A lumped mass numerical model for cellular materials deformed by impact

When impacted by a relatively rigid body, cellular materials undergo severe deformation and extensive material failure. However, such behaviour may no t be well described using traditional numerical approaches such as the fini te element method. This paper presents a lumped mass numerical model which can accommodate high degrees of deformation and material failure. The essen ce of this model is to discretize a block of material into contiguous eleme nt volumes, each represented by a mass point. Interactions between a node a nd its neighbours are accounted for by defining 'connections' that represen t their interfaces which transmit stresses. Strains at a node are calculate d from the co-ordinates of the surrounding nodes; these also determine the stresses on the interfaces. The governing equations for the entire solution domain are then converted into a system of equations of motion with nodal positions as unknowns. Failure criteria and possible combinations of 'conne ction' breakage are incorporated to model the occurrence of damage. A pract ical contact algorithm is also developed to describe the contact interactio ns between cellular materials and rigid bodies. Simulations for normal and oblique impacts of rigid rectangular; cylindrical and wedge-tipped impacter s on crushable foam blocks are presented to substantiate the validity of th e model. The generally good correlation between the numerical and experimen tal results demonstrates that the proposed numerical approach is able to mo del the impact response of the crushable foam. However some limitations in modelling crack propagation in oblique impacts by a rigid impactor on foam blocks are observed. Copyright (C) 2001 John Wiley & Sons, Ltd.