Stress, strain, and deformation of elastic solids under load
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0.100
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Physics
The elasticity tensor Cijkl relates stress σij = Cijkl εkl to strain. For isotropic materials, only two constants are needed: Young's modulus E and Poisson's ratio ν. Tension: longitudinal strain ε_xx → transverse contraction ε_yy = -ν·ε_xx. Shear: shear modulus G = E/2(1+ν). Poisson's ratio near 0.5 (rubber) means nearly incompressible (volume-preserving). Negative ν (auxetic materials) is possible and leads to unusual behavior.