8
The previous development of IMR has considered only a limited material stretch ratio regime, neglecting to incorporate
inelastic material behavior. This study aims to identify the critical material stretches exhibited at the transition from viscoelastic to inelastic material behavior and develop new experimentation for the modulation of LIC bubble amplitudes.
Experimental methods to achieve these aims include varying cavitation laser energy and using micron-sized heat sink particles to drive bubble nucleation. This characterization will pave the way for future work in the development and incorporation of damage and failure mechanisms into the theoretical framework.
2.2 Background
Generally, cavitation is the process in which a void emerges in a liquid or solid medium due to localized pressure changes [2].
LIC is an experimental method for generating spatially controlled cavitation bubbles in soft materials and has proven to be reliable and robust. A high-energy laser pulse focused within a soft material results in the ionization and formation of a bubble consisting of an approximate two-phase vapor and gas mixture. The resulting oscillating bubble interacts with the surrounding
material and is modeled to determine constitutive behavior to predict material stresses and strains at high strain-rates.
IMR uses the experimentally obtained high-speed time- lapse data of bubble oscillations within the given material of interest, and for spherically symmetric bubbles computes the temporal evolution of the bubble radius, R(t) [1]. The normalized
value R(t)/R eq is also defined to be the material stretch, λ(t). Assuming spherical bubble symmetry and near- field material
incompressibility, the 1D momentum balance and conservation of mass equations, with the incorporation of traction and
kinematic boundary conditions of the bubble, present the Keller-Miksis equation,
1
3
2
1 3
1 1
2
2
-
æ
è
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ö
ø
÷
+
-
æ
è
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ö
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÷ =
+
æ
è
ç
ö
ø
÷
-
+ -
æ
¥
R
c
R R
R
c
R
R
c
p
R
S p
¨
r
g
b
è è
ç
ö
ø
÷ +
-
+
æ
è
ç
ö
ø
÷
1
2
r
g
R
C
p
R
S
b
(2.1)
R is bubble radius, c is material wave speed, ρ is mass density, p b is bubble pressure, γ is surface tension, and p ∞ is far-field
pressure. S describes the constitutive material behavior as a function of hoop and radial stress. IMR employs the least squares
method to best fit material parameters across several constitutive models to determine the best material fit.
However, the model may fail to capture the complete bubble dynamics due to unaccounted inelastic material behavior.
Experimentally, this can be reflected by loss of bubble amplitude, as well as bubble asphericity. As schematically depicted in
Fig. 2.1, experimental bubble radius vs. time is compared to its simulated IMR curve. The first peak consistently fits well,
but there is a discrepancy for subsequent peaks unaccounted for by the current IMR nonlinear viscoelastic model. In order
to improve this discrepancy, there is an experimental need to explore the critical material stretches in which elasticity breaks
down and incorporate the dominating inelastic material behavior into IMR.
Experimental R(t)
IMR simulation
Normalized time, t*
Normalized Radius, R*
1
0.5
0
0
1
2
3
4
Inelastic material
behavior
Fig. 2.1 Schematic of IMR simulation at large material stretches and experimental discrepancy
S. Buyukozturk and C. Franck
The previous development of IMR has considered only a limited material stretch ratio regime, neglecting to incorporate
inelastic material behavior. This study aims to identify the critical material stretches exhibited at the transition from viscoelastic to inelastic material behavior and develop new experimentation for the modulation of LIC bubble amplitudes.
Experimental methods to achieve these aims include varying cavitation laser energy and using micron-sized heat sink particles to drive bubble nucleation. This characterization will pave the way for future work in the development and incorporation of damage and failure mechanisms into the theoretical framework.
2.2 Background
Generally, cavitation is the process in which a void emerges in a liquid or solid medium due to localized pressure changes [2].
LIC is an experimental method for generating spatially controlled cavitation bubbles in soft materials and has proven to be reliable and robust. A high-energy laser pulse focused within a soft material results in the ionization and formation of a bubble consisting of an approximate two-phase vapor and gas mixture. The resulting oscillating bubble interacts with the surrounding
material and is modeled to determine constitutive behavior to predict material stresses and strains at high strain-rates.
IMR uses the experimentally obtained high-speed time- lapse data of bubble oscillations within the given material of interest, and for spherically symmetric bubbles computes the temporal evolution of the bubble radius, R(t) [1]. The normalized
value R(t)/R eq is also defined to be the material stretch, λ(t). Assuming spherical bubble symmetry and near- field material
incompressibility, the 1D momentum balance and conservation of mass equations, with the incorporation of traction and
kinematic boundary conditions of the bubble, present the Keller-Miksis equation,
1
3
2
1 3
1 1
2
2
-
æ
è
ç
ö
ø
÷
+
-
æ
è
ç
ö
ø
÷ =
+
æ
è
ç
ö
ø
÷
-
+ -
æ
¥
R
c
R R
R
c
R
R
c
p
R
S p
¨
r
g
b
è è
ç
ö
ø
÷ +
-
+
æ
è
ç
ö
ø
÷
1
2
r
g
R
C
p
R
S
b
(2.1)
R is bubble radius, c is material wave speed, ρ is mass density, p b is bubble pressure, γ is surface tension, and p ∞ is far-field
pressure. S describes the constitutive material behavior as a function of hoop and radial stress. IMR employs the least squares
method to best fit material parameters across several constitutive models to determine the best material fit.
However, the model may fail to capture the complete bubble dynamics due to unaccounted inelastic material behavior.
Experimentally, this can be reflected by loss of bubble amplitude, as well as bubble asphericity. As schematically depicted in
Fig. 2.1, experimental bubble radius vs. time is compared to its simulated IMR curve. The first peak consistently fits well,
but there is a discrepancy for subsequent peaks unaccounted for by the current IMR nonlinear viscoelastic model. In order
to improve this discrepancy, there is an experimental need to explore the critical material stretches in which elasticity breaks
down and incorporate the dominating inelastic material behavior into IMR.
Experimental R(t)
IMR simulation
Normalized time, t*
Normalized Radius, R*
1
0.5
0
0
1
2
3
4
Inelastic material
behavior
Fig. 2.1 Schematic of IMR simulation at large material stretches and experimental discrepancy
S. Buyukozturk and C. Franck