1. Micro-valve Estimated Time for Completion: ~30min Experience Level: Lower MSC.Patran 2005 r2 MSC.Marc 2005 r2

2. 2 Topics Covered Topics covered in Modeling Importing Geometry file with FEA data. Neutral format (.out) Creating Non Spatial Fields by Tabular Input. Specify the time dependent temperature input. Applying Initial and Final Temperature Increase Temperature by multiplying the final temperature and the temperature scaling factors. Topic covered in Analysis Applying Large Displacement/Large Strains Analysis. Applying Coupled (Thermal-Mechanical) Analysis Topics covered in Review Creating XY plots Load vs. Displacement plot Animation

3. 3 Thermal actuators are very popular actuators in MEMS. This example demonstrates the thermal-mechanical coupled problem. A micro-valve is actuated by increasing the temperature of the structure Problem Description Close at Initial temperature, T i Open at Final temperature, T f =T i +ΔT

4. 4 Problem Description Given Parameters Dimensions Size : 16mm x 0.83mm Thin layer thickness= 30μm Material properties (μMKS units) Simplifying the problem To apply the symmetric condition, the rotation at the center is fixed. Nickel: t=30μm Silicon: t=30μm 0.4mm 8mm Bonded (Nickel&Silicon) Bonded (Si&Si) Not Bonded PropertiesSiliconNickel Young’s Modulus (MPa)190e3200e3 Poisson’s Ratio0.260.3 Density (kg/μm 3 )2.330e-158.930e-15 Thermal Expansion Coeff. (1/K)0.23e-50.3e-5 Thermal Conductivity (pW/μmK)157e680e6 Specific Heat (pJ/kgK)7.53e144.55e14 Yield/Fracture Stress (MPa)6e30.23e3

5. 5 Goal Find the displacement vs. temperature plot at the center of the valve. What is the minimum ΔT for the required displacement, 100μm? Find the location and value of the maximum stress during the loading (increasing temperature) process. From the stress analysis, find the maximum operating ΔT.

6. 6 Expected Results Initial at T=0 Deformed at T=100 Deformation Stress

7. 7 Create Database file and Import Geometry Create a New Database file called ‘microvalve.db’ Use Marc as the analysis Code Select Coupled as the Analysis Type Import the Neutral Geometry file called ‘microvalve.out’, and Node and element information will be imported. Imported elements and nodes Maximum dimension is about 8000μm

8. 8 Create Nonspatial Field Create a time dependent Nonspatial Field called Temp_time Map f=t to generate Field Table This will increase the temperature from initial to the final values

9. 9 Load Case Defined a Time Dependent Load Case called IncreasingTempCase. To define the time dependent Load/BCs, a time dependent Load Case must be defined first. Make sure the current Load Case is time dependent. This can be automatically done by turning the checkbox on

10. 10 Boundary Conditions Displacement Constraints Fixed_x This will prevent the right end of the structure from moving to x-direction. Fixed_y This will prevent the bottom of the structure from moving to y-direction. Sym Symmetric boundary condition. Initial Temperature Temp_initial Temp (Thermal) : time dependent Temp_increase Fixed_x Temp_Initial Temp_increase sym Fixed_y

11. 11 Boundary Conditions Deformable Contact Bodies Create four deformable bodies Glue condition will be applied to the following pairs Nickel & Si_up Si_anch & Si_low Nickel Si_up Si_low Si_anch

12. 12 Materials Material properties To simplify, apply isotropic properties to the Crystal Silicon. Use μMKS units. Silicon Nickel

13. 13 Properties Element Properties Create 2D Solid properties called Nickel_prop and Si_prop Nickel_prop Material Name: Nickel Thickness: 3mm Si_prop Material Name: Silicon Thickness: 3mm Si_prop Nickel_prop

14. 14 Load Cases Modify the previously defined Load Case Name: IncreasingTempCase Apply following BCs/Load Displacement Fixed_x Fixed_y Sym Temperature Temp_initial Temp_increase Contact Nickel Si_anch Si_up Si_low

15. 15 Analysis Single Load Steps Name: IncreasingTempStep Load Case selected: IncreasingTempCase Solving Options Large Displacement/Large Strain Fixed Increment Type Initial Time Step Size : 1.0 Total Time : 1.0

16. 16 Review Results Select the reference information Reference nodes to review the displacement and stress results Reference increment to compare the results based on time (load factor) and increment (solving step) Reference node for the displacement axis Reference nodes for the von-Mises stress Reference increments for Loading and unloading results: Select the increment results with the time increasing.

17. 17 Results Temperature vs. displacement Curve The valve cap moves upward about 160μm when ΔT increases to 100K. For the required opening (100μm), ΔT must be at least 52K.

18. 18 Results Stress Analysis Von Mises stress in Nickel The maximum value is about 300MPa > Yield Stress of Maximum principal stress in Crystal Silicon The maximum value is about 225MPa << Fractural Stress Maximum operating ΔT is about 56K.

19. 19 Animation (Displacement_uy)