Optimal pulse shapes for SHPB tests on soft materials

For split Hopkinson pressure bar (SHPB) tests on soft materials, the goals of homogeneous deformation and uniform uniaxial stress in the specimen present experimental challenges, particularly at higher strain rates. It has been known for some time that attainment of these conditions is facilitated by reducing the thickness of the specimen or by appropriately shaping the loading pulse. Typically, both methods must be employed. Pulse shapes are often tailored to deliver a smooth and sufficiently slow rise to a constant axial strain rate, as this promotes equality of the mean axial stress on the two faces of the specimen, a condition referred to as dynamic equilibrium. However, a constant axial strain rate does not eliminate radial acceleration, which may result in large radial and hoop stresses and large radial variations in the radial, hoop and axial stresses. An approximate analysis (assuming homogeneous deformation and incompressibility) indicates that these radial inertia effects would be eliminated if the radial strain rate were constant. Motivated by this result, we consider loading pulses that deliver a constant radial strain rate after an initial ramp-up. The corresponding axial strain rate is no longer constant on any time interval, but for sufficiently thin specimens the resulting departure from dynamic equilibrium may be small enough to be tolerable. This is explored here by comparing the analytical predictions for the conventional and "optimal" loading pulse shapes with corresponding numerical simulations of SHPB tests on a soft, nearly incompressible material.