Divergence of the Initial and Peak Secant Stiffness in the Low-Velocity Impact Response of Curved Woven T300/914 Panels and Energy-Equivalent Delamination Area

The low-velocity impact response of woven T300/914 carbon/epoxy cylindrical shell panels was examined numerically at six curvature levels extending from the flat plate to the half cylinder, with a constant projected span of 125 mm and a thickness of 1 mm, using SC8R continuum shell models carrying Hashin intralaminar damage and three cohesive interfaces, at an energy of 6.70 J. Curvature raised the initial tangent stiffness by 74 per cent while it lowered the peak force by 18 to 23 per cent and extended the contact duration from 17.2 ms to 20.0 to 21.9 ms. The initial stiffness predicts these two trends in the opposite direction. The divergence between the initial and peak stiffnesses begins before damage, and the ratio of the secant stiffness at first damage to the initial stiffness is 1.33 in the flat plate and 0.60 in the half cylinder. The hoop stresses taken along the arc are consistent with this divergence. While the flat plate carries an average tension of 141 MPa on the outer arc at the peak force, this value remains between 2.5 and 31 MPa in the curved panels, and the hoop compression near the contact turns into tension around first damage. In this series, in which the impactor mass is 232 to 367 times the panel mass, the contact duration is consistent with the expression π√(m/Ksec) within 8.9 per cent. Since Ksec is read from the response itself, this relation is reported as consistency, not as prediction. The relation D/Gc = d/(r − (r − 1)d) between the damage variable and the dissipated energy was derived from the bilinear cohesive law. For the card used, r = 112.6, and 0.9 per cent of the fracture energy is dissipated at the 0.5 level of d. For a mode-dependent card, r remains between 207 and 327. The energy-equivalent area defined with this relation is between 122 and 262 mm². The area of the 0.5 threshold is 3 to 12 times this, and the fully separated area is 1.6 to 4.5 times below it. The results belong to a numerical framework without experimental validation, solved with a single mesh, a single impact energy and a single impactor mass.