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exam2_review1

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

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Stress/Strain σ 11 σ 12 σ 13 Stress = Force Cross sectional area = σ face direction = σ ij = σ 21 σ 22 σ 23 normal σ σ σ 31 32 33 stresses (applied+hydrostatic forces) on diagonal, symmetric Simple shear: fixed bottom. σ 12 = σ 21 0 biaxial tension σ 11 , σ 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 α = 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 ε Incompressible? υ = 0.5 → transverse ε ε 11 + ε 22 + ε 33 = 0 = Vol Vol axial [1] Equilibrium ( σ ) [2] Compatibility ( ε ) [3] Constitutive Laws ( σ - ε )

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

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