Stochastic behavior of polymers at high strain rates

This dissertation introduces a method for modeling the rate-dependent effects in polymer chains, based on the use of stochastic techniques. This method of modeling polymers accounts for the configurational nonequilibrium that occurs at high strain rates.; A combined Langevin-Liouville derivation results in conservation equations for a single polymer chain. From these equations, we recover the thermal force in the polymer in the limit of quasi-static behavior of the chain. Additional modifications are included to account for the behavior of the chain in the case of limiting extensibility. For static circumstances, the equations provide an excellent match with known behavior of polymers.; A reduction of the three-dimensional equations to a one-dimensional formulation is described. This equation is used in the exploration of the mechanical response of a polymer chain under various rate-dependent loadings. From the results, a single chain constitutive equation is developed. The derivation of this equation introduces a non-equilibrium parameter that describes configurational nonuniformity in the chain.; The macro-scale behavior of the polymer exhibits a complicated response from the interaction of the single chains and the network in which they lie. We develop a homogenization method based on the Voigt assumption, which gives an upper bound on the stress when the strain field is prescribed. The homogenization accounts for the explicit contribution to the stress from each chain by using the single chain constitutive equation projected along the orientation of each chain. The orientation of each chain is allowed to change based on the deformation applied. This causes the chains to rotate in the direction of loading. The result is a stiffening the material response, which is seen as a configurational hardening effect in the stress-strain curve.; A numerical implementation of the homogenization method is used to compute solutions that are compared with rate-dependent experimental data for plasticized Estane. The method is also used to predict the response of the material under more complicated loadings. The results of these complicated loadings illustrate the ability of the homogenization method to provide an anisotropic response in polymers.