LITERATURE SURVEY SUMMARY OF HYPERELASTIC MODELS FOR PDMS

Transcription

1 LITERATURE SURVEY SUMMARY OF HYPERELASTIC MODELS FOR PDMS ZHAO Feihu 0 P age

2 CONTENT 1. Mooney- Rivlin Model Publication 1. Analysis of Circular PDMS Microballoons With Ultralarge Deflection for MEMS Design Publication2. Deformation of PDMS membrane and microcantilever by a water droplet: Comparison between Mooney Rivlin and linear elastic constitutive models Publication3. Non-Linear Elastromeric Spring Design Using Mooney-Rivlin Constant Publication4. Computational Modeling of Elactromechanical Behaviors of Dielectric Elastromer Actuators Publication Publication6. Mechanical Characterization of Hyperelastic Polydimethylsiloxane by simple Shear Test Publication7. An Elastomeric Material for Facial Prostheses: Synthesis, Experimental and Numerical Testing Aspects Publication8. Physical Properties of Polymer Handbook Neo-Hookean Model Publication9. Optical Transmission Grating Tuned by Electro Active Polymers Publication 10. Modelisation of a Hyperelastic Polymer Membrane Deformation Publication11. Design and Performance of Metal Conductors for Stretchable Electronic Circuit A Non-linear Rubber Elasticity Model Publication12. Non-linear mechanical behaviour of the elastomer polydimethylsiloxane (PDMS) used in the manufacture of microfluidic device P age

3 MOONEY- RIVLIN MODEL The strain energy density function for an incompressible Mooney- Rivlin material is: Where, C 10 (C 1 ), C 01 (C 2 ), D 1 are empirically determined material constants; are the first and the sencond invariant of the deviatoric componet of the left Cauchy-Green deformation tensor: Where, F is the deformation gradient; for an incompressible material, J=1. For consistency with linear elasticity in the limit of small strain, it is necessary that Cauchy Stress: ii = i Loading condition classification: (1) Uniaxial extension then the true stress is:, For simple tension: =0 2 P age

4 (2) Equibiaxial tension, then the stress can be expressed as: (3) Pure shear 1 = ; 2 =1/ ; 3 =1 then the stress can be calculated as: (4) Simple shear The deformation gradient for a simple shear deformation has the form: Where, e 1, e 2 are reference orthonormal basis vectors in the plane of deformation and the shear deformation is give by: In matrix form, the deformation gradient and the left Cauchy-Green deformation tensor can be expressed as: 3 P age

5 Then the Cauchy stress will be: For consistency with linear elasticity, shear modulus µ=2(c 1 +C 2 ). For more information about Mooney-Rilvin solid, please refer to: 4 P age

6 Publication 1. Analysis of Circular PDMS Microballoons With Ultralarge Deflection for MEMS Design PDMS Type A Sylgard 184 silicone elastomer kit (Dow Corning Corporation, Midland, MI) mixed at 10:1 ratio is spun coated on the trichlorosilane-treated Si wafer, followed by curing at a temperature of 20 C for 48 h. t 0 r 0 d c r s d s Values Loading The stress and strain measured through an equibiaxial loading condition (bulging test) Condition MR C 10 C 01 Values/kPa P age

7 Publication2. Deformation of PDMS membrane and microcantilever by a water droplet: Comparison between Mooney Rivlin and linear elastic constitutive models PDMS Type 1. The ratio of monomer and curing agent is 5:1 2. The ratio of monomer and curing agent is 20:1 a a l Values/m Loading Condition Uniaxial Tension MR C 1 C 2 C 1 C 2 Values/MPa P age

8 Publication3. Non-Linear Elastromeric Spring Design Using Mooney-Rivlin Constant PDMS Type Not PDMS! Natural Rubber (Without any treatment) V -shaped object. This is half of it. Depth Width Height Values/inch Loading Condition Tension Biaxial Shear MR C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 Values P age

9 Publication4. Computational Modeling of Elactromechanical Behaviors of Dielectric Elastromer Actuators PDMS Type Not PDMS! Dielectric Elastromer R r (electrode of radius) d (thickness of electrode) Values/mm Loading Uniaxial Tension (Set C 01 =0) Equi-biaxial Extension Conditions MR C 10 C 01 Prarmeters Values/MPa * P age

10 Publication5. PDMS Type - Length Width Thickness Values/mm Loading Condition Pure Compression MR C 1 C 2 Values/MPa P age

11 Publication6. Mechanical Characterization of Hyperelastic Polydimethylsiloxane by simple Shear Test PDMS Type - w D L t a t Values/mm Loading Simple Shear Condition MR C 1 C 2 L=35mm L=42mm L=51mm L=35mm L=42mm L=51mm Values/MPa P age

12 Publication7. An Elastomeric Material for Facial Prostheses: Synthesis, Experimental and Numerical Testing Aspects Constituents of Silicone Rubber Formulation Materials Discription PDMS base polymer (V46) High molecular weight vinyl end blocked poly(dimethylsiloxane) PDMS base polymer (V21) Low molecular weight vinyl end blocked poly(dimethylsiloxane) PDMS Filler Surface treated hydrophobic silica Type Cross- linker Hydride functional silicone polymer ABCR, Manchester Catalyst Platinum complex Bimodal Formulations Developed Formulation Polymer Ratio Polymer Content Filler Content 1 V46 80%, V (ABCR) 20% 2 V46 85%, V (ABCR) 15% 3 V46 95%, V21 5% 75 25(ABCR) 4 V46 80%, V (ABCR) 20% cuboid Length Width Thickness Values/mm Loading Condition Formulation 2 was deemed to have the best compromise of tear hardness and viscosity properties and therefore further tensile testing was performed on this formulation. Stress strain curves were obtained by at constant cross head speeds of 0.2, 2 and 6 MR Values/kPa mm/min C 1 C 2 v=0.2mm/ v=2mm/min v=6mm/ v=0.2mm/min v=2mm/min v=6 min min mm/min P age

13 Publication8. Physical Properties of Polymer Handbook Table for Mooney- Rivlin parameters of the stress- strain isotherms for different networks system Polymer Diluent f Cross-linker T/ 2C 1 /MPa (2C 1 +2C 2 )/MPa PDMS[111] Lin.PDMS 4 -irradiation PDMS[111] Lin.PDMS 4 -irradiation PDMS[111] Lin.PDMS 4 -irradiation P age

14 NEO-HOOKEAN MODEL The strain energy density function for an incompressible Neo-Hookean material is W=C 1 (I 1-3) Where, C1 is a material constant, and I1 is the first invariant of the left Cauchy-Green Deformation Tensor, i.e., Where i are the principal stretches. I Cauchy Stress: ii = i Shear Modulus: µ=2c 1 (1) Uniaxial extension Therefore, 1 =, 2 = 3 =1/ 1/2 Assume no traction on the sides, =0, so we can write: Where 11-1 is the engineering strain. 11 =6C 1 =3µ The equivalent Young s modulus of a neo-hookean solid in uniaxial extension is 3. (2) Equibiaxial extension 1 = 2 = ; 3 =J/ 2 ; I 1 =2 2 +J 2 / 4 Therefore, 13 Page

15 (3) Simple shear For the case of simple shear the deformation gradient in terms of components with respect to a reference basis is of the form: Where is the shear deformation. Therefore the left Cauchy-Green deformation tensor is Cauchy stress can be obtained as: For more information about Neo-Hookean solid, please refer to: Hookean_solid 14 P age

16 Publication9. Optical Transmission Grating Tuned by Electro Active Polymers PDMS PDMS (Sylgard184, Dow Corning) Type Thin Film Thickness Values/µm 75 Loading Biaxial Stretch Condition NH µ Values/MPa P age

17 Publication 10. Modelisation of a Hyperelastic Polymer Membrane Deformation PDMS Type - Edge Length Thickness Values/µm Loading Vaccum (Stretch & deflection in vertical direction) Condition NH Shear Modulus Values/kPa P age

18 Publication11. Design and Performance of Metal Conductors for Stretchable Electronic Circuit PDMS Type Sylgard Values - Loading Biaxial Load Condition NH C01 Values/MPa P age

19 For simple tension: A NON-LINEAR RUBBER-ELASTICITY MODEL Where, S is the power-conjugate engineering stress; is defined as an effective stretch; L is the network locking stretch; is the inverse of the Langevin function; µ R is the rubber modulus; µ is the shear modulus. 18 P age

20 Publication12. Non-linear mechanical behaviour of the elastomer polydimethylsiloxane (PDMS) used in the manufacture of microfluidic device PDMS Type Samples of PDMS with compositions of 5:1, 10:1 and 20:1 were prepared by mixing the appropriate composition for 1 minute and degassing for 2 minutes in a Thinky Hybrid Defoaming Mixer. The mixed and degassed mixtures of PDMS were carefully poured into different molds, and the excess was carefully removed. The filled molds were cured at 80 C for 8 hours. The thin-film tension specimens of 5:1, 10:1, and 20:1 compositions were then carefully peeled from the molds. Large- deformation tension and Microscale tension Parameter s compression Thickness Thickness Values/mm Loading Conditions Model Parameter s Values Range Large-deformation tension Largedeformatio n tension Large-deformation compression µ R /MPa L Largedeformation compressio n Microscal e tension Largedeformatio n tension Microscale tension, The specimen was extended approximately 5 mm at 20 m/s. Largedeformation compressio n Microscal e tension 5: : : : : : P age