Constitutive Modeling of Polymers Subjected to High Strain Rates

A biaxial test procedure is used to assess the constitutive properties of polymers in tension. The constitutive constants are derived for high strain rate applications such as those associated with crashworthiness studies. The test procedure is used in conjunction with a time- and strain-dependent quasi-linear viscoelastic constitutive law consisting of a Mooney-Rivlin formulation combined with Maxwell elements. The procedure is demonstrated by describing the stress vs. strain relationship of a rubber specimen subjected to a step-relaxation input. The constitutive equation is transformed from a nonlinear convolution integral to a set of first order differential equations. These equations, with the appropriate boundary conditions, are solved numerically to obtain transient stresses in two principal directions. Material constants for use in the explicit LS-Dyna non-linear finite element code are provided.