Mathematical and numerical approach for a crashworthy problem

Vehicle crashworthiness has been improving in recent years with attention mainly directed towards reducing the impact of the crash on the passengers. An optimal way to achieve this target is by exclusive use of specific impact attenuators, such as strategically placed tubular elements. Many of the mechanical devices are designed to absorb impact energy under axial crushing, bending and/or combined loading. An important requirement is that these structural members must be able to dissipate large amount of energy by controlled collapse in the event of a collision. Generally, the total energy dissipated depends on the governing deformation phenomena of all or part of the structural components of simple geometry, such as thin-walled tubes, cones, frames and sections. The energy absorbing capacity differs from one component to the next in a manner which depends on the mode of deformation involved and the material used. During the last decades the attention given to crash energy management has been centred on composite structures. The use of fibre-reinforced plastic composite materials in automotive structures 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. Most of the studies have been directed towards the axial crush analysis, because it represents more or less the most efficient design. In the present paper, a mathematical approach on the failure mechanisms, pertaining to the stable mode of collapse (Mode I) of thin-walled composite circular tubes subjected to axial loading, was investigated. The analysis was conducted from an energetic point of view; it is therefore necessary to identify the main energy contributions and then equate the total internal energy to the work done by the external load. The average crush load can be obtained minimizing the force contribution, function of several variables, on a domain using a numerical approach. Comparison between theory and experiments concerning crushing loads and total displacements was analysed, showing how the proposed analytical model is efficient for predicting the energy absorption capability of axially collapsing composite shells.