Skip to main content
. 2026 Feb 5;18(3):411. doi: 10.3390/polym18030411
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
E¯f The equivalent Young’s modulus of the film
E¯s 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
A˙t The first derivative of A(t) with respect to t
A¨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
ω¯ The dimensionless frequency of external excitation
τ The dimensionless time
c¯ The dimensionless damping coefficient
W¯ The potential energy function
ε fracture The fracture strain
ε peak The peak strain