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A mathematical model representing the dynamic behaviour (both plastic deformation and fracture) of a clamped beam under impact loading is developed. Indentation at the impact point, transverse deformation, formation and propagation of plastic hinge, arrest of plastic hinge leading to plastic work concentration and finally failure are the physical processes which constitute the basis of the derived model. The effect of imperfection is also incorporated. Imperfection is considered in the form of aπ -shaped notch located at the impact point, at supports or at both. The distinct feature of the present formulation is that it accommodates different possible deformation and failure modes in a single model. Final plastic deformation, time histories of different field variables and failure modes as predicted from the derived model are found to be in good agreement with the corresponding experimental and numerical results. This model provides a quick understanding of the dynamic behaviour of beam under impact and also the effect of various underlying parameters which may be useful for forming design provisions for impact-resistant structures.

A generalized model for dynamic deformation and failure of clamped beam under impact loading