Cellular solids modelling and applications for passive safety of vehicles

The aim of the thesis is the analysis and development of cellular solids modelling oriented to the optimal design of components for impact energy absorption and the improvement of passive safety of vehicles. Cellular solids, also called foams, are largely used in industry because of their structural and energy absorbing capabilities combined with a low weight. Typical applications are the usage as core materials in structural sandwiches and as absorbers of impact energy. In automotive industry they are widely used in internal padding and in the external body for passengers passive safety in car crash. Compared to traditional materials they allow to design their mechanical properties by taking action on several parameters such as choice and formulation of the constitutive material, porosity (directly affecting apparent density) and micro-structure. This flexibility is paid in terms of complexity of mechanical behaviour, which means the need to perform a quite high number of experimental tests for the material characterisation and the model identification. A brief description of structure, mechanics and modelling techniques is outlined. Some of the main models defined in literature and implemented in FEM codes are reported. Some models are further analysed, developed and compared by means of experimental tests performed on plastic foams. Cellular solids models can be divided in two categories: phenomenological models and micromechanical models. The phenomenological models are defined by formulations developed to reach the maximum similarity with the experimental stress-strain curve but are not related to the physical principles which rule the phenomenon. The micro-mechanical models are based on the analysis of deformation mechanisms on the micro-cell structure under loading. Experimental data on four types of rigid plastic foams and a weighted least square procedure was used in order to identify the parameters of five cellular solid models. The tested foams are namely EPP, PUR (Bayfill EA), EPS and PPO/PS (Noryl GTX) at different densities. The models used are the Gibson model, the Rusch model, a modified version of the Gibson model, a modified version of the Rusch model and a new proposed empirical model. The relationship between material density and model parameters was analysed for tested foams and for some cellular solid models. Laws expressing the parameters of a phenomenological model as a function of the foam density permits the identification of any density foam derived from the same solid material and with the same micro-structure by means of a minimum set of experimental tests. At the same time the availability of a large quantity of experimental data is helpful to reach a higher level of confidence of the model parameter values. The identified models and the corresponding density dependence laws of parameters can be considered a complete modelling of a whole class of foams and its use is proposed not only for simulation but also for design purposes. In the design development it is of highest importance the choice of the proper type of foam at the proper density level and the modelling is useful to assist the optimal design of foam components for the specific application. The main goal, in the design of a cellular solid for impact applications, is to make it able to absorb the impact energy amount maintaining a defined maximum level of stress and deceleration. To meet this requirement, the proper base material, density of the foam, shape, and dimensions, of the component have to be selected on the basis of the available information. This information comes from experimental data and modelling techniques. In particular, the type and quality of the model can reduce the number of tests necessary to have information on the complete design domain. Energy absorption diagrams and efficiency versus density can be adequately described by means of the experimentally identified models and not only with a dispersed set of experimental points or linearly interpolated curves or other empirical interpolation curves of tests results. The modelling was used in order to construct, by means of numerical procedures, some graphical tools for the evaluation and choice of the optimal foam for specific energy absorption applications. Finally, an automotive application for passive safety improvement is reported. The effect of a foam component for knee padding during frontal car crash was analysed and a stochastic sensitivity analysis was performed by means of fem simulations in order to evaluate the effect of foam model parameters on some biomechanical responses. The work in this thesis describes new possibilities to model the mechanical behaviour of cellular solids in order to improve the description of their properties, to reduce the number of experimental tests needed for the parameters identification and to enlarge the design possibilities through a more rigorous choice of the optimal cellular materials.