Lecture04-Notes - ME 382 Lecture 04 1 M ULTIAXIAL...

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Unformatted text preview: ME 382 Lecture 04 1 M ULTIAXIAL STRAIN & STIFFNESS Isotropic linear elasticity • Normal stresses and strains are related by: i) Young’s modulus: E ii) Poisson’s ratio: ν − 1 ≤ ν ≤ 0.5 For most materials 0.2 ≤ ν ≤ 0.5 • Shear stresses and strains related by: ε xx = σ xx / E ε zz = σ zz / E ε yy = ε zz = − νε xx = − νσ xx / E ε xx = ε yy = − νε zz = − νσ zz / E (no cross terms for shear) ε yy = σ yy / E γ xy = τ xy / G ε xx = ε zz = − νε yy = − νσ yy / E γ xz = τ xz / G γ yz = τ yz / G ME 382 Lecture 04 2 In general : 3-D Hooke’s Law ε xx = σ xx − νσ yy − νσ zz ( ) / E ε yy = − νσ xx + σ yy − νσ zz ( ) / E ε zz = − νσ xx − νσ yy + σ zz ( ) / E γ xy = τ xy / G γ xz = τ xz / G γ yz = τ yz / G Special cases: (i) Plane stress: One stress = 0; e.g. , σ zz = 0 (such as at free surface) (ii) Plane strain: One strain = 0; e.g. , ε zz = 0 (constraint in rigid die) Volumetric strain: Original volume:...
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This note was uploaded on 09/08/2011 for the course MECHENG 382 taught by Professor Thouless during the Fall '08 term at University of Michigan.

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Lecture04-Notes - ME 382 Lecture 04 1 M ULTIAXIAL...

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