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UID:46e31b85cfe5035e6ef40d084e6919f6
CATEGORIES:Applied and Computational Math Seminar
CREATED:20241013T141745
SUMMARY:Geometry and mechanics of shape-programmed shells
LOCATION:Hill 005
DESCRIPTION:<p>Shape-programmed shells morph from flat into curved shapes upon stimulat
 ion by light, heat, or chemistry. They are ubiquitous throughout biology, a
 nd their synthetic counterparts show great promise as soft large-strain act
 uators. I’ll present several theoretical/computational advances towards ass
 embling a zoo of mechanically strong shape-morphing "mechanisms". A central
  theme is encoding Gauss curvature (GC) via patterns of in-plane deformatio
 n, due to the mechanical strength inherited by the resultant structures, as
  Gauss understood centuries ago. The canonical example is a pattern of azim
 uthal contraction that morphs a planar disk into a cone, which cannot be fl
 attened without energetically costly stretch because its tip bears concentr
 ated GC. In that spirit, I’ll demonstrate novel designs for nematic pattern
 s that encode concentrated GC at generalized "tips" (via topological defect
 s), along ridges (via seams between smooth patterns), and within the centra
 l holes of annuli (via spirals). Then, to investigate mechanical strength m
 ore quantitatively, we’ll turn to the load-bearing capacity of perfect coni
 cal shells. This classical-sounding problem is in fact rather subtle; I wil
 l present a new boundary-layer solution, leading to an asymptotic critical 
 force $propto t^{5/2}$. This surprising scaling is novel, and has broad imp
 lications for shell buckling more generally. I also explore deep postbuckli
 ng, finding further instabilities producing intricate states with multiple 
 Pogorelov-type curved ridges arranged in concentric circles or Archimedean 
 spirals. Finally, I investigate the forces exerted by such states, which li
 mit lifting performance in shape-morphing cones.</p>
CONTACT:Daniel Duffy, University of Michigan
DTSTAMP:20260827T141934
DTSTART;TZID=America/New_York:20241014T140000
DTEND;TZID=America/New_York:20241014T150000
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