• combining stress–velocity gauge;
  • dynamic measurement;
  • Hopkinson pressure bar;
  • Lagrangian analysis;
  • rate-dependent constitutive relation

Abstract:  The Lagrangian analysis method is re-analysed. It is shown that when a series of particle velocity profiles (or strain profiles) are measured to determine the dynamic stress–strain relation by the Lagrangian analysis, the crux is attributed to how to simultaneously measure both the stress and particle velocity wave profiles at a Lagrangian position by a combining stress–velocity gauge. The related experimental technique has not been satisfactorily solved yet. Thus, a new method combining the Lagrangian analysis with the Hopkinson pressure bar (HPB) technique is proposed. It is shown that the interface between the HPB and the specimen in fact provides such a combining gauge (called 1sv). Based on this technique, the so-called ‘1sv + nv’ inverse analysis method is developed when particle velocity profiles are measured at n Lagrangian positions, and similarly the so-called ‘1sv + nε’ inverse analysis method are developed when strain profiles are measured at n Lagrangian positions. The feasibility of the new method is evaluated by numerical simulations for a typical rate-dependent viscoelastic material polymethyl methacrylate. The good agreement between the known ‘characteristics solutions’ and the present solutions confirms the validity of the proposed new method.