Pergamon Int. d. Impact En,qn# Vol. 16, No. 4, pp. 637 649, 1995 Elsevier Science Ltd Printed in Great Britain 0734-743X(94)OOO59-X 0734-743X/95 $9.50+ 0.00 A NOTE ON THE INERTIA AND STRAIN-RATE EFFECTS IN THE TAM AND CALLADINE MODEL D. KARAGIOZOVAt and NORMAN JONES + t Bulgarian Academy of Sciences, Institute of Mechanics, Sofia, Bulgaria and {Impact Research Centre, Department of Mechanical Engineering, The University of Liverpool, P.O. Box 147, Liverpool L69 3BX, U.K. (Received 31 March 1994; in revised form 4 August 1994) Summary--The dynamic behaviour of a simple plate structure subjected to an axial impact is studied using an elastic-plastic model which takes into account inertia effects and the influence of material strain-rate sensitivity. The entire time-dependent deformation process, including elastic unloading and plastic reloading is obtained. The predictions for the absorbed energy are in reasonable agreement with the corresponding experimental results reported by Tam and Calladine and the detailed behaviour provides some further insight into the dynamic plastic buckling of structural elements. h b 1 m m! r t v0 Yo E Et FA K, K~ KE L1, L2 M Mb P~ fl ~o gu 2 fro O" u tTy NOTATION thickness of a single plate of the specimen in Fig. 1 width of a single plate of the specimen length of the specimen mass of the specimen mass of the model in Fig. 3(a) h/l = L I/L 2 time initial velocity of the striking mass axial displacement in Fig. 3(b) Young's modulus hardening modulus spring coefficients defined in Fig. 3(c) initial kinetic energy of striker length of the members shown in Fig. 3(a) mass of striker bending moment static buckling load of the specimen in Fig. 1 softening characteristic of the non-linear spring at A in Fig. 3(b) strain rate uniaxial yield strain ultimate strain in uniaxial tension Kt/ K M/m lateral displacement of A in Fig 3(b) initial imperfection indicated in Fig. 3(a) static uniaxial yield stress of the material ultimate stress in uniaxial tension dynamic yield stress of the material 1. INTRODUCTION From the viewpoint of impact design, it is important to determine the energy absorbing capacity of structures as well as various other features of the dynamic response. In many cases, the simplification of a quasi-static method of analysis is not acceptable because of the importance of inertia forces and material strain-rate effects. Simplified methods of analysis and idealized models can provide some insight and guidelines into the accuracy of quasi-static methods of analysis and other approximations. 637