A new methodology for determining the mechanical behavior of polymers exploiting Lie symmetries: application to a stick-like material

Dynamic tests at high strain rates involving a weight dropped from different heights (1s-1≲ε˙≲20s-1) have been carried out on acrylic stick cylindrical specimens, in order to determine their mechanical behavior. The experimental device consists of a mass M   dropped from an initial height H0H0, impacting the plate of a compressive apparatus lying on the upper surface of the specimen. The stress and the strain are derived from measurements of the compressive force and relative displacement of the upper plate. Regarding theoretical aspects, a novel strategy for a constitutive model, based on a combination of measurements and the use of Lie groups analysis, is proposed. The methodology consists in condensing experimental data obtained for different initial drop heights into master curves, which are further interpreted as Lie symmetries of the postulated constitutive equation for the stick sample. The constitutive model involves two functions of the strain rate, obtained from the Lie symmetry condition; this condition expresses the postulated invariance of the material behavior when the impact conditions vary. The material parameters are obtained from the adjustment of the constitutive model with experimental data. The model is found to be similar to the one used in [Naik, N.K., Perla, Y., 2008. Mechanical behavior of acrylic under high strain rate tensile loading. Polymer Testing 27, 504–512] for acrylic. Predictions of the model at constant strain rates show a viscoelastic behavior typical of such polymers.