Elasticity and other constituitive relations

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Elasticity and other constituitive relations
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T, P and composition control mechanical properties
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Elasticity
Strain is recoverable
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SYMMETRY PRESERVED
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Persistence of deformation
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Brittle-elastic

• Low T
• Low deviatoric stress
• Limited total strain
• Time scale dependence

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Elasticity
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Isotropic, linear elasticity
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Crustal elastic parameters
rock
E (x 1010 Pa)
?
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Elastic uniaxial stress
Only one stress is nonzero.
Typical stress 100 MPa
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Perfect incompressibility
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Elastic uniaxial strain
Nonzero stress is weight of sedimentary
overburden.
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Lithostatic stress
What happens with erosion?
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Elastic plane stress
Only one stress is zero.
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Special homogenous strains
pure shear
simple shear
shortening or extension
transform faults
?
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Elasticity
Strain is recoverable
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Elastic waves
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Seismic cycle
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Elastic bending
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Elastic bending
Calculate deflection by assuming equilibrium
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Elastic bending
vertical force
horizontal force
torque
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Elastic bending
(from vertical force balance)
Differentiate wrt. x and substitute
plate deflection
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Elastic bending
Convert to stresses and strains by
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Elastic bending
If ?20, then
and
and by geometry
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Elastic bending
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Elastic bending
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Flexure at islands
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Flexure of a free end
Va
L
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Compressive buckling
Critical load when
L
Nonlinear amplitude