From viral capsids to architectural domes, slender shells are ubiquitous in natural and engineered structures. Their Mechanics is tightly intertwined with the underlying geometry and the onset for instability is a classic problem in structural Mechanics. At the flexLab, we have revived this old field by an innovative experimental approach that focuses on the postbuckling regime, where strong geometric nonlinearities and energy focusing can emerge. Central to this effort, we have devised a robust, versatile,and precise fabrication mechanism to rapid prototype thin shells in a lab setting. We are also interested in problems involving the large deformation of elastic plates, for example when loaded under aerodynamic or hydrodynamic conditions.
Topics that we have investigated on plates and shells include: predicting knockdown factor in the buckling of pressurized shells, periodic patterning of shellsubstrate systems, formfinding in gridhells, stressfocusing in buckled shells and tearing of thin sheets. A more detailed account of these examples and other problems is provided below.
Evolution of critical buckling conditions in imperfect bilayer shells with: Anna Lee, Dong Yan, Matteo Pezzulla, and Douglas P. Holmes 


Publications: 
Form finding in elastic gridshells with: Changyeob Baek, Andrew O. SagemanFurnas, and Mohammad K. Jawed 


We have also studied what sets the rigidity of elastic gridshells under point load indentation, finding scaling law in terms of the dimension of the structure and the number of the rods it contains, as well as the geometric and material properties of the individual rods. Our proposed empirical relation for the rigidity also points to the underlying nonlocal nature of the mechanical response of gridshells, in contrast to the local response of isotropic continuum shells. We further assess this nonlocality by quantifying the resulting radial displacement field as well as inspecting the effect of the location of the indentation point on the rigidity Publications: • C. Baek and P.M. Reis, “Rigidity of hemispherical elastic gridshells under point load indentation” Journal of the Mechanics and Physics of Solids, 124, 411426 (2019). [html, pdf]. 
Buckling patterns in biaxially prestretched bilayer shells with: Rashed AlRashed, Francisco López Jiménez, and Joel Marthelot 


We have also studied what sets the rigidity of elastic gridshells under point load indentation, finding scaling law in terms of the dimension of the structure and the number of the rods it contains, as well as the geometric and material properties of the individual rods. Our proposed empirical relation for the rigidity also points to the underlying nonlocal nature of the mechanical response of gridshells, in contrast to the local response of isotropic continuum shells. We further assess this nonlocality by quantifying the resulting radial displacement field as well as inspecting the effect of the location of the indentation point on the rigidity Publications: 
Reversible patterning of spherical shells through constrained buckling with: Joel Marthelot, PierreThomas Brun, and Francisco López Jiménez 


Videos that summarize this project can be found in the following links [Video1] [Video2]. Publications: 
Imperfection sensitivity: Critical buckling pressure of precisely imperfect shells with: Anna Lee, Francisco López Jiménez, Joel Marthelot, and John W. Hutchinson 


To the best of our knowledge, this is the first time that experimental results on the knockdown factors of imperfect spherical shells have been accurately predicted, through both finite element modeling and shell theory solutions. A video that summarizes this project can be found in the following link [Video]. This project was done in collaboration with John Hutchinson (Harvard University). Publications: 
Rapid fabrication of slender elastic shells with: Anna Lee, PierreThomas Brun, Joel Marthelot, Gioele Balestra, and François Gallaire 


In this project we have studied the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities. A video that summarizes this project can be found in the following link [Video]. This project was done in collaboration with the group of François Gallaire at EPFL (Switerzland). Publications: Press coverage: 
Mechanics of thin elastic shells: GeometryInduced Rigidity and Localization with: Arnaud Lazarus, Bastiaan Florijn, Amin Ajdari and Ashkan Vaziri 

We have introduced a predictive framework for the rigidity of thin elastic shells which can also account for the situation when the shell is overpressurized. Our concept of GeometryInduced Rigidity can be used in reverse, as a precision nondestructive tool, to measure parameters of a shell (e.g. thickness) upon knowing the geometry of the underlying surface and the local mechanical response. The scaleinvariance of GeometryInduced Rigidity suggests that our framework should find uses across length scales: from the mechanical testing of viral capsids through Atomic Force Microscopy, to ocular tonometry procedures or in the design of architectural shells. All this work was inspired by the remarkable physics of an elegant eggshell! 


Videos of Scones of a thin shell under indentation: [Experiments, FEM Simulations] Publications: Press coverage: 
The Buckliball and Buckligami: bucklinginduced encapsulation and soft Actuation with: Jongmin Shim, Elizabeth Chen, Claude Perdigou and Katia Bertoldi 




Publications: Press coverage: 
Wrinklons as Buildingblocks in Wrinkling Cascades: 


Publications: Press coverage: 
Rolling of Flexible Ribbons with: Pascal Raux, John Bush and Christophe Clanet 


Publications: Press coverage: 
Delamination of thin films from an elastic substrate with: Dominic Vella, Benoit Roman, José Bico and Arezki Boudaoud 


Publications: Press coverage: 