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Strengthening and weakening of shells through differential swelling

with Dong Yan, Matteo Pezzulla, Douglas P. Holmes and Pedro M. Reis


We propose and investigate a minimal mechanism that makes use of differential swelling to modify the critical buckling conditions of elastic bilayer shells, as measured by the knockdown factor. Our shells contain an engineered defect at the north pole and are made of two layers of different crosslinked polymers that exchange free molecular chains. Depending on the size of the defect and the extent of swelling, we can observe either a decreasing or increasing knockdown factor. FEM simulations are performed using a reduced model for the swelling process to aid us in rationalizing the underlying mechanism, providing a qualitative agreement with experiments. We believe that the working principle of our mechanism can be extended to bimetallic shells undergoing variations in temperature and to shells made of pH-responsive gels, where the change in knockdown factor could be changed dynamically.

Related publications:

  • Anna Lee, Dong Yan, Matteo Pezzulla, Douglas P. Holmes and Pedro M. Reis, "Evolution of critical buckling conditions in imperfect bilayer shells through residual swelling," Soft Matter 15, 6134 (2019).​ [pdf]

Buckling of a shell subjected to a probing force

probing_대지 1.jpg

We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry of the probe, we study the effect that the probe-induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predictions from the literature. Inspired by a nondestructive technique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells.

Related publications:

  • Joel Marthelot, Francisco López-Jiménez, Anna Lee, John W. Hutchinson, and Pedro M. Reis, "Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force," Journal of Applied Mechanics 84, 121005 (2017).​ [pdf]

Critical buckling pressure of precisely imperfect shells


We study the effect of a dimplelike geometric imperfection on the critical buckling load of spherical elastic shells under pressure loading. This investigation combines precision experiments, finite element modeling, and numerical solutions of a reduced shell theory, all of which are found to be in excellent quantitative agreement. In the experiments, the geometry and magnitude of the defect can be designed and precisely fabricated through a customizable rapid prototyping technique. Our primary focus is on predictively describing the imperfection sensitivity of the shell to provide a quantitative relation between its knockdown factor and the amplitude of the defect. In addition, we find that the buckling pressure becomes independent of the amplitude of the defect beyond a critical value. The level and onset of this plateau are quantified systematically and found to be affected by a single geometric parameter that depends on both the radius-to-thickness ratio of the shell and the angular width of the defect. 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.

Related publications:

  • Anna Lee, Francisco López-Jiménez, Joel Marthelot, John W. Hutchinson, and Pedro M. Reis, “The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells,” Journal of Applied Mechanics 83 (11), 111005 (2016). [pdf]

  • Francisco López-Jiménez, Joel Marthelot, Anna Lee, John W. Hutchinson, and Pedro M. Reis, “Knockdown Factor for the Buckling of Spherical Shells Containing Large-amplitude Geometric Defects,” Journal of Applied Mechanics 84, 034501 (2017). [pdf]

Fabrication of thin elastic shells by the coating of curved surfaces


Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable. Here, we study 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.

Related publications:

  • Anna Lee, Pierre-Thomas Brun, Joel Marthelot, Gioele Balestra, François Gallaire, and Pedro M. Reis, “Fabrication of Slender Elastic Shells by the Coating of Curved Surfaces,” Nature Communications 7, 11155 (2016). [pdf]

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