Nonuniform shear strains in torsional Kolsky bar tests on soft specimens

Abstract

Abstract : We investigate inertial effects in torsional Kolsky bar tests on nearly incompressible, soft materials. The results are relevant for materials with instantaneous elastic shear modulus on the order of 1 1000 kPa and density on the order of water. Examples include brain tissue and many other soft tissues and tissue surrogates. We have conducted one- and three-dimensional analyses and simulations to understand the stress and strain states that exist in these materials in a torsional Kolsky bar test. We demonstrate that the short loading pulses typically used for high strain-rate (e.g., 700 = s) tests do not allow the softer specimens to ring-up to uniform stress and strain states and that consequently the shear stress versus shear strain data reported in the literature are erroneous. We also show that normal stress components, which are present even in quasistatic torsion of nonlinear elastic materials, can be amplified in dynamic torsion tests on soft materials. Kolsky bar tests are widely used to study strain-rate effects in inelastic solids [Gray 2000; Chen and Song 2011]. In a compression Kolsky bar test, a relatively thin specimen is sandwiched between two bars. Impact at one end of the incident bar generates a compressive wave that travels along the bar, through the specimen, and into a transmission bar. The goal of this test is to subject the specimen to uniform uniaxial stress and uniform (biaxial) strain at a prescribed axial strain-rate. These uniform conditions can often be achieved after an initial ring-up period involving multiple wave reflections from the specimentransmission bar and specimen-incident bar interfaces. Once uniform conditions have been achieved in the specimen, the axial stress, axial strain, and axial strain-rate histories in the specimen can be deduced from strain gage measurements on the elastic bars: the axial stress is proportional to the strain in the transmission bar, and the axial strain-rate is proportional to the strain in t