Analytical modeling to predict the low velocity impact response of circular GLARE fiber–metal laminates

Abstract

GLARE is a fiber–metal laminated material primarily used in aerospace structures, which are frequently subjected to impact damages. In this paper, analytical expressions concerning the dynamic response of thin circular clamped GLARE plates, subjected to low velocity impact by a lateral hemispherical impactor are derived. This impact scenario is a typical test method in order to study the impact strength of laminates. Our previously published differential equations of motion derived using a spring–mass model, which correspond to loading and unloading impact stages, are now written as Duffing equations and treated analytically. Internal damage due to delamination is taken into account. The position where delamination occurs, the maximum central plate deflection and the maximum impact load are determined analytically, and employed to calculate the impact load, velocity and kinetic energy of the impactor as a function of its position. Furthermore, the impact load, position, velocity and kinetic energy time histories are calculated. Also, the position where the impact load becomes zero and the total impact duration are predicted. The derived analytical expressions are applied successfully to GLARE 4-3/2 and GLARE 5-2/1 plates, subjected to low velocity impact. The predicted load-time history response is compared with published experimental data and a good agreement is found. No other analytical solution of this problem is known to the authors.