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Elasticity, Geometry and Buckling
Published on Jan 09, 20172731 Views
In this colloquium we present how geometrical shape affects the mechanical properties of thin solid shells and how buckling instabilities change the geometry of periodic microstructures in materials.
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Chapter list
Elasticity, Geometry and Buckling00:00
Research Interests00:09
Thin solid shells and structures01:27
Deformations of thin shells02:03
Shape deformations due to internal stress02:48
Challenges03:51
Outline04:34
Mechanics of crumpled paper05:06
Intuitive description of mechanical properties05:51
Warped shells06:58
Shallow shell equations08:35
Mechanical properties of warped shells - 110:26
Mechanical properties of warped shells - 211:17
Thermal fluctuations of microscopic shells12:56
Thermal fluctuations of microscopic sheets13:30
Thermalized sheets under uniform tension15:05
Area extension under uniform tension16:29
Thermal length scale for various shells17:46
Bending rigidity of graphene 19 sheets at room temperature - 119:37
Bending rigidity of graphene 19 sheets at room temperature - 220:39
Thermal and frozen fluctuations of graphene membranes21:09
Graphene kirigami22:11
How thermal fluctuations affect the mechanics of spherical shells?23:54
Elastic length scale24:21
Mechanics of thermalized spherical shells25:50
Thermal fluctuations reduce critical buckling pressure27:29
Potential experimental test with polymersomes30:05
Outline31:01
Periodic elastic structures31:10
Negative Poisson’s ratio31:24
Spontaneous chiral symmetry breaking32:02
Buckled structures as sensors32:30
Regulation of color33:27
How periodic elastic structures deform upon compression?35:03
Geometrical frustration in compressed triangular frames35:20
Analogy with antiferromagnetic spins36:30
Additional interactions between triangles37:21
Buckling into higher modes38:18
Comparison with experiments39:38
Compression of periodic structures with holes39:57
Elastic dislocation dipoles40:17
Elastic dipole-dipole interactions41:58
Lattice of elastic dipoles in external stress field42:30
Elastic dipoles on lattices43:28
Compression of triangular lattice in different directions44:30
Future directions: Structures on curved surfaces44:55
Future directions: Design principles?46:09
Summary46:37
Acknowledgements46:44