I am interested in classical mechanics. You can find some recent work below.
Please note that I recommend the arXiv versions of the linked articles, as they are less encumbered with copyediting errors and the influence of humorless referees.
There is a lot of counterintuitive physics associated with moving discontinuities (in geometry, contact, … more info to come)
A chain dropped onto a table falls faster than it would if the table were not there.
A classical approach to sleeve constraints, peeling, and similar problems.
This paper is about contact discontinuities in extended bodies, particularly how the geometry depends on whether you are picking something up or laying it down. Examples include peeling tapes, moored structures, and some musical instruments.
RODS AND PLATES
(…and strips and membranes and… more info to come)
Expanding a point in the below paper, in praise of Biot strains for thin structures.
Some observations on variational elasticity and its application to plates and membranes
Resolving and raising some issues that have been bothering me for a while.
Fun with SO(3). Multi-stability. Snapping movies. Unexpected problems with strip models.
An old problem revisited. Classification of elastica
by momentum and pseudomomentum.
METRICALLY CONSTRAINED DYNAMICS OF FLEXIBLE BODIES
Objects such as chains, cables, and sheets are effectively inextensible in one or two dimensions and perfectly flexible in the others. Their motion preserves a metric of lower dimension than the space in which they live. The simplest example, and an effective model for many engineering systems, is the classical string whose study was pioneered by Routh
in the 19th century. I am trying to understand the motions
of strings and their higher-dimensional analogues.
The classical catenaries are a one-parameter family of curves that don't change shape under translation and axial flow. Stick them in a fluid and they do, picking up four additional shape parameters. These solutions include towing, sedimentation, and other problems as subcases.
This note is about a constant arising in dynamical equilibria of thin bodies (likely related to the Eshelby tensor, and more indirectly to conservation of Kelvin circulation and, in some steady geometries, the Bernoulli equation). We also use symmetry arguments to provide the solutions for rotating, flowing strings, such as the steady state of a piece of unspooling yarn.
The paper is about propagating discontinuities in thin structures, either in geometry or applied forces. I show how to derive momentum and energy jump conditions using an action principle for a non-material volume. Relevant phenomena include kinks, shocks, partial contact, impact, cracking, tearing, and peeling. The video is an example of two propagating contact discontinuities.
Here we examine the rotation of a flowing, flexible membrane. We find that a minimal model of metrically constrained dynamics generates peaked waves, just like this
- At the end of a moving string Hanna, Santangelo
Awaiting revival of Rejecta Mathematica | [arXiv:1209.1332]
- Unwrapping chains Cambou, Gamari, Hamm, Hanna, Menon, Santangelo, Walsh
Gallery of Fluid Motion submission [arXiv:1209.0481]
At the free end of a moving string, the stress has to vanish, and a result is that the motion of the end is nontrivial. We still don't understand what is happening, but we had fun making our video.
These are the three-dimensional "jumpropica" or rigidly rotating strings, generalizing the known planar
Take a pile of chain or rope sitting on a surface, and pull one end really fast. A strange archlike feature appears; we had to take a high speed video to catch it. Our paper talks about several interesting issues that came up while we thought about this problem, although at present my guess is that the real physical structure has more mundane origins.
A surface is mathematically required to satisfy certain relationships between its intrinsic
curvatures, quantities related to the physical concepts of stretching and bending. This coupling can be exploited to program shapes by growth, thermal expansion or other swelling processes
, insertion of real or virtual point defects or Eshelby
inclusions, topological surgery and so on. Optimal strategies for design, as well as the mechanics of the resulting structures, are open fields of study.
Overcurvature induced multistability of linked conical frusta: How a 'bendy straw' holds its shape
Bende, Yu, Corbin, Dias, Santangelo, Hanna, Hayward
A bendy straw, which can stably adopt just about any one-dimensional shape, only works because it's pre-stressed. Cut one length-wise and watch it relax to a larger radius. An incompatible four-bar linkage works similarly.
In a sheet of paper, a cone is a monopole: a point singularity in intrinsic curvature. So what's a dipole? There are actually two kinds.
Designing responsive buckled surfaces by halftone gel lithography Kim, Hanna, Byun, Santangelo, Hayward
Science 335 (6073), 1201-1205 (2012) | sorry, no arXiv
Thermally responsive rolling of thin gel strips with discrete variations in swelling Kim, Hanna, Hayward, Santangelo
Soft Matter 8 (8), 2375-2381 (2012) | sorry, no arXiv
Programmed buckling by controlled lateral swelling in a thin elastic sheet Dias, Hanna, Santangelo
Physical Review E 84, 036603 (2011) | [arXiv:1105.0704]
These are our adventures in making 3D surfaces by swelling flat 2D sheets. The first version of the Dias et al.
paper had a better title, which you can still see thanks to the arXiv.
A selection of other work.