  A thermo-mechanical continuum theory is proposed for dynamically loaded
glassy polymers. The theory is based on an ansatz for the Helmholtz free energy
where both the deviatoric and the volumetric contributions to the free energy
are rate-dependent. The requirement that the free energy is fully rate
dependent arises from the need to model the full range of conditions between
those found in quasi-static applications to those common in high-rate shock
loading scenarios. Using a purely equilibrium equation of state is found to be
insufficient. The resulting model, called the Glassy Amorphous Polymer (GAP)
model, suitably captures the thermo-mechanical behavior of both equilibrium
properties, but also high-rate phenomena like the shock Hugoniot.
Polymethylmethacrylate (PMMA) is used as a representative polymer because it is
one of the few polymers where sufficient experiments have been done to
determine many of the parameters required by the GAP model. An important part
of the GAP model is the Hierarchical Flow Stress (HFS) model, which is shown to
accurately represent the stress-strain behavior of PMMA over a broad range of
strain rates and temperatures. The HFS model replicates the details of stress
plateau, softening, and hardening behavior observed in glassy amorphous
polymers. The theory is not restricted to isothermal conditions. Analysis is
devoted to several issues associated with a non-equilibrium equation of state
(EOS). Because data is insufficient for the full determination of the model's
non-equilibrium EOS, several plausible conditions called the quasi-equilibrium
hypothesis are put forth to complete the model. Comparisons of experimental and
theoretical results over a wide-range of loading rates and conditions are
reported.
