self-folds better.
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Variational Level Set Method for Topology Optimization of Origami Fold Patterns
Abstract With specific fold patterns, a 2D flat origami can be converted into a complex 3D structure under an external driving force. Origami inspires the engineering design of many self-assembled and re-configurable devices. This work aims to apply the level set-based topology optimization to the generative design of origami structures. The origami mechanism is simulated using thin shell models where the deformation on the surface and the deformation in the normal direction can be simplified and well captured. Moreover, the fold pattern is implicitly represented by the boundaries of the level set function. The folding topology is optimized by minimizing a new multiobjective function that balances kinematic performance with structural stiffness and geometric requirements. Besides regular straight folds, our proposed model can mimic crease patterns with curved folds. With the folding curves implicitly represented, the curvature flow is utilized to control the complexity of the folds generated. The performance of the proposed method is demonstrated by the computer generation and physical validation of two thin shell origami designs.
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- Award ID(s):
- 1762287
- NSF-PAR ID:
- 10351911
- Date Published:
- Journal Name:
- Journal of Mechanical Design
- Volume:
- 144
- Issue:
- 8
- ISSN:
- 1050-0472
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This data set for the manuscript entitled "Design of Peptides that Fold and Self-Assemble on Graphite" includes all files needed to run and analyze the simulations described in the this manuscript in the molecular dynamics software NAMD, as well as the output of the simulations. The files are organized into directories corresponding to the figures of the main text and supporting information. They include molecular model structure files (NAMD psf or Amber prmtop format), force field parameter files (in CHARMM format), initial atomic coordinates (pdb format), NAMD configuration files, Colvars configuration files, NAMD log files, and NAMD output including restart files (in binary NAMD format) and trajectories in dcd format (downsampled to 10 ns per frame). Analysis is controlled by shell scripts (Bash-compatible) that call VMD Tcl scripts or python scripts. These scripts and their output are also included.
Version: 2.0
Changes versus version 1.0 are the addition of the free energy of folding, adsorption, and pairing calculations (Sim_Figure-7) and shifting of the figure numbers to accommodate this addition.
Conventions Used in These Files
===============================Structure Files
----------------
- graph_*.psf or sol_*.psf (original NAMD (XPLOR?) format psf file including atom details (type, charge, mass), as well as definitions of bonds, angles, dihedrals, and impropers for each dipeptide.)- graph_*.pdb or sol_*.pdb (initial coordinates before equilibration)
- repart_*.psf (same as the above psf files, but the masses of non-water hydrogen atoms have been repartitioned by VMD script repartitionMass.tcl)
- freeTop_*.pdb (same as the above pdb files, but the carbons of the lower graphene layer have been placed at a single z value and marked for restraints in NAMD)
- amber_*.prmtop (combined topology and parameter files for Amber force field simulations)
- repart_amber_*.prmtop (same as the above prmtop files, but the masses of non-water hydrogen atoms have been repartitioned by ParmEd)Force Field Parameters
----------------------
CHARMM format parameter files:
- par_all36m_prot.prm (CHARMM36m FF for proteins)
- par_all36_cgenff_no_nbfix.prm (CGenFF v4.4 for graphene) The NBFIX parameters are commented out since they are only needed for aromatic halogens and we use only the CG2R61 type for graphene.
- toppar_water_ions_prot_cgenff.str (CHARMM water and ions with NBFIX parameters needed for protein and CGenFF included and others commented out)Template NAMD Configuration Files
---------------------------------
These contain the most commonly used simulation parameters. They are called by the other NAMD configuration files (which are in the namd/ subdirectory):
- template_min.namd (minimization)
- template_eq.namd (NPT equilibration with lower graphene fixed)
- template_abf.namd (for adaptive biasing force)Minimization
-------------
- namd/min_*.0.namdEquilibration
-------------
- namd/eq_*.0.namdAdaptive biasing force calculations
-----------------------------------
- namd/eabfZRest7_graph_chp1404.0.namd
- namd/eabfZRest7_graph_chp1404.1.namd (continuation of eabfZRest7_graph_chp1404.0.namd)Log Files
---------
For each NAMD configuration file given in the last two sections, there is a log file with the same prefix, which gives the text output of NAMD. For instance, the output of namd/eabfZRest7_graph_chp1404.0.namd is eabfZRest7_graph_chp1404.0.log.Simulation Output
-----------------
The simulation output files (which match the names of the NAMD configuration files) are in the output/ directory. Files with the extensions .coor, .vel, and .xsc are coordinates in NAMD binary format, velocities in NAMD binary format, and extended system information (including cell size) in text format. Files with the extension .dcd give the trajectory of the atomic coorinates over time (and also include system cell information). Due to storage limitations, large DCD files have been omitted or replaced with new DCD files having the prefix stride50_ including only every 50 frames. The time between frames in these files is 50 * 50000 steps/frame * 4 fs/step = 10 ns. The system cell trajectory is also included for the NPT runs are output/eq_*.xst.Scripts
-------
Files with the .sh extension can be found throughout. These usually provide the highest level control for submission of simulations and analysis. Look to these as a guide to what is happening. If there are scripts with step1_*.sh and step2_*.sh, they are intended to be run in order, with step1_*.sh first.
CONTENTS
========The directory contents are as follows. The directories Sim_Figure-1 and Sim_Figure-8 include README.txt files that describe the files and naming conventions used throughout this data set.
Sim_Figure-1: Simulations of N-acetylated C-amidated amino acids (Ac-X-NHMe) at the graphite–water interface.
Sim_Figure-2: Simulations of different peptide designs (including acyclic, disulfide cyclized, and N-to-C cyclized) at the graphite–water interface.
Sim_Figure-3: MM-GBSA calculations of different peptide sequences for a folded conformation and 5 misfolded/unfolded conformations.
Sim_Figure-4: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.
Sim_Figure-5: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 295 K.
Sim_Figure-5_replica: Temperature replica exchange molecular dynamics simulations for the peptide cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) with 20 replicas for temperatures from 295 to 454 K.
Sim_Figure-6: Simulation of the peptide molecule cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) in free solution (no graphite).
Sim_Figure-7: Free energy calculations for folding, adsorption, and pairing for the peptide CHP1404 (sequence: cyc(GTGSGTG-GPGG-GCGTGTG-SGPG)). For folding, we calculate the PMF as function of RMSD by replica-exchange umbrella sampling (in the subdirectory Folding_CHP1404_Graphene/). We make the same calculation in solution, which required 3 seperate replica-exchange umbrella sampling calculations (in the subdirectory Folding_CHP1404_Solution/). Both PMF of RMSD calculations for the scrambled peptide are in Folding_scram1404/. For adsorption, calculation of the PMF for the orientational restraints and the calculation of the PMF along z (the distance between the graphene sheet and the center of mass of the peptide) are in Adsorption_CHP1404/ and Adsorption_scram1404/. The actual calculation of the free energy is done by a shell script ("doRestraintEnergyError.sh") in the 1_free_energy/ subsubdirectory. Processing of the PMFs must be done first in the 0_pmf/ subsubdirectory. Finally, files for free energy calculations of pair formation for CHP1404 are found in the Pair/ subdirectory.
Sim_Figure-8: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) where the peptides are far above the graphene–water interface in the initial configuration.
Sim_Figure-9: Two replicates of a simulation of nine peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.
Sim_Figure-9_scrambled: Two replicates of a simulation of nine peptide molecules with the control sequence cyc(GGTPTTGGGGGGSGGPSGTGGC) at the graphite–water interface at 370 K.
Sim_Figure-10: Adaptive biasing for calculation of the free energy of the folded peptide as a function of the angle between its long axis and the zigzag directions of the underlying graphene sheet.
This material is based upon work supported by the US National Science Foundation under grant no. DMR-1945589. A majority of the computing for this project was performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF grants CHE-1726332, CNS-1006860, EPS-1006860, and EPS-0919443. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562, through allocation BIO200030. -
null (Ed.)Abstract Origami-based fabrication strategies open the door for developing new manufacturing processes capable of producing complex three-dimensional (3D) geometries from two-dimensional (2D) sheets. Nevertheless, for these methods to translate into scalable manufacturing processes, rapid techniques for creating controlled folds are needed. In this work, we propose a new approach for controlled self-folding of shape memory polymer sheets based on direct laser rastering. We demonstrate that rapidly moving a CO2 laser over pre-strained polystyrene sheets results in creating controlled folds along the laser path. Laser interaction with the polymer induces localized heating above the glass transition temperature with a temperature gradient across the thickness of the thin sheets. This gradient of temperature results in a gradient of shrinkage owing to the viscoelastic relaxation of the polymer, favoring folding toward the hotter side (toward the laser source). We study the influence of laser power, rastering speed, fluence, and the number of passes on the fold angle. Moreover, we investigate process parameters that produce the highest quality folds with minimal undesired deformations. Our results show that we can create clean folds up to and exceeding 90 deg, which highlights the potential of our approach for creating lightweight 3D geometries with smooth surface finishes that are challenging to create using 3D printing methods. Hence, laser-induced self-folding of polymers is an inherently mass-customizable approach to manufacturing, especially when combined with cutting for integration of origami and kirigami.more » « less
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Origami folding and thin structure buckling are intensively studied for structural transformations with large packing ratio for various biomedical, robotic, and aerospace applications. The folding of circular rings has shown bistable snap‐through deformation under simple twisting motion and demonstrates a large area change to 11% of its undeformed configuration. Motivated by the large area change and the self‐guided deformation through snap‐folding, it is intended to design ring origami assemblies with unprecedented packing ratios. Herein, through finite‐element analysis, snap‐folding behaviors of single ring with different geometries (circular, elliptical, rounded rectangular, and rounded triangular shapes) are studied for ring origami assemblies for functional foldable structures. Geometric parameters' effects on the foldability, stability, and the packing ratio are investigated and are validated experimentally. With different rings as basic building blocks, the folding of ring origami assemblies including linear‐patterned rounded rectangular rings, radial‐patterned elliptical rings, and 3D crossing circular rings is further experimentally demonstrated, which show significant packing ratios of 7% and 2.5% of the initial areas, and 0.3% of the initial volume, respectively. It is envisioned that the reported snap‐folding of origami rings will provide alternative strategies to design foldable/deployable structures and devices with reliable self‐guided deformation and large area change.
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Abstract The southern Patagonian Andes record Late Cretaceous–Paleogene compressional inversion of the Rocas Verdes backarc basin (RVB) and development of the Patagonian fold-thrust belt (FTB). A ductile décollement formed in the middle crust and accommodated underthrusting, thickening, and tectonic burial of the continental margin (Cordillera Darwin Metamorphic Complex (CDMC)) beneath the RVB. We present new geologic mapping, quartz microstructure, and crystallographic preferred orientation (CPO) fabric analyses to document the kinematic evolution and deformation conditions of the décollement. Within the CDMC, the décollement is defined by a quartz/chlorite composite schistose foliation (S1-2) that is progressively refolded by two generations of noncylindrical, tight, and isoclinal folds (F3–F4). Strain intensifies near the top of the CDMC, forming a >5 km thick shear zone that is defined by a penetrative L-S tectonite (S2/L2) and progressive noncylindrical folding (F3). Younger kink folds and steeply inclined tight folds (F4) with both north- and south-dipping axial planes (S4) overprint D2 and D3 structures. Quartz textures from D2 fabrics show subgrain rotation and grain boundary migration recrystallization equivalent to regime 3, and quartz CPO patterns indicate mixed prism <a> and [c] slip systems with c-axis opening angles indicative of deformation temperatures between ~500° and >650°C. Approximately 40 km toward the foreland, the shear zone thins (~1 km thick) and is defined by the L-S tectonite (S2/L2) and tightening of recumbent isoclinal folds (F3). Quartz textures and CPO patterns indicate subgrain rotation recrystallization typical of regime 2 and dominantly basal <a> slip, and c-axis opening angles are consistent with deformation temperatures between ~375° and 575°C. Deformation occurred under greenschist and amphibolite facies conditions in the foreland and hinterland, respectively, indicating that the shear zone dipped shallowly toward the hinterland. The Magallanes décollement is an example of a regional ductile shear zone that accommodated distributed middle to lower crustal thickening below a retroarc FTB.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4053925
