Mechanical Instabilities
We investigate nonlinear deformation and instability in thin and deformable structures, including buckling, wrinkling, and inflation. Our studies combine experiments, theory, and numerical simulations to understand how geometry, material properties, and loading conditions determine the onset and evolution of these behaviros.
Combined influence of shallowness and geometric imperfection on the buckling of spherical shells
with Kanghyun Ki, Jeongrak Lee and Anna Lee
We investigate the combined influence of shallowness and geometric imperfection on the pressure-induced buckling behavior of clamped spherical shells. The buckling phenomenon in spherical shells has gained significant interest in diverse fields, such as soft robotics and biomechanics, due to its distinct and drastic shape morphing characteristics. However, a notable discrepancy between analytic solutions and experimental results persists, necessitating further research to comprehend the buckling behavior of spherical shells with varying shallowness and geometric imperfection. To address this gap, we experimentally investigate the buckling of clamped spherical shells under uniform pressure while controlling the shell shallowness over a wide range. The experimental results validate finite element simulations, enabling analysis of the variation in buckling pressure and behaviors by manipulating the shell shallowness and geometric imperfection. Our analysis reveals decaying oscillatory variations in the buckling strength versus the shallowness curves, eventually converging to stable buckling strength for sufficiently deep shells. Moreover, these curves exhibit changes in level and shape with varying geometric imperfection. We also observe non-axisymmetric buckling modes in shells with small geometric imperfection and specific shallowness ranges. Through parametric studies, we identify the geometric conditions influencing the buckling behavior, particularly the non-snap-through criteria and non-axisymmetric buckling modes. This comprehensive investigation sheds light on the interplay between shallowness and geometric imperfection affecting the buckling behavior of clamped spherical shells. The findings contribute to a deeper understanding of shell buckling phenomena and have implications for various shell design applications.
Related Publication:
Kanghyun Ki+, Jeongrak Lee+, and Anna Lee*, "Combined influence of shallowness and geometric imperfection on the buckling of clamped spherical shells," Journal of the Mechanics and Physics of Solids 185, 105554 (2024). [pdf]
Evolution of critical buckling conditions in imperfect bilayer shells through residual swelling
with Dong Yan, Matteo Pezzulla, Douglas P. Holmes, 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 Publication:
Anna Lee, Dong Yan, Matteo Pezzulla, Douglas P. Holmes, Pedro M. Reis*, "Evolution of critical buckling conditions in imperfect bilayer shells through residual swelling," Soft Matter 15 , 6134-6144 (2019). [pdf]
Critical buckling pressure of precisely imperfect shells
with Francisco López-Jiménez, Joel Marthelot, John W. Hutchinson, and Pedro M. Reis
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, 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]
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]
Tissue-scale in vitro epithelial wrinkling and wrinkle-to-fold transition
with Jaeseung Youn, Dohui Kim, Hyunsu Kwak and Dongsung Kim
Although epithelial folding is commonly studied using in vivo animal models, such models exhibit critical limitations in terms of real-time observation and independent control of experimental parameters. Here, we develop a tissuescale in vitro epithelial bilayer folding model that incorporates an epithelium and extracellular matrix (ECM) hydrogel, thereby emulating various folding structures found in in vivo epithelial tissue. Beyond mere folding, our in vitro model realizes a hierarchical transition in the epithelial bilayer, shifting from periodic wrinkles to a single deep fold under compression. Experimental and theoretical investigations of the in vitro model imply that both the strainstiffening of epithelium and the poroelasticity of ECM influence the folded structures of epithelial tissue. The proposed in vitro model will aid in investigating the underlying mechanism of tissue-scale in vivo epithelial folding relevant to developmental biology and tissue engineering.
Related Publication:
Jaeseung Youn, Dohui Kim, Hyunsu Kwak, Anna Lee, and Dong Sung Kim*, "Tissue-scale in vitro epithelial wrinkling and wrinkle-to-fold transition," Nature Communications 15, 7118 (2024). [pdf]
Effect of aspect ratio and axial tensile load on the inflation of cylindrical tubes
with Jinwoo Lee and Byungho Lee
We explore the snap-through instability in hyper-elastic cylindrical tubes during inflation, specifically investigating the influences of geometry and imposed axial tensile loads on both the bulging shape profiles and the initiation pressure of the bulge. We perform bulging experiments on latex rubber tubes with different parameters such as the length-to-diameter aspect ratio and axial tension. To complement these experiments, finite element simulations across various geometries and a theoretical analysis of an infinite-length tube are conducted. Our simulations reveal a critical aspect ratio that divides the bulging into two possibilities: short tubes exhibit whole bulging, while longer tubes show localized bulging. Both experimental and simulation findings indicate that as the aspect ratio and axial tensile load increase, the initiation pressure diminishes and then converges. Notably, when the axial tensile load surpasses the shear modulus, it obstructs snap-through in shorter tubes and neutralizes the influence of the aspect ratio on the initiation pressure. The outcomes of this research offer valuable perspectives on modulating the bulging mode and initiation pressure in tubular structures within soft devices, including soft pneumatic actuators and energy harvesters.
Related Publication:
Jinwoo Lee, Byungho Lee, and Anna Lee*, "Effect of aspect ratio and axial tensile load on the inflation of cylindrical tubes," Extreme Mechanics Letters 71, 102189 (2024). [pdf]