Inversion for the complex elastic modulus of material from spherical wave propagation data in free field

Abstract

A spherical wave experiment is conducted for polymethyl methacrylate (PMMA), with a spherical explosive charge of 0.125 g TNT as the source. The aim is to investigate the dynamic mechanical behavior of a viscoelastic material from the multiple measured radial particle velocities during the spherical wave propagation in a free field. Without using conventional mathematical models, a brief and effective method is suggested to determine the complex elastic modulus of the material through the combination of the viscoelastic spherical stress wave theory and the measured radial particle velocities at different radii in a free field. The complex elastic modulus, determined from the spherical wave data under different stress states, is compared with those evaluated through the conventional mathematical models or experimental results selected from the literature. The results show that PMMA behaves viscoelastically under spherical explosion loading. With increasing the propagation distance of spherical wave, the radial stress decreases from 682 to 40 MPa, and the radial strain decreases from 59.5 × 10−3 to 4.2 × 10−3. Meanwhile, the average storage modulus of PMMA, at high frequencies after approximately 300 kHz, decreases from 7.14 to 5.97 GPa. This indicates that the complex elastic modulus of PMMA is dependent on the stress–strain state, and the published parameters of viscoelastic materials, determined by different experimental techniques under different stress–strain states, should be used with caution.