Collapse of Orthotropic Spherical Shells

Abstract

We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes emerges upon variation of shell slenderness and degree of orthotropy. Our extensive numerical simulations are in agreement with experiments using fabricated polymer shells. The shell buckling pathways and corresponding strain energy evolution are shown to depend strongly on material orthotropy. We find surprisingly robust orthotropic structures with strong similarities to stomatocytes and tricolpate pollen grains, suggesting that the shape of several of Nature's collapsed shells could be understood from the viewpoint of material orthotropy. arXiv:1903.09476v2 [cond-mat.soft]

Deformable and Robust Core–Shell Protein Microcapsules Templated by Liquid–Liquid Phase‐Separated Microdroplets

“…When the shell became nearly incompressible, then the inward buckling step began at the weakest or thinnest part of the shells, including flattening and inward concaving (Figure 3c,f). [70,71] The deflection, or the indentation, of the shell was perpendicular to the concentrated compressive stresses, further increased by the osmotic pressure (Figure 3f). The buckling caused a concave surface and a convex surface of the microcapsule, and the work done by osmotic pressure was transformed into the strain energy stored in the microcapsule.…”

“…[10] Bending energy and elastic energy are closely related to the conformations of the buckled invagination, and the critical external pressure required to trigger the buckling scales with t 2 /R 2 (R, capsule radius; see Supporting Information and Figure S11, Supporting Information, for a justification of this scaling law). [10,70,71] With increasing loss of the capsule volume, the bucked zone can even experience a transition from an axisymmetric dimple (primary buckling) to asymmetrical wrinkles (secondary buckling). [72,73] Capsules with a lower bending stiffness and with a larger volume loss are more likely to develop secondary buckling.…”

“…One reason that we do not observe polygonal instabilities might be the relatively uniform shell thickness (Figures 1e and 3); the other possible reason is that the microcapsules are not as thin as those in other studies, and the shell elasticity plays a key role in maintaining the morphological smoothness during buckling (Figure 1e). [10,[70][71][72][73] The key parameter that controls this is the Föppl-von-Kármán-number γ FvK = 12R 2 (1 − ν 2 )/t 2 , where R, ν, and t are the outer radius, Poisson ratio, and thickness of the capsule, respectively. [72] Previous theoretical work showed that if , then only the primary buckling is observed, not the secondary buckling event.…”

Mechanical design of apertures and the infolding of pollen grain

“…Studies of instabilities and buckling in thin shells (31)(32)(33)(34)(35) have shown that a perfectly homogeneous spherical shell exposed to uniform pressure or undergoing a change in volume will develop depressions in unpredictable positions due to the high symmetry of the problem (35,36). The buckling behavior can, however, be altered and guided by creating local weak spots in an otherwise uniform shell (28)(29)(30), and this elastic inhomogeneity of the shell can also be realized by varying its thickness (37)(38)(39). Similar considerations can be applied to pollen grains (40), where the high sporopollenin content makes exine a very stiff material (41)(42)(43) while the apertures can be seen as elastic soft spots in the pollen wall (25).…”

Post-buckling dynamics of spherical shells

“…Existing studies are essentially focused on understanding the scenario of the buckling instability that occurs beyond a certain threshold of compression or deflation, and on characterizing the stability branches [22,24,25,29]. More recently, shells made of non-isotropic material have also attracted some attention [31–33]. In terms of dynamics, the reaction of shells to a steep increase of pressure have been recently studied [15,34], while an experimental study has highlighted the role of dissipation within the shell while reaching the stable buckled state [29].…”