Wrinkling - Oxford Mathematics Research Seminar

Explore the mathematics of wrinkling in this 56-minute Oxford Mathematics Research Seminar presented by Dominic Vella. Delve into complex mathematical concepts, from basic mechanisms to the Theorem Egregium, as they apply to everyday objects like bicycles and empanadas. Examine the elastica, wasting lengths, and the simplest wrinkling problem before progressing to instability analysis and practical applications. Investigate the Lamé problem, isometries, and the forcing of Gaussian curvature through experiments and theoretical discussions. Learn about the effects of finite sheet size, mean interfacial shape, and poking force on wrinkling phenomena. Discover the energetic structure behind curved shapes, wrinkle numbers, and mirror buckling. Conclude with insights into variational principles and take-home messages that bridge the gap between advanced mathematics and real-world observations.

Intro
MOTIVATION
BASIC MECHANISM
THEOREMA EGREGIUM
THE ELASTICA
WASTING LENGTH
SIMPLEST WRINKLING PROBLEM
ANOTHER WAY OF THINKING
WHAT HAPPENS BEYOND ONSET?
INSTABILITY ANALYSIS
A PROBLEM
SOME (SCHOOL) GEOMETRY
ESSENTIAL IDEA
APPLICATION TO EXPERIMENT
INTERPRETATION
LAMÉ PROBLEM: REVISITED
RECAP ON ISOMETRIES
FORCING GAUSSIAN CURVATURE
EXPERIMENTS
EVOLUTION OF STRESS
FINITE SHEET SIZE MATTERS
MEAN INTERFACIAL SHAPE
POKING FORCE
ENERGETIC STRUCTURE Why is curved shape allowed?
WRINKLE NUMBER
MIRROR BUCKLING
WHAT REALLY HAPPENS
THE WRINKLED SHAPE
INCREASE IN GAUSSIAN CURVATURE
WHITHER GAUSS?
VARIATIONAL PRINCIPLES
TAKE HOME MESSAGES
FUNDING ACKNOWLEDGMENTS