Progressive collapse of foam-filled conical frustum using kinematically admissible mechanism

•An analytical model is presented for the progressive collapse of a foam-filled frustum.•Instantaneous crushing load is derived from energy conservation viewpoint.•Foam/shell interaction is modelled via an internal pressure from foam plateau strength.•Full crushing history curve is compared with experimental and numerical results.•Dependence of fold length on folding parameter is investigated by upper-bound theorem.

A kinematically admissible mechanism is presented for the progressive collapse of a foam-filled and unfilled circular frustum. The mechanism uses a three-limb model of collapse for the frustum shell, taking into account the plastic strain and circumferential strain energy dissipation during collapse. For the foam-filled case, the energy dissipation due to the plastic collapse of the foam and the interaction effects between it and outer frustum shell were considered. To account for the interaction effects, a pressure equivalent to the stress plateau of the foam was applied only to the inward bending proportion of the frustum. This is the result of our extensive experimental studies, which shows that Poisson's effects are negligible and that there will be no transverse strains resulting from the axial collapse of the frustum. We have further conducted analysis of empty frustum. A comparative analysis for the developed mechanism and previously conducted experimental studies showed good agreement between the two. Lastly, a parametric study of the mechanism correctly predicts that the magnitude of the crushing load depends on the length and proportion of the inward folds. Our upper-bound model gives a closed form solution for the collapse of foam-filled and unfilled frusta that can be used for crash energy management in automobiles.