Bending and Wrinkling as Competing Relaxation Pathways of Strained Free-Hanging Films

d

1

[nm]

d

2

[nm]

ν

1

ν

2

Y

1

[GPa]

Y

2

[GPa]

ε

An equilibrium phase diagram for the shape of compressively strained free-hanging films is developed by minimizing the total strain energy. For small strain gradients

Δε

, the film wrinkles, while for sufficiently large

Δε

, a phase transition from wrinkling to bending occurs. The average strain in the bilayer film is denoted

ε

. Thickness, Poisson's ratio, and the Young modulus for the first and second layers are denoted by

d

1

,

ν

1

,

Y

1

and

d

2

,

ν

2

,

Y

2

. The equilibrium radius of rolled-up tube is represented by

R

eq

and the wavelength of wrinkles by

λ

.