mae315 Constitutive Equation Summary Chapt 3

2 mae 315 r wetherhold constitutive equation summary

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Unformatted text preview: γ ∝ Τ ∝ Τ (5) E⁄ 1 Eν⁄ 1 Note these plane stress ≠ of the general 3-D equation (3) (Question: Could you handle another plane?) 2 MAE 315 R. Wetherhold Constitutive Equation Summary, Chapt 3 (also eqn 2.34) PLANE STRAIN (isothermal) Choose (x,y) plane Set 0 i.e. 0 0 0 cause effect ≠ 0 but is dependent Use the 3-D compliance equation (1) to eliminate stress 0 Can be solved for stress effect (6) Dependent, may be eliminated Substitute back into constitutive equations to eliminate e.g. Similarly 3 MAE 315 R. Wetherhold Constitutive Equation Summary, Chapt 3 (also eqn 2.34) Thus the compliance equation ε ⁄E 1 ε ⁄E 1 γ 0 ⁄E ⁄E 1 1 0 0 0 G (7) Note: constraints change the effective compliance (higher stiffness from constraints lower compliance ) S S 0 S S 0 Where 0 0 G S S 2 1 E 1 E Stiffness for plane strain (p127) comes from inverting equation (7) ex: 2G 2G 2G 0 Where 0 ε 0 ε 0 Gγ (8) = the Lame constant (p. 93, equation 2.38) 4...
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