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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) Youngs modulus: E ii) Poissons ratio: 1 0.5 For most materials 0.2 0.5 Shear stresses and strains related by: xx = xx / E zz = zz / E yy = zz = xx = xx / E xx = yy = zz = zz / E (no cross terms for shear) yy = yy / E xy = xy / G xx = zz = yy = yy / E xz = xz / G yz = yz / G ME 382 Lecture 04 2 In general : 3-D Hookes Law xx = xx yy zz ( ) / E yy = xx + yy zz ( ) / E zz = xx yy + zz ( ) / E xy = xy / G xz = xz / G yz = yz / G Special cases: (i) Plane stress: One stress = 0; e.g. , zz = 0 (such as at free surface) (ii) Plane strain: One strain = 0; e.g. , zz = 0 (constraint in rigid die) Volumetric strain: Original volume:...
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