Finite-element based determination of response spectra of viscoelastic materials subjected to low-velocity impact loading

This work investigates by means of the finite element method the behaviour of viscoelastic materials subjected to an impact loading by a non-deformable sphere. The results are presented in form of dimensionless parameters; hence, the complexity of the problem is significantly reduced. Thus, it is possible to represent the governing relations through so-called master curves in accessible two-dimensional graphs. For the scaling of the dimensional problem parameters the time history of the impactor’s penetration is used together with the analytical solution for the impact event in case of a purely elastic half-space according to Heinrich Hertz. Thus, a comparatively small initial velocity is used which results in a rather long contact duration. Consequently, a part of the energy introduced by the impactor may be dissipated through viscoelastic processes. This effect is utilised by protective equipment designed to minimise the forces occurring in unintentional impact situations. Thus, it is necessary to tune the viscoelastic material behaviour to the impact event such that a minimal loading due to the deceleration of the impactor is obtained. On the other hand, a too large penetration of the impactor owing to the increase in material compliance during contact must be prevented. The consideration of these two conflicting design criteria is realised in this work by a multi-objective optimisation. Moreover, the response spectra can be used for the determination of unknown model parameters of a viscoelastic material sample by means of impact experiments. This application may be utilised e. g. in the quality control of viscoelastic products. The procedure developed in this work is validated by laboratory experiments using polyurethane foams.