## Patterns Around Us

#### Title

Wrinkling in Buckling and a Thin Sheet

#### Publication Date

2014

MA Science frameworks:

5.3 Explain how the forces of tension, compression, torsion, bending, and shear affect the performance of bridges.

#### Abstract

Module 1: Euler Buckling

Learning Objectives:

• What is an instability? A sudden change in behaviour in response to a small change in conditions.

• Instabilities usually involve a change in symmetry from a more symmetric situation to a less symmetric one

• The mechanism for an instability usually involves two competing forces (one force stabilizing the symmetric state, and the other one destabilizing it), with one suddenly winning the contest

• These competing forces in thin objects are often the forces of compression (destabilizing force - favors buckling or wrinkling) and of bending (stabilizing force).

Understanding by data collapse, the power of using dimensionless (unit-less) numbers, rather than dimensional parameters (measured in units of length, time, force, energy, etc).

Module 2: Wrinkling

Learning Objectives:

• What is the wavelength of a pattern? What decides the wavelength: reinforcing the idea of competition between many forces.

• Expanding and reinforcing concepts: What symmetry is broken in the wrinkling instability? Data collapse and dimensionless numbers

You know what wrinkling is – it’s what you see when you look in mirror, or pinch the flesh on your arm. What we’re trying to do in this experiment, is to have you realize that this is an example of buckling but one that involves a repeating pattern caused by buckling.

BucklingWrinklingTeacherPage.docx (26 kB)
Teacher Notes

COinS