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Stress-Induced Wrinkling in Thin Films. Rui Huang Center for Mechanics of Solids, Structures and Materials Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin. Wrinkles.

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stress induced wrinkling in thin films

Stress-Induced Wrinkling in Thin Films

Rui Huang

Center for Mechanics of Solids, Structures and Materials

Department of Aerospace Engineering and Engineering Mechanics

The University of Texas at Austin


“Wrinkles occur on scales varying from a few nanometers (in thin films) to hundreds of kilometers (on the surface of the earth), in a variety of natural phenomena (see above).”


applications of wrinkling
Applications of Wrinkling

- Stretchable interconnects/electrodes for flexible electronics

- Optical scattering, grating, and waveguide structures

- Mechanical characterization of polymer thin films

- Reliability of integrated devices containing soft organic materials

(Jones et al., MRS Symp. Proc. 769, H6.12, 2003 )

mechanics of wrinkling
Mechanics of Wrinkling
  • Elastic film on elastic substrate
    • Equilibrium and Energetics
  • Elastic film on viscous substrate
    • Non-equilibrium and Kinetics
  • Elastic film on viscoelastic substrate
    • Evolution of wrinkle patterns
freestanding film euler buckling

Other equilibrium states: energetically unfavorable

Freestanding film: Euler buckling

Critical load:

  • Buckling relaxes compressive stress
  • Bending energy minimizes at long wavelength
on elastic substrates

Elastic substrate

On elastic substrates
  • Deformation of the substrate disfavors wrinkling of long wavelengths and competes with bending to select an intermediate wavelength

Wrinkling: short wavelength, on soft substrates, no delamination

Buckling: long wavelength, on hard substrates, with delamination

critical condition for wrinkling
Critical Condition for Wrinkling

Thick substrate (hs >> hf):

The critical strain decreases as the substrate stiffness decreases.

In general, the critical strain depends on the thickness ratio and Poisson’s ratios too.

In addition, the interface must be well bonded.

equilibrium wrinkle wavelength
Equilibrium Wrinkle Wavelength

Thick substrate (hs >> hf):

Measure wavelength to determine film stiffness

The wrinkle wavelength is independentof compressive strain.

The wavelength increases as the substrate stiffness decreases.

In general, the wavelength depends on thickness ratio and Poisson’s ratios too.

equilibrium wrinkle amplitude
Equilibrium Wrinkle Amplitude

Thick substrate (hs >> hf):

Measure amplitude to determine film stress/strain.

The wrinkle amplitude increases as the compressive strain increases.

For large deformation, however, nonlinear elastic behavior must be considered.

equilibrium wrinkle patterns
Equilibrium Wrinkle Patterns

In an elastic system, the equilibrium state minimizes the total strain energy.

However, it is extremely difficult to find such a state for large film areas.

More practically, one compares the energy of several possible patterns to determine the preferred pattern.

How does the pattern emerge?

How to control wrinkle patterns?

kinetics on a viscous substrate

Fastest mode

GrowthRate s


Viscous layer

Rigid substrate




Euler buckling

Kinetics: on a viscous substrate

(For hs >> hf)

  • Viscous flow controls the growth rate: long-wave wrinkling grows slowly, and an intermediate wavelength is kinetically selected.
kinetically constrained equilibrium wrinkles

Viscous layer

Rigid substrate

Kinetically Constrained Equilibrium Wrinkles

Infinitely many:each wavelength (  > c) has an equilibrium state

Energetically unstable: longer wavelength  lower energy

Kinetically constrained: flow is very slow near the equilibrium state

  • Elastic film is bent in equilibrium.
  • Viscous layer stops flowing.

Huang and Suo, J. Appl. Phys. 91, 1135 (2002).

simultaneous expansion and wrinkling

Viscous layer

Rigid substrate

Simultaneous Expansion and Wrinkling

Expansion starts at the edges and propagates toward center

Wrinkle grows before expansion relaxes the strain

Long annealing removes wrinkles by expansion

Liang et al., Acta Materialia 50, 2933 (2002).

wrinkling on viscoelastic substrates

Wrinkle Amplitude

Rubbery State

Glassy State


Compressive Strain

Wrinkling on Viscoelastic Substrates

Cross-linked polymers

  • Evolution of wrinkles:
  • Viscous to Rubbery
  • Glassy to Rubbery
wrinkling kinetics i
Wrinkling Kinetics I:

Wrinkles of intermediate wavelengths grow exponentially;

The fastest growing mode dominates the initial growth.


Fastest mode



For hs >> hf :

The kinetically selected wavelength is independent of substrate!


Wrinkling Kinetics II:

Instantaneous wrinkle at the glassy state:

Kinetic growth at the initial stage:

Long-term evolution:


Numerical Simulation

t = 0

Growing wavelengths

t = 1104


t = 1105

Equilibrium wavelength

t = 1107


Evolution of Wrinkle Wavelength

Initial stage: kinetically selected wavelengths

Intermediate stage: coarsening of wavelength

Final stage: equilibrium wavelength at the rubbery state


Evolution of Wrinkle Amplitude

Initial stage: exponential growth

Intermediate stage: slow growth

Final stage: saturating


2D Wrinkle Patterns I

t = 0

t = 104

t = 105

t = 107

t = 106


2D Wrinkle Patterns II

t = 0

t = 105

t = 106

t = 5X106

t = 2X107


2D Wrinkle Patterns III

t = 5X105

t = 0

t = 104

t = 107

t = 106


On a Patterned Substrate

t = 0

t = 104

t = 105

t = 107

t = 106


Circular Perturbation

t = 0

t = 104

t = 105

t = 107

t = 5105

t = 106

evolution of wrinkle patterns
Evolution of Wrinkle Patterns
  • Symmetry breaking in isotropic system:
    • from spherical caps to elongated ridges
    • from labyrinth to herringbone.
  • Symmetry breaking due to anisotropic strain
    • from labyrinth to parallel stripes
  • Controlling the wrinkle patterns
    • On patterned substrates
    • By introducing initial defects
what else
What else?
  • Ultra-thin films
    • Effect of surface energy and surface stress
    • Effect of thickness-dependent modulus
    • Effect of temperature, molecular weight, cross-linking
    • Other effect at nanoscale?
  • Nonlinear elastic/viscoelastic behavior
    • Nested wrinkles?