A New Analytical Model for Progressive Damage in <scp>CFRP</scp> Composite Beams Under Low‐Velocity Impact

ABSTRACT Low‐velocity impact (LVI) on carbon fiber‐reinforced polymer (CFRP) composite structures is a critical concern in the aerospace and automotive industries due to its potential to induce internal damage while leaving minimal external signs. This study proposes a simplified but powerful analytical mass‐spring model capable of accurately predicting the mechanical response of composite beams under LVI conditions. The model incorporates a stepwise stiffness degradation to simulate damage progression from initial contact to complete failure. A single‐degree‐of‐freedom formulation is used, and damage is introduced through two key parameters, including the damage coefficient and the damage displacement threshold. Experimental LVI tests were conducted on CFRP beams at energy levels ranging from 2 to 20 J using a drop‐weight impact machine. The model was calibrated and validated against energy‐time and force‐time histories. In the elastic regime (2–7.5 J), the model accurately captured a sinusoidal response with minimal energy loss, predicting transferred energy within 5% of measured values. For the damaged regime (10–15 J), where stiffness degraded progressively, predicted absorbed energies were in the range of 2.2 J to 7.77 J, closely matching experimental results. In the failure regime (17.5–20 J), the model predicted full absorption of impact energy and complete stiffness loss, with damage displacement around 4 mm. The proposed model presents a physically insightful and simple analytical approach for predicting LVI‐induced responses, enabling accurate estimation of force evolution, peak and damage displacements, and energy dissipation across different impact regimes. However, it does not account for material damping or delamination propagation, which may influence high‐frequency oscillations and post‐impact behavior.