Approximation of Nonlinear Unloading Effects in the Strain Rate Dependent Deformation Analysis of Polymer Matrix Materials Utilizing a State Variable Approach

An experimental and analytical program is carried out to explore key behaviors in the loading and unloading behavior of polymers. Specifically, the effects of strain rate and hydrostatic stresses on the nonlinear portions of the deformation response are examined. Tension, compression, and shear load only and load/unload tests are conducted on a representative polymer across a range of strain rates, and key features of the experimental results are identified. To conduct a preliminary exploration of how the key features of the deformation response could be simulated analytically, a previously developed set of constitutive equations, which were developed to analyze the strain rate dependent, nonlinear deformation of polymers including the effects of hydrostatic stresses, were modified in order to approximate key features of the nonlinear unloading behavior observed in the polymer. The constitutive relations are based on state variable constitutive equations originally developed for metals. The nonlinear unloading observed in the experiments is approximated by reducing the unloading modulus of the material as the effective inelastic strain is increased. The effects of the hydrostatic stress state on the unloading modulus are also simulated analytically. To examine the revised formulation, the loading and load/unload responses of the representative polymer in tension, compression, and shear are examined at several strain rates. Results computed using the developed constitutive equations were found to correlate reasonably well with the experimental data.