Studies on nonlinear visco-elastic spherical waves by characteristics analyses and its application

Based on the ZWT nonlinear visco-elastic constitutive model, the governing equations for nonlinear visco-elastic spherical waves are formulated. By use of characteristics method, the problem of solving those five partial differential equations is reduced to solve five ordinary differential equations along 3 sets of characteristics. Numerical results are given, illustrating the non-ignored viscosity effects and nonlinear effects. The attenuation law for visco-elastic spherical shock wave is analytically derived. A new inversion method is proposed, by which the high-strain-rate visco-elastic parameters could be inversely determined from a series of particle velocity profiles measured in a spherical wave experiment.

► Difficulties in nonlinear visco-elastic spherical waves are overcome by ZWT model. ► By using characteristics method, the problem becomes much easier to be solved. ► Numerical results show, the effects of viscosity and nonlinearity can not be ignored. ► New attenuation law for visco-elastic spherical shock wave is analytically derived. ► By a new method the high ɛ˙ visco-elastic parameters are inversely determined.