Mechanical Properties

· The elastic constant matrix, C_ijkl , is a 9x9 array that can be reduced to a 6x6 array by symmetry and by defining: γ_ij = 2ε_ij = 2ε_ji
· The general form of Hooke's law for a material of arbitrary symmetry is then written in matrix notation as:

where: σ_ii = σ_i , ε_ii = ε_i , and τ_ij = τ_ji
· For this material subjected to a uniaxial stress, σ₁, the elastic response is given by: σ₁ = C₁₁ε₁ + C₁₂ε₂ + C₁₃ε₃ + C₁₄γ₂₃ + C₁₅ γ₃₁ + C₁₆ γ₁₂

From: Hull, "An Introduction to Composite Materials" Cambridge (1992)