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Jiao W, Shu H, Tournat V, Yasuda H, Raney JR. Phase transitions in 2D multistable mechanical metamaterials via collisions of soliton-like pulses. Nat Commun 2024; 15:333. [PMID: 38184613 PMCID: PMC10771479 DOI: 10.1038/s41467-023-44293-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Accepted: 12/07/2023] [Indexed: 01/08/2024] Open
Abstract
In recent years, mechanical metamaterials have been developed that support the propagation of an intriguing variety of nonlinear waves, including transition waves and vector solitons (solitons with coupling between multiple degrees of freedom). Here we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we numerically show, using an experimentally validated model, that the critical nucleus can be formed via collisions of soliton-like pulses. Moreover, the rich direction-dependent behavior of the nonlinear pulses enables control of the location of nucleation and the spatio-temporal shape of the growing phase.
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Affiliation(s)
- Weijian Jiao
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
| | - Hang Shu
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA
| | - Vincent Tournat
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université, Le Mans, France
| | - Hiromi Yasuda
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA
- Aviation Technology Directorate, Japan Aerospace Exploration Agency, Mitaka, Tokyo, Japan
- Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Kanagawa, Japan
| | - Jordan R Raney
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA.
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He Q, Yin R, Hua Y, Jiao W, Mo C, Shu H, Raney JR. A modular strategy for distributed, embodied control of electronics-free soft robots. SCIENCE ADVANCES 2023; 9:eade9247. [PMID: 37418520 DOI: 10.1126/sciadv.ade9247] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 06/02/2023] [Indexed: 07/09/2023]
Abstract
Robots typically interact with their environments via feedback loops consisting of electronic sensors, microcontrollers, and actuators, which can be bulky and complex. Researchers have sought new strategies for achieving autonomous sensing and control in next-generation soft robots. We describe here an electronics-free approach for autonomous control of soft robots, whose compositional and structural features embody the sensing, control, and actuation feedback loop of their soft bodies. Specifically, we design multiple modular control units that are regulated by responsive materials such as liquid crystal elastomers. These modules enable the robot to sense and respond to different external stimuli (light, heat, and solvents), causing autonomous changes to the robot's trajectory. By combining multiple types of control modules, complex responses can be achieved, such as logical evaluations that require multiple events to occur in the environment before an action is performed. This framework for embodied control offers a new strategy toward autonomous soft robots that operate in uncertain or dynamic environments.
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Affiliation(s)
- Qiguang He
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Rui Yin
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Yucong Hua
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Weijian Jiao
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Chengyang Mo
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Hang Shu
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Jordan R Raney
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
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Deng B, Zareei A, Ding X, Weaver JC, Rycroft CH, Bertoldi K. Inverse Design of Mechanical Metamaterials with Target Nonlinear Response via a Neural Accelerated Evolution Strategy. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2206238. [PMID: 36103610 DOI: 10.1002/adma.202206238] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2022] [Indexed: 06/15/2023]
Abstract
Materials with target nonlinear mechanical response can support the design of innovative soft robots, wearable devices, footwear, and energy-absorbing systems, yet it is challenging to realize them. Here, mechanical metamaterials based on hinged quadrilaterals are used as a platform to realize target nonlinear mechanical responses. It is first shown that by changing the shape of the quadrilaterals, the amount of internal rotations induced by the applied compression can be tuned, and a wide range of mechanical responses is achieved. Next, a neural network is introduced that provides a computationally inexpensive relationship between the parameters describing the geometry and the corresponding stress-strain response. Finally, it is shown that by combining the neural network with an evolution strategy, one can efficiently identify geometries resulting in a wide range of target nonlinear mechanical responses and design optimized energy-absorbing systems, soft robots, and morphing structures.
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Affiliation(s)
- Bolei Deng
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Ahmad Zareei
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Xiaoxiao Ding
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - James C Weaver
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Chris H Rycroft
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Computational Research Division, Lawrence Berkeley Laboratory, Berkeley, CA, 94720, USA
| | - Katia Bertoldi
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
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Miyazawa Y, Chong C, Kevrekidis PG, Yang J. Rogue and solitary waves in coupled phononic crystals. Phys Rev E 2022; 105:034202. [PMID: 35428101 DOI: 10.1103/physreve.105.034202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 02/04/2022] [Indexed: 06/14/2023]
Abstract
In this work we present an analytical and numerical study of rogue and solitary waves in a coupled one-dimensional nonlinear lattice that involves both axial and rotational degrees of freedom. Using a multiple-scale analysis, we derive a system of coupled nonlinear Schrödinger-type equations in order to approximate solitary waves and rogue waves of the coupled lattice model. Numerical simulations are found to agree with the analytical approximations. We also consider generic initialization data in the form of a Gaussian profile and observe that they can result in the spontaneous formation of rogue-wave-like patterns in the lattice. The solitary and rogue waves in the lattice demonstrate both energy isolation and exchange between the axial and rotational degrees of freedom of the system. This suggests that the studied coupled lattice has the potential to be an efficient energy isolation, transfer, and focusing medium.
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Affiliation(s)
- Y Miyazawa
- Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195, USA
| | - C Chong
- Department of Mathematics, Bowdoin College, Brunswick, Maine 04011, USA
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003-4515, USA
| | - J Yang
- Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195, USA
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Abstract
Material phase transitions offer promise for driving motion and managing high-rate energy transfer events; however, engineering conventional phase transitions at a molecular or atomic level is challenging. We overcome this challenge by coupling multiple interacting fields within a metamaterial framework. Specifically, we embed magnetic domains, with nonlinear, orientationally dependent force interactions, within elastic structures to control reversible phase transitions and program high–strain-rate deformation. The resulting high-rate energy transformations are used to enhance elastic recoil, which could be used to drive high-power motion and to quickly dampen impact loading events. The developed Landau free energy–based model for this material system broadens the impact of this advance, setting the stage for metamaterials with wide-ranging compositions, interacting fields, and engineered properties. Solid–solid phase transformations can affect energy transduction and change material properties (e.g., superelasticity in shape memory alloys and soft elasticity in liquid crystal elastomers). Traditionally, phase-transforming materials are based on atomic- or molecular-level thermodynamic and kinetic mechanisms. Here, we develop elasto-magnetic metamaterials that display phase transformation behaviors due to nonlinear interactions between internal elastic structures and embedded, macroscale magnetic domains. These phase transitions, similar to those in shape memory alloys and liquid crystal elastomers, have beneficial changes in strain state and mechanical properties that can drive actuations and manage overall energy transduction. The constitutive response of the elasto-magnetic metamaterial changes as the phase transitions occur, resulting in a nonmonotonic stress–strain relation that can be harnessed to enhance or mitigate energy storage and release under high–strain-rate events, such as impulsive recoil and impact. Using a Landau free energy–based predictive model, we develop a quantitative phase map that relates the geometry and magnetic interactions to the phase transformation. Our work demonstrates how controllable phase transitions in metamaterials offer performance capabilities in energy management and programmable material properties for high-rate applications.
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Li J, Chockalingam S, Cohen T. Observation of Ultraslow Shock Waves in a Tunable Magnetic Lattice. PHYSICAL REVIEW LETTERS 2021; 127:014302. [PMID: 34270308 DOI: 10.1103/physrevlett.127.014302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 05/20/2021] [Indexed: 06/13/2023]
Abstract
The combination of fast propagation speeds and highly localized nature has hindered the direct observation of the evolution of shock waves at the molecular scale. To address this limitation, an experimental system is designed by tuning a one-dimensional magnetic lattice to evolve benign waveforms into shock waves at observable spatial and temporal scales, thus serving as a "magnifying glass" to illuminate shock processes. An accompanying analysis confirms that the formation of strong shocks is fully captured. The exhibited lack of a steady state induced by indefinite expansion of a disordered transition zone points to the absence of local thermodynamic equilibrium and resurfaces lingering questions on the validity of continuum assumptions in the presence of strong shocks.
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Affiliation(s)
- Jian Li
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - S Chockalingam
- Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Tal Cohen
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Characterization, stability, and application of domain walls in flexible mechanical metamaterials. Proc Natl Acad Sci U S A 2020; 117:31002-31009. [PMID: 33219120 DOI: 10.1073/pnas.2015847117] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Domain walls, commonly occurring at the interface of different phases in solid-state materials, have recently been harnessed at the structural scale to enable additional modes of functionality. Here, we combine experimental, numerical, and theoretical tools to investigate the domain walls emerging upon uniaxial compression in a mechanical metamaterial based on the rotating-squares mechanism. We first show that these interfaces can be generated and controlled by carefully arranging a few phase-inducing defects. We establish an analytical model to capture the evolution of the domain walls as a function of the applied deformation. We then employ this model as a guideline to realize interfaces of complex shape. Finally, we show that the engineered domain walls modify the global response of the metamaterial and can be effectively exploited to tune its stiffness as well as to guide the propagation of elastic waves.
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Liang X, Crosby AJ. Programming Impulsive Deformation with Mechanical Metamaterials. PHYSICAL REVIEW LETTERS 2020; 125:108002. [PMID: 32955335 DOI: 10.1103/physrevlett.125.108002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2020] [Accepted: 08/17/2020] [Indexed: 06/11/2023]
Abstract
Impulsive deformation is widely observed in biological systems to generate movement with high acceleration and velocity. By storing elastic energy in a quasistatic loading and releasing it through an impulsive elastic recoil, organisms circumvent the intrinsic trade-off between force and velocity and achieve power amplified motion. However, such asymmetry in strain rate in loading and unloading often results in reduced efficiency in converting elastic energy to kinetic energy for homogeneous materials. Here, we demonstrate that specific internal structural designs can offer the ability to tune quasistatic and high-speed recoil independently to control energy storage and conversion processes. Experimental demonstrations with mechanical metamaterials reveal that certain internal structures optimize energy conversion far beyond unstructured materials under the same conditions. Our results provide the first quantitative model and experimental demonstration for tuning energy conversion processes through internal structures of metamaterials.
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Affiliation(s)
- Xudong Liang
- Polymer Science and Engineering Department, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
| | - Alfred J Crosby
- Polymer Science and Engineering Department, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
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Deng B, Chen L, Wei D, Tournat V, Bertoldi K. Pulse-driven robot: Motion via solitary waves. SCIENCE ADVANCES 2020; 6:eaaz1166. [PMID: 32494671 PMCID: PMC7195187 DOI: 10.1126/sciadv.aaz1166] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 01/17/2020] [Indexed: 06/11/2023]
Abstract
The unique properties of nonlinear waves have been recently exploited to enable a wide range of applications, including impact mitigation, asymmetric transmission, switching, and focusing. Here, we demonstrate that the propagation of nonlinear waves can be as well harnessed to make flexible structures crawl. By combining experimental and theoretical methods, we show that such pulse-driven locomotion reaches a maximum efficiency when the initiated pulses are solitons and that our simple machine can move on a wide range of surfaces and even steer. Our study expands the range of possible applications of nonlinear waves and demonstrates that they offer a new platform to make flexible machines to move.
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Affiliation(s)
- Bolei Deng
- Harvard John A. Paulson School of Engineering and Applied Sciences Harvard University, Cambridge, MA 02138, USA
| | - Liyuan Chen
- Harvard John A. Paulson School of Engineering and Applied Sciences Harvard University, Cambridge, MA 02138, USA
| | - Donglai Wei
- LAUM, CNRS, Le Mans Université, Av. O. Messiaen, 72085 Le Mans, France
| | - Vincent Tournat
- Kavli Institute, Harvard University, Cambridge, MA 02138, USA
| | - Katia Bertoldi
- Harvard John A. Paulson School of Engineering and Applied Sciences Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Cambridge, MA 02138, USA
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Vangelatos Z, Micheletti A, Grigoropoulos CP, Fraternali F. Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography. NANOMATERIALS 2020; 10:nano10040652. [PMID: 32244533 PMCID: PMC7221601 DOI: 10.3390/nano10040652] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/16/2020] [Revised: 03/29/2020] [Accepted: 03/30/2020] [Indexed: 01/01/2023]
Abstract
A bistable response is an innate feature of tensegrity metamaterials, which is a conundrum to attain in other metamaterials, since it ushers unconventional static and dynamical mechanical behaviors. This paper investigates the design, modeling, fabrication and testing of bistable lattices with tensegrity architecture and nanoscale features. First, a method to design bistable lattices tessellating tensegrity units is formulated. The additive manufacturing of these structures is performed through multiphoton lithography, which enables the fabrication of microscale structures with nanoscale features and extremely high resolution. Different modular lattices, comprised of struts with 250 nm minimum radius, are tested under loading-unloading uniaxial compression nanoindentation tests. The compression tests confirmed the activation of the designed bistable twisting mechanism in the examined lattices, combined with a moderate viscoelastic response. The force-displacement plots of the 3D assemblies of bistable tensegrity prisms reveal a softening behavior during the loading from the primary stable configuration and a subsequent snapping event that drives the structure into a secondary stable configuration. The twisting mechanism that characterizes such a transition is preserved after unloading and during repeated loading-unloading cycles. The results of the present study elucidate that fabrication of multistable tensegrity lattices is highly feasible via multiphoton lithography and promulgates the fabrication of multi-cell tensegrity metamaterials with unprecedented static and dynamic responses.
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Affiliation(s)
- Zacharias Vangelatos
- Department of Mechanical Engineering, University of California, Berkeley, CA 94709, USA;
| | - Andrea Micheletti
- Department of Civil and Computer Science Engineering, University of Rome Tor Vergata, 00133 Rome RM, Italy;
| | - Costas P. Grigoropoulos
- Department of Mechanical Engineering, University of California, Berkeley, CA 94709, USA;
- Correspondence: ; Tel.: +1-510-642-2525
| | - Fernando Fraternali
- Department of Civil Engineering, University of Salerno, 84084 Fisciano SA, Italy;
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