Variational analysis of cracked angle-ply laminates

Stiffness reduction of angle-ply laminates of the type [θm(2)/θn(1)]s containing intralaminar cracks in the middle laminae is analyzed. Using the principle of minimum complementary energy an optimal admissible stress field is derived that satisfies equilibrium, boundary and traction continuity conditions. The method provides a lower bound for the stiffness matrix of a cracked angle-ply. Results for longitudinal stiffness of a cracked Glass/Epoxy [0°/45°]s[0°/45°]s laminate are in very good agreement with experimental data. Asymptotic behavior of the laminate stiffness when the crack densities are low or high is derived and its importance is discussed.