Experimental investigation on dynamic constitutive behavior of aluminum foams by new inverse methods from wave propagation measurements

The SHPB technique is experiencing a serious challenge by cellular material. In order to experimentally investigate the dynamic constitutive behavior of cellular materials, a new method of Lagrangian analysis (called “nV + T0” for short) is proposed, of which the main advantage is that no pre-assumption for the constitutive model and no any combining gauge are required. Based on the measurements of a series of particle velocity waves v(Xi, t) and the pre-known zero initial condition, the dynamic constitutive response of cellular material can be inversely determined. The experiments are performed on the conventional Taylor bar set-up and the v(Xi, t) are measured by means of a high speed camera and the dynamic Digital Image Correlation (DIC) technique. The dynamic stress–strain curves determined by such “nV + T0” inverse analysis show marked difference from the quasi-static one. In parallel, another inverse analysis based on the simplified Dynamic Rigid-Linear Hardening Plastic-Rigid Unloading (D-R-LHP-R) constitutive model is developed. The experiments are conducted on the Taylor bar-single Hopkinson bar set-up. The dynamic stress–strain curves obtained by such simplified model are in quite good agreement with those obtained by the nV + T0 method, except the initial peak part. The comparison between those two dynamic stress–strain curves and the quasi-static one indicates that the strain rate effect must be taken into account.