|
h
f
|
The thickness of the film |
|
H
|
The thickness of the substrate |
|
v
f
|
Poisson’s ratios of the film |
|
vs
|
Poisson’s ratios of the substrate |
|
|
The equivalent Young’s modulus of the film |
|
|
The equivalent Young’s modulus of the substrate |
|
u
|
The axial displacement function |
|
εx
|
The central axial strain of the thin film |
|
ε
|
The strain of the thin film |
|
w
|
The lateral displacement of the thin film |
|
t
|
Time |
|
A(t) |
The time-varying wrinkle amplitude of this structure |
|
k
|
The characteristic wave number |
|
U
b
|
The bending energy of the film |
|
U
m
|
The membrane energy of the film |
|
A
|
The abbreviation of A(t) |
|
U
s
|
The strain energy of the substrate |
|
U
total
|
The total energy |
|
|
The first derivative of A(t) with respect to t
|
|
|
The second derivative of A(t) with respect to t
|
|
E
|
The total kinetic energy of the film/substrate structure |
|
ρ
f
|
The density of the film |
|
ε
applied
|
The amplitude of the external excitation strain |
|
ε
pre
|
The pre-strain |
|
κ
|
The curvature of the substrate |
|
c
|
The damping term |
|
ω
|
The frequency of the external excitation |
|
|
The dimensionless frequency of external excitation |
|
τ
|
The dimensionless time |
|
|
The dimensionless damping coefficient |
|
|
The potential energy function |
|
ε
fracture
|
The fracture strain |
|
ε
peak
|
The peak strain |