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 not be well described using traditional numerical approaches such as the nite element method. This paper presents a lumped mass numerical model which can accommodate high degrees of deformation and material failure. The essence of this model is to discretize a block of material into contiguous element volumes, each represented by a mass point. Interactions between a node and its neighbours are accounted for by de ning `connectionsʹ that represent their interfaces which transmit stresses. Strains at a node are calculated 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 `connectionʹ breakage are incorporated to model the occurrence of damage. A practical contact algorithm is also developed to describe the contact interactions between cellular materials and rigid bodies. Simulations for normal and oblique impacts of rigid rectangular, cylindrical and wedge-tipped impactors on crushable foam blocks are presented to substantiate the validity of the model. The generally good correlation between the numerical and experimental results demonstrates that the proposed numerical approach is able to model 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