Correction method and verification of radial inertia and friction effects under a unified deformation framework in SHPB experiments on soft materials

During the split Hopkinson pressure bar (SHPB) experiments, significant measurement errors can arise due to severe radial inertia and friction effects. Previous studies have developed various correction methods for these two effects. However, these methods have problems such as over-reliance on the volume invariance assumption of the specimen and inconsistent assumptions on the deformation patterns of the two effects, which limit their universality and effectiveness. Therefore, this paper integrates the radial inertia effect and friction effect in a unified deformation framework through reasonable assumptions, and proposes a method to correct the specimen from a complex stress state to a uniaxial stress state. SHPB numerical simulation experiments demonstrate that this method effectively eliminates the combined effects of radial inertia and friction on measurement results for both elastic and viscoelastic materials, including the size effect associated with these two factors. Additionally, the paper presents a scheme to determine the friction coefficient using the size effect of the specimens when the friction coefficient between the specimen and the bar is unknown. Finally, the method was applied to correct the stresses measured in SHPB experiments on silicone rubber of different diameters. It successfully eliminated discrepancies in the stress-strain relationships between specimens of various sizes and determined a friction coefficient that fell within a reasonable range.