Elasticity

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• Elasticity

• Elasticity is more general than structural
  mechanics.
• No restrictions on relative dimensions of
  bodies.
• No restrictions on loading.
• Bodies remain in the linear elastic region of
  the stress-strain curve ?xE?x.

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Isotropic Stress-Strain Relations
E2G(1?)
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Relations Among the Elastic Constants
R. Reismann and P.S. Pawlik, Elasticity Theory
and Practice, Robert E. Krieger Publishing
Company , 1991
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Uniaxial Loading
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Anisotropic Materials
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Cubic Material (Single Crystal Silicon)

• There are 3 independent elastic constants C11,
  C12, C44
• For silicon C11 166 GPa, C12 64 GPa, C44 80
  GPa
• Appendix C
• where l1, l2, l3 are the direction cosines of
  the angle between the direction of interest and
  the x,y,z directions respectively, e.g.
  l1cos(x,dir).

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• For Poissons ratio
• where the (l1, l2, l3) and (m1, m2, m3) are the
  direction cosines defining two perpendicular are
  the directions.

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Thermal Expansion
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Thermal Actuator
Micromechanical Switch
http//www-g.eng.cam.ac.uk/edm/images/research/mem
s/thermal_actuators_1.jpg
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Amplified Thermomechanical In-Plane Microactuator
(ATIM)
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Bending T-MEMS
Patricia Nieva, MS Thesis, Northeastern
University 1999
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SEM micrographs of a bending T-MEMS thermometer
array successfully fabricated with a 0.5 mm
silicon oxide bottom layer and a 0.5 mm nitride
top layer
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SEM micrographs bending T-MEMS thermometer array
successfully fabricated with a 1 ?m SiO2 bottom
layer and a 7500 Å polysilicon top layer
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Breaking TMEMS
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Breaking TMEMS Array
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SEM micrograph of a breaking T-MEMS thermometer
array of shape 3 after fabrication and before
heating
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SEM of a breaking T-MEMS thermometer array heated
to 1100 ?C. Brittle fracture at the neck can be
clearly observed
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General Stress-Strain with Thermal Effects
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Residual Stresses
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P.J. Ryan, G.G. Adams, N.E. McGruer, Journal of
Applied Mechanics, 75, 031008
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Stress-Gradient

Mr
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Sources of Residual Stress

• Thermal mismatch
• Chemical reactions far from equilibrium
• Oxidation of silicon
• LPCVD deposition of silicon nitride
• Rapid deposition processes
• Sputtering
• Evaporation

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Limit of Elasticity