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In previous works, a finite element model of the shock absorbing characteristics of athletics tracks was developed, able to give sufficiently reliable predictions from laboratory tests performed on suitable material samples. The model proved to be effective in discriminating the effects of geometry (i.e. thickness) and material properties (essentially the elastic characteristics) on force reduction, thus allowing a first optimization of the tracks in view of their approval by the International Association of Athletics Federations (IAAF). This simplified 2D model neglected the real track structure, considering it as a single layer of material having homogenized properties. In the present study, a new 3D model was developed to accurately describe the structure of multi-layered tracks, with properties and geometrical construction (e.g. solid or honeycomb) differing from one layer to another. Several tracks having different combinations of top/bottom layers varying in both material formulation (i.e. chemical composition) and geometry were thus considered. Mechanical properties of the individual elements constituting the track were measured with small-scale laboratory tests, taking into account their strain-rate dependence. The 3D model allowed a complete representation of the loads acting on the track and it gave results which are in very good agreement with the experiments. This proves it to be a valuable tool for the purpose of optimizing the track in terms of material formulation as well as layer geometrical construction and arrangement: as an example, the effect of changing the cell size of the honeycomb pattern was investigated.

Bike and ski helmets are mainly made up of two layers: the external shell and the foam liner. The foam liner, typically made of expanded polystyrene (EPS) or polypropylene (EPP), is asked to provide energy absorption in case of impacts. Standard helmet design requires the foam to maximize this energy absorption, thus achieving large deformations (up to 25% in compression) while maintaining the stress level below a threshold value. To optimize the helmet construction in terms of foam composition, structure and density, reliable numerical models are required, which in turn need to be fed with accurate experimental data. A characterisation of several foams was performed, including EPS and EPP having varying densities, under tensile and compressive stress states at varying strain rates. Typical mechanical parameters (elastic moduli and plateau stress in compression, Poisson's ratio) were compared with literature data and applicability of existing models to experimental results was discussed. A marked strain rate dependence – very important for impact applications – was accurately described using the Nagy phenomenological model. The foam microstructure was investigated using scanning electron microscopy (SEM) to assess structural changes before and after compression. The aforementioned mechanical features were then adopted in a rate-dependent constitutive law for crushable foams, to model the shock attenuation properties of helmets and validate the approach against available data. Finally, a microelectromechanical system based in-helmet wireless micro monitoring system was developed and inserted in a helmet prototype. The system is capable of acquiring impact load spectra, providing valuable information to investigate generic impacts with varying angles and energy. In particular, it can monitor the effect of repeated micro-impacts on the residual energy absorption characteristics of the foam.

The Force Reduction (FR) impact test, performed by means of an apparatus called artificial athlete, has been chosen by IAAF (International Association of Athletics Federations) as a standard to evaluate the performance of athletics tracks. The test procedure consists in dropping a mass on the sample, recording the evolution of the impact force and taking its maximum value normalized with respect to a reference one. In this work a Finite Element (FE) model of the FR test was developed to investigate the effects of sample thickness and material properties. Two athletics tracks and, for comparison, a sample of natural rubber were considered. Their mechanical behaviour was characterized, extrapolated to the strain rate of interest and modelled using hyperelastic constitutive equations. With data so derived a number of numerical (FE) simulations of the FR test on the three materials with varying thickness were performed. The FR values predicted by the simulations resulted to be in very good agreement with experimental FR data, particularly for thicknesses of practical interest. Finally, the suitability of an alternative model based on a linear elastic constitutive relationship was considered and results were discussed.