The document discusses constitutive modeling and simulation of shape memory polymers. It begins with an introduction to shape memory materials and how shape memory polymers work. It then discusses developing a thermo-mechanical framework for modeling glassy shape memory polymers and crystalline shape memory polymers. The document outlines simulations conducted including modeling the shape memory cycle of a glassy polymer under uniaxial deformation and the torsion of a polymer cylinder. It concludes with discussing future work such as further developing the glassy polymer model and solving inhomogeneous boundary value problems.

1. Constitutive Modeling and Simulation of Shape Memory Polymers Defense Proposal ADVISOR: DR I.J. RAO DATE : 11/17/2008 MAHESH KHANOLKAR

2. Outline Introduction What are shape memory materials. Different types of shape memory materials How shape memory polymers work Modeling Natural Configurations Thermo-mechanical Framework Model development Glassy SMP Model Application of Crystallizable SMP Model Simulations and Results Conclusions

3. What Are Shape Memory Materials? “ Remember” the original shape even after undergoing significant deformation Revert back to original shape by a suitable trigger Most common trigger: heating above a recovery temperature, TR Other triggers: Magnetic fields, electromagnetic radiation etc. Trigger

4. Overview of SMP’s Mechanism for “remembering” original shape and transient shape. Common mechanisms: Entanglements, Crosslinks and hard-domains. Transient shape fixed usually with crystalline phase or the glassy state. Revert back to original shape by heating. Heating above Tm (if the crystalline phase is used to fix the transient shape) Heating above Tg (if the glassy phase is used to fix the transient shape)

5. How Shape Memory Polymers Work Original: Chemical Cross-Links Temporary: Glassy Phase Lendlein et al. Original: Crystalline Hard domains (Physical cross-links) Temporary: Crystallites Original: Chemical Cross-Links Temporary: Crystallites

6. Shape Memory Alloys (SMA) - Extensive work has been carried out in the last 10 years. - Constitutive equations and modeling fairly well developed. Shape Memory Polymers (SMP) - Advantages - SM effect can be seen for large deformation - Manufacturing methods are conventional and cheap - Bio-compatible - Recovery temperature can be adjusted - Disadvantage - Actuation force (SMP) << Actuation force (SMA) Types of Shape Memory Materials

7. Shape Memory Polymers Representative Application Biodegradable Shape Memory Polymer for Suturing wounds. (Langer 2002)

8. Shape Memory Polymers Representative Application Time series photographs that show the recovery of a shape-memory tube. (a)- (f) Start to finish of the process takes a total of 10 s at 50°C (Marc Behl et al 2007).

9. Shape Memory Polymers Applications SMP fibers for comfort wear MEMS devices, temperature sensors Damping elements Intravenous needles and implantable Medical device Films and fibers used in insulation applications Rewritable digital storage devices Morphing Aircraft Wings many more…

10. Shape Memory Mechanism in CSMP’s Deform Cool Unload Heat Amorphous polymer Cross-link Crystallite Legend Melting Crystallization T > T r T < T r State 1 State 4 State 2 State 3 Stretch Nominal Stress 1 2 3 4

11. Shape Memory Mechanism in GSMP’s Deform Cool Unload Heat Amorphous polymer Cross-link Glassy polymer Legend Glass Transition T > T r T < T r State 1 State 4 State 2 State 3 Stretch Nominal Stress 1 2 3 4

12. Modeling (Salient Features) ‏ Constitutive Modeling – Mathematical description of how a material responds to deformations. It is a relation between two physical quantities (often described by tensors). Modeling of polymers– Write equations for stress tensor in terms of deformation gradient. Change in Entropy and internal energy is macroscopic manifestation of changes in microstructure. Non-linear response.

13. Modeling (Salient Features) ‏ Above Tr the material behavior is rubber like Hard domains act as cross-links in thermoplastic SMP’s Chemical cross-links in the case of thermoset SMP’s Cooling in deformed shape causes partial crystallization / glass transition Crystallization – drop in stress Glass-Transition- stress remains constant or increases Semi-crystalline polymer is anisotropic Unloading the the specimen below Tr, a small recovery strain observed. Heating above Tr, return to original shape

14. Modeling Framework Need to account for the influence of each phase Amorphous rubbery phase above the recovery temperature. Semi-crystalline polymers: amorphous and crystalline phases Glassy polymers: amorphous and glassy phases (mixture region) Each phase can have its own stress free state

15. Modeling - Natural Configurations In most traditional approaches the response of the material is assumed to be known from a single configuration. Well known that a body can be stress-free in more than one configuration Solid which can exist in two different phases (e.g. Austenite and Martensite) with different symmetries. Polymers, which can exist in the amorphous and crystalline phase Deform Unload

16. Modeling - Natural Configurations Natural configurations associate with a viscoelastic melt

17. Modeling - Glassy SMP (Amorphous Rubbery Phase) Model as an incompressible hyperelastic material Stress is given by: Based on Rubber elasticity: entropic in origin.

18. Modeling – Glassy SMP 100 % conversion into glass during vitrification Glassy phase is viscoelastic Glassy phase is formed in stressed state Little Change in length on cooling, iso-stress, Mather(2006)

19. Modeling – Glassy SMP (Mixture of rubbery and glassy phase) Stress in nascent glass = stress in rubbery phase Stress is given by: Current configuration of glassy phase Current configuration of amorphous phase Natural configuration of amorphous phase

20. Modeling – Glassy SMP (Mixture of rubbery and glassy phase) Constrained Cooling below the glass transition temperature. Increase in thermal stress. Natural configurations evolve as the material is cooled/deformed. Natural configuration associated with the previously formed material shifts to a new position. Increase in mechanical deformation gradient, decrease in thermal deformation gradient, so that the total deformation gradient remains constant (constrained cooling).

21. Modeling – Glassy SMP (Mixture of rubbery and glassy phase) Natural Configurations associated with the glassy-rubbery phase solid phase mixture

22. Modeling – Glassy SMP Cycle - Equations Loading: where T is the stress in the rubbery part of the polymer and µ a is the modulus Cooling:

23. Modeling – Glassy SMP Cycle - Equations Unloading Melting

24. Modeling – Glassy SMP Cycle Stress–strain–temperature diagram illustrating the thermo mechanical behavior of a shape memory polymer under different strain/stress constraint conditions

25. Simulation and Results (Uniaxial Deformation Cycle GSMP) Stress vs Strain for the complete SMP Cycle T L (K) 273 T g (K) 343 T H (K) 358 (Mpa) 8.8 MPa (Mpa) 750 MPa

26. Simulation and Results (Uniaxial Deformation Cycle GSMP) Stress vs Temperature

27. Simulation and Results (Uniaxial Deformation Cycle GSMP) Stress vs Strain plot (Yiping Liu et al, 2005)

28. Nanoparticle Reinforced Glassy SMP Reinforcing Glassy SMP with nanoparticles increases its stiffness. Rubbery Phase: Glassy phase: where K is the concentration of nanoparticles

29. Simulation and Results (Uniaxial Deformation Cycle GSMP) Effect of Nanoreinforcemnts Elastic moduli of the SMP and SMP composite at 26 and 118°C (Yiping Liu et al 2003) .

30. Simulation and Results (Uniaxial Deformation Cycle GSMP) Effect of Nanoreinforcemnts Stress vs Strain Above the glass transition

31. Torsion of a Cylinder Undeformed Cylinder Deformation after applying Torsion Motion: Deformation gradient: M (in sec -2 ) (MPa) (MPa) 0.33 120 1200 0.00007 0.256 50

32. Simulation and Results: Torsion of a Cylinder Moment vs Time (Torsion of a cylinder)

33. Simulation and Results: Torsion of a Cylinder Moment vs Shear (Torsion of a cylinder)

34. Simulation and Results: Torsion of a Cylinder Shear vs Time (Torsion of a cylinder)

35. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Shape memory cycle on a single element using an UMAT (User Defined Material) A strain of 100% (large deformation) has been applied to the element and the resulting deformation is seen Steps involved in the shape memory cycle. Large Deformation on the single element Constraining the element to retain its temporary shape Removing load – Small amount of strain recovery Return to Original Shape

36. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Applied load to the Element

37. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 1 Large Deformation on the single element

38. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 2 Constraining the element to retain its temporary shape

39. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 3 Removing load – Small amount of strain recovery

40. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 4 Back to Original Shape

41. Conclusion and Future Work Developed a model for SMP’s undergoing glass transition using the notion of natural configurations. Developed model takes in to account the thermal expansion of polymers. Reinforcements have a impact (increased modulus) on SMP’s. Illustrated application of a CSMP Model for a non-homogenous deformation (Torsion of a cylinder). Illustrated application of CSMP Model using ABAQUS. Further develop GSMP model within a full thermodynamic framework. Solve inhomogeneous boundary value problems of importance.

42. THANK YOU