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T07 Constitutive Relations (1)

T07 Constitutive Relations (1) - Constitutive Relations T07...

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Constitutive Relations T07
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Lab Experiments Tension Test (E) Torsion Test (G) Red vectors depict loading applied by test apparatus on specimen.
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Tension Test D L P s =P/A e = D /L A s e Well defined yield plateau Not a well defined yield plateau
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Typical “Tension” Test Results tension compression
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(Y. Roiter and S. Minko, J. Am. Chem. Assoc., 127(45): 15688-15689) Microstructure: Polymers (Fluent.com)
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Microstructure: Low Carbon Steel
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Torsion Test t = ? g = ? T L d f, angle of twist
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Microstructure: Magnetorheological Fluid
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Stress - Strain : C s e =
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Linear Elastic, Isotropic Material: 3D 1 1 1 1 1 1 1 2 2(1 ) 1 2 2(1 ) 1 2 2(1 ) 1 0 0 0 1 0 0 0 1 0 0 0 (1 ) 0 0 0 0 0 (1 )(1 2 ) 0 0 0 0 0 0 0 0 0 0 xx xx yy yy zz zz yz yz zx zx xy xy E s e s e s e t g t g t g = Recall: Neither stress nor strain are vectors! xx xy xz xy yy yz xz yz zz s t t t s t t t s 1 1 2 2 1 1 2 2 1 1 2 2 xx xy xz xy yy yz xz yz zz e g g g e g g g e
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Elastic Properties Young’s modulus, E Shear modulus, G Poisson’s ratio, Bulk modulus, k Lamé constant, l Of these 5 constants, only 2 are independent
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