Nick and Eric, thank you especially for all the fun times exploring Pasadena and SoCal. 52 3.13 Cavitation results: (a) Results for cavitation at different anisotropies pa-. b) Progress of cavitation solution through individual case numbers.
INTRODUCTION
- Nematic elastomers
- Actuation
- Beyond actuation from flat sheets
- Microstructure formation
- Viscoelasticity and damping in nematic elastomers
- Nematic elastomers as an engineering material
- Thesis outline
The degree of order observed in the liquid crystal molecules determines the degree of anisotropy, denoted by 𝑟 in this thesis. A combination of the reorientation of the liquid crystal molecules and the viscosity of the polymer chains provides a mechanism to dissipate and absorb applied mechanical energy.
ACTUATION OF CYLINDRICAL NEMATIC ELASTOMER BALLOONS
- Introduction
- Large deformation model of nematic elastomers
- Inflation of a nematic cylinder
- Pump
- Conclusion
An important observation is that the lower critical pressure (point E) of the pressure-volume curve at high temperature is higher than the upper critical pressure (point B) of the pressure-volume curve at low temperature. Meanwhile, the pressure-volume curve of the pump also changes to that of the hot material.
UNIVERSAL DEFORMATIONS OF NEMATIC ELASTOMERS
Introduction
Energy
Note that the trace formula is simply an extension of the neo-Hookean model for rubbers. Since a nematic elastomer is isotropic, our free energy density must be a function of the three invariants of the left Cauchy-Green tensorb:
Stress
Based on previous work done in this area [1, 65], the free energy density in equation 3.25 is not convex in 𝑠or𝑡. The relaxed form of this energy is:. 3.32).
Ericksen’s “universal deformations"
Bending, stretching, and shearing of a rectangular block
Straightening, stretching, and shearing of a sector of a tube
- Spherical balloon
- Cylindrical balloon
- Cavitation DeformationDeformation
- Bending
- Conclusion
In case 3, the entire balloon is in region 𝑀. The two boundary conditions for this case are: Radius of neutral axis, 𝜌 = 𝜅state in region 𝐿. The ends of the beam are located at 𝜌1.
A GENERAL CONSTITUTIVE MODEL FOR A NON-IDEAL ISOTROPIC-GENESIS POLYDOMAIN NEMATIC ELASTOMER
Introduction
It is a powerful tool that can be used to analyze nematic elastomers in arbitrarily complex deformations, which will contribute to nematic elastomers becoming an accessible engineering material.
Formulation of the constitutive relation
We explore four specific deformations in the following sections: uniaxial (U) extension, planar extension (PE), equibiaxial (EB) extension, and odd-biaxial (UB) extension. Uniaxial extension (U) In the uniaxial case, the body is subjected to uniaxial loading in the 𝑥 direction and no tension in the 𝑦 and 𝑧 directions. Plane extension (PE) In the plane extension deformation, the stretch in the 𝑦 direction is fixed in the ratio 1, giving 𝜆𝑦 = 1, and the body is tension-free in the 𝑧 direction.
Equibiaxial extension (EB) In the equibiaxial deformation, the stretch in the 𝑥 direction and the 𝑦 direction is equal, and the body is tension-free in the 𝑧 direction. Unequal biaxial extension (UB) With unequal biaxial extension, the body is tension-free in the 𝑧 direction.
Implementation in ABAQUS
2 (ln𝐽)2, (4.48) where F is the deformation gradient, 𝐽 =detF is the determinant of the deformation gradient, and b=F F> is the left Cauchy-Green tensor. We assume an additive decomposition of the Piola-Kirchhoff stress P into an elastic part and a viscosity part:. enP𝑣 = 𝛽 𝐽dF->is the viscosity part. Within the UMAT we will be using an external optimization algorithm called NLOpt (documentation here) to do the constrained optimization of the internal variables.
For algorithms using a gradient-based method, we need to calculate the derivatives of the objective function with respect to the internal variables𝜆and𝛿. 3, and the square root of the eigenvalues are collected in the main stretching matrix is.
Results from the ABAQUS implementation Verification of the modelVerification of the model
As seen in Figure 4.18, the material response has correspondingly less hysteresis for slower loading rates, as expected. The angle 𝐷 𝐻 describes the angle that one end of the cylinder turns in relation to the other end, as seen in figure 4.20. Figures 4.26 and 4.27 show𝜆and𝛿 for varying nodes with radii𝑟1through𝑟5 in the cross-section halfway through the height of the cylinder (see Figure 4.25).
However, the normal stress and torsional stress behavior shown in Figure 4.23 is a new finding. The eigenvalues from the first mode are plotted as a function of the anisotropy parameter in Figure 4.29, where the eigenvalues for 𝑟 > 1 begin to move away from the isotropic (𝑟 = 1) eigenvalue.
Conclusion
Introduction
Using a microscope can help to study a sample more closely and reveal information about anisotropy and fields. Finally, Section 5.4 shows the stress-strain curves resulting from the tests at different temperatures, and the code used to perform the experiments can be found in Appendix D.2.
Sample preparation MaterialsMaterials
Wearing gloves, place the mold in the center of the middle rack of the vacuum oven. Whenever the samples have come out of the molds, they can be UV cured at room temperature (as long as the samples were made with HHMP, the photoinitiator). Keep the tip of the micropipette immersed in the liquid you are drawing at all times.
Then another 24 hours should pass before the samples are taken out of the vacuum oven (if necessary, slightly more than 24 hours can pass, but not less). Then you can carefully remove the samples from the molds about 30 minutes after they have been removed from the vacuum oven.
Experimental setup
Clamping the specimen can be difficult, depending on the stiffness and texture of the specimen. Connect the 3 USB connectors to the computer: the linear stage controller, the iNet600 data acquisition (DAQ) and the camera. Put the insulation on top of the chamber to keep the load cell cool.
This code causes the linear table to move to its reference position at 153mm, which is exactly in the middle of the 306mm long table. The next block of code calculates the extension of the linear phase, the velocity, and the time the test will last.
Experimental results
Figures 5.11b, 5.12a, and 5.12b show the load and unload curves for the samples that were pulled at the fastest, average, and slowest strain rates, respectively. The specimens fractured in the clamps extremely quickly at high temperature, so not much stress-strain data was collected in these tests. Strain rate does not have the expected effect on the stress-strain curves in Figure 5.15a; the faster strain rate corresponds to the softer sample and the slower strain rate corresponds to the harder sample.
However, when analyzing the temperature effect in Figure 5.15b, the three high-temperature samples are all stiffer than the three low-temperature samples, which is the expected effect. The stress at 200% strain decreases with the number of cycles, while the stress at which mesogen reorientation occurs increases with the number of cycles.
Conclusion
CONCLUSION AND FUTURE OUTLOOK
Summary and impact of the findings
Finally, Chapter 4 discussed the new constitutive relation we developed to describe non-ideal nematic elastomers with a polydomain of isotropic genesis. Previous work on nematic elastomers has focused on the study of homogeneous deformations, so this chapter is an important step towards understanding nematic elastomers under various inhomogeneous deformations. In Chapter 4, we developed a completely new constitutive model to describe non-ideal nematic elastomers of polydomain isotropic genesis.
Experimental characterization of rate dependence and temperature dependence in polydomain and monodomain nematic elastomers. We have presented the results for the uniaxial stretching of polydomain and monodomain nematic elastomers tested at their isotropic and nematic temperatures.
Future outlook
The finite element model using our constitutive relation from Chapter 4 is an important step towards a tool that can study nematic elastomers as an engineering material. Due to the optical properties of nematic elastomers derived from the underlying liquid crystals, we were able to obtain valuable information by viewing samples under cross polarizers. The click-through instability of Chapter 2 and the buckling instability of Chapter 4 are both interesting phenomena resulting from finite elasticity under large deformation, and it would be interesting to continue studying other similar instabilities in nematic elastomers.
Thermotropic nematic elastomers are fast to heat, but the cooling time can be slow in ambient air based on the temperature difference and the geometry of the sample. The combination of such nematic elastomers that respond to multiple stimuli, or the combination of various active materials that respond to multiple stimuli, can create multifunctional structures in which the sequence and magnitude of the responses can be controlled and tuned for the desired actuation.
BIBLIOGRAPHY
Engineering of Complex Order and the Macro-scopic Deformation of Liquid Crystal Polymer Networks. Angewandte Chemie International Edition. Liquid Crystal Elastomers: Influence of Orientational Distribution of Crosslinks on Phase Behavior and Reorientation Processes. Macromolecular chemistry and physics. On the changes in the dimensions of a steel wire when it is twisted and on the pressure of the twisting waves in steel.
Shear modulus of polydomain, monodomain and non-mesomorphic side chain elastomers: influence of the nematic order. Liquid-crystalline elastomers: microstructure dynamics and relaxation. Philosophical Transactions of the Royal Society A.
SUPPLEMENTARY INFORMATION IN DEVELOPING THE GENERALIZED MOONEY-RIVLIN MODEL
Principal stretches
Minimization of the energy with respect to the nematic director Energy based on the first invariantEnergy based on the first invariant
1, minimizing the energy about the director yields the result that is parallel to the eigenvector corresponding to the largest eigenvalue, 𝜆2.
Simplification of the regions
DERIVING DDSDDE FOR THE UMAT
Useful items for deriving the material Jacobian Here is a useful derivative:Here is a useful derivative
Auxiliary remark for the material Jacobian
Auxiliary remark for the material Jacobian
SYNTHESIS AND TESTING
Chemical details
Synthesis template SynthesisSynthesis
- 𝜇 L Toluene 0.0549
- 𝜇 L Mix catalyst solution on vortex mixer
Tensile test template Name:Name
CODE
MATLAB code for the thermo-mechanical characterization experiments We include the code to run a uniaxial test using our custom setup, as discussed in
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