Inversion of Constitutive Parameters for Visco-Elastic Materials from Radial Velocity Measurements of Spherical Wave Experiments

The inversion of visco-elastic constitutive relation from the measured data of a spherical wave experiment is a challenging research. Starting from the governing equations for linear visco-elastic spherical waves which are based on the ZWT visco-elastic constitutive relation, the analytical expression for the attenuation of strong-discontinuous visco-elastic spherical wave front is derived, and consequently a new method is proposed, by which the high-strain-rate visco-elastic parameters could be inversed from a series of particle velocity profiles measured in a spherical wave experiment. The first step is to determine the high-strain-rate elastic module from wave velocity measurements when the quasi-static material parameters are known. Then the high-strain-rate relaxation time can be determined from the attenuation factor. Thus the required visco-elastic constitutive relation can be obtained. Using those material parameters obtained by such a new inversion method, the visco-elastic spherical wave profiles are calculated by the characteristics method. The good agreement between the numerical predictions and the experimental results well supports this proposed new inversion method.