exam2_review1

exam2_review1 - Stress/Strain 11 12 13 = facedirection = ij...

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Stress/Strain σ 11 12 13 Stress = Force Cross sectional area = face direction = ij = 21 22 23 normal 31 32 33 stresses (applied+hydrostatic forces) on diagonal, symmetric Simple shear: fixed bottom. 12 = 21 0 biaxial tension 11 , 22 0 Strain = ε ij = 1 2 x u i j + u x i j symmetric tensor uniform strain = nonuniform displacement! Uniform displacement = translation Normal strain: lengths; Shear strain: angles deformation u shear strain = α tan = original length x - gradient of u1 in the x2 direction Linear Elasticity: material response is time independent Assumptions : homogeneous, isotropic, linear (stress is linear function of strain), elastic (stress-strain are directly related, no time component). uniaxial tension Incompressible? υ = 0.5 → transverse 11 + 22 + 33 = 0 = Vol Vol axial [1] Equilibrium ( σ ) [2] Compatibility ( ε ) [3] Constitutive Laws ( σ - ε ) symmetry isotropy ij ijkl ij C Æ 81 constants 36 → =
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exam2_review1 - Stress/Strain 11 12 13 = facedirection = ij...

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