A crashworthy problem on composite structures using a mathematical approach

During the last decades the attention given to vehicle crash energy management has been centred on composite structures. The use of fibre-reinforced plastic composite materials in automotive structures, in fact, may result in many potential economic and functional benefits due to their improved properties respect to metal ones, ranging from weight reduction to increased strength and durability features. Although significant experimental work on the collapse of fibre-reinforced composite shells has been carried out, studies on the theoretical modelling of the crushing process are quite limited since the complex and brittle fracture mechanisms of composite materials. Moreover most of the studies have been directed towards the axial crush analysis, because it represents more or less the most efficient design. A mathematical approach on the failure mechanisms, pertaining to the stable mode of collapse of thin-walled composite structures subjected to axial loading, is investigated. The analysis is conducted from an energetic point of view. The main energy contributions to the absorption (bending, petal formation, circumferential delamination, friction) are identifies and then the total internal energy is equated to the work done by the external load. The total crushing process can be seen as a succession of deformation states, each responsible for a partial absorption. The minimum configuration for each impact force in the specific state of deformation, function of several variables and dependent on geometric and material parameters is obtained. A comparison between theory and experiments concerning crushing loads and total displacements is presented, showing how the proposed analytical model is effective in predicting the energy absorption capability of axially collapsing composite shells.