Inversion of Constitutive Parameters for Visco-Elastic Materials from Radial Velocity Measurements of Spherical Wave Experiments
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摘要: 如何由球面波实测数据反演黏弹性材料本构关系是一个富有挑战性的问题。从基于ZWT线性黏弹性本构方程建立的黏弹性球面波的控制方程组出发，根据强间断波阵面的衰减特性，提出了一个由一系列质点速度实测波形求试件动态黏弹性本构方程的新方法。首先，当材料准静态特性已知时，通过实测球面波的传播速度可确定材料的高频弹性模量；再通过实测强间断波的衰减因子可确定材料的高频松弛时间，从而可确定全部黏弹性本构参数。由反演获得的黏弹性本构模型，用特征线数值法计算黏弹性球面波，其质点速度波形的预示与实测取得了令人满意的一致性结果。Abstract: 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.
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