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Mechanics of Materials and Structures at Harvard


Harvard University
Design of active structures through buckling
Katia Bertoldi

December 2015


Most of the devices have a unique function and thus have a unique form, but there is a need for reconfigurable devices. Examples include active materials for on-demand drug delivery, photonic crystals with tunable lensing effects and soft robots that can rapidly change their shape and functionality. Can we design a new class of devices whose response can be tuned by an external stimulus with exciting applications in drug delivery, robotics, civil and bio engineering? Mechanical instabilities have been traditionally viewed as an inconvenience, with research focusing on how to avoid them. For almost two centuries researchers were always focusing on the maximum load carrying capacity of a structure and emphasis has been placed on the conditions of the onset of bifurcation. Can we change this prospective and exploit instabilities to design a new class of devices that sense the surroundings and tune their shape? 


We exploit the non-linear behavior of soft structures with deliberately designed patterns to create a new class of active structures and materials that use their large deformation and dramatic geometric rearrangements induced by instabilities to rapidly change their shape and functionality. To gain deep insight into the response of these structures we use a combination of computational analyses and experiments. Moreover, since the design of a new class of active structures requires a wide range of expertises, we are collaborating with a number of groups including those lead by Pedro Reis (MIT), Nick Fang (MIT) and Joanna Aizenberg (Harvard).


The Hoberman Twist-O is a commercial toy which comprises a rigid network of struts connected by rotating hinges and can easily collapse into a ball having a fraction of its original size. It inspired us, in collaboration with Pedro Reis (MIT), to design a spherical device, the Buckliball that collapses and re-expands, not with hinges but through mechanical instabilities, opening avenues for a new class of active encapsulation systems. The geometry of the Buckliball comprises a spherical shell patterned with a regular array of circular voids. When a syringe extracts the air out of the Buckliball, at a critical point the narrow ligaments between the voids suddenly buckle, leading to a cooperative buckling cascade of the skeleton of the ball. This ligament buckling leads to closure of the voids and a reduction of the total volume of the shell by up to 54%, while remaining spherical, thereby opening the possibility of encapsulation. Our combined experimental, numerical, and theoretical approach allows us to rationalize the underlying mechanical ingredients and yielded a series of simple design guidelines, including a master curve, for bucklinginduced encapsulation. Finally, because the folding mechanism that characterizes the Buckliball exploits a mechanical instability that is general, our study raises the possibility for reversible, tunable, and controllable encapsulation, over a wide range of length scales.


The Buckliball provides the first example of a structure where buckling and soft materials in novel structural layouts are successfully combined to design an active device. We believe that many mechanical systems based on the same principles will follow, with exciting applications over a wide range of length scales. Applications might include lightweight, self-assembling portable shelters at the meter scale, robots built from a single piece of material that can squeeze themselves through small openings and into tight places at the centimeter scale, and nanometre-scale drug-delivery capsules that would expand and release their cargo only after they had passed through the bloodstream and reached their target.

Selected Publications

1. Shim J, Perdigou C, Chen ER, Bertoldi K, Reis PM
"Buckling-induced encapsulation of structured elastic
shells under pressure." Proc. Natl. Acad. Sci. U.S.A.,
109, 5978-5983, 2012.
2. Krieger K "Buckling down" Nature, 488, 146-
 147, 2012.
3. K. Bertoldi, P.M. Reis, S. Willshaw and T. Mullin.
 Negative Poisson's Ratio Behavior Induced by
 an Elastic Instability. Advanced Materials, 22,
 361, 2010.
4. J.H. Jang, C.Y. Koh, K. Bertoldi, M.C. Boyce and
 E.L. Thomas. Combining Pattern Instability and
 Shape-Memory Hysteresis for Phononic
 Switching. Nano Letters, 9, 2113-2119, 2009.
5. T. Mullin, S. Deschanel, K. Bertoldi and M.C.
 Boyce. Pattern Transformation Triggered by
 Deformation. Physical Review Letters 99,
 084301, 2007.

Core Competencies

  • Modeling of the non-linear response of materials and structures .
  • Analysis of buckling and post-buckling; waves propagations.
  • High performance computing and numerical simulations tools.

Top: Hoberman Twist-O. Bottom: Buckliball (photo from Nature [2])

Current Research Team Members:
 Katia Bertoldi (PI)
 Jia Liu (Ph.D. Candidate)
 Sicong Shan (Ph.D. Candidate)
 Pai Wang (Ph.D. Candidate)
 Sahab Babee (Ph.D. Candidate)
 Bas Overvelde (Ph.D. Candidate)
 Jongmin Shim (Postdoc)
 David Hennan (Postdoc)
 Tianxiang Su (Postdoc)
 Sung Hoon Kang (Postdoc)
 Michael Taylor (Postdoc)

Current Research Collaborations:
 Pedro Reis (MIT), Nick Fang (MIT)
 Joanna Aizenberg (Harvard), Kit Parker
(Harvard), David Clarke (Harvard)
 Shreyas Mandre (Brown)