- A framework is presented for analyzing the low temperature inelastic behavior of amorphous glassy polymers with full account taken of finite deformations and inertial effects. Two classes of viscoplastic constitutive equations are explored: rate-sensitive Drucker-Prager type models and an elaborate macromolecular model. These constitutive equations are integrated using a forward gradient time integration scheme. The capabilities of the framework are illustrated by finite element solutions of initial/boundary-value problems under plane-strain conditions. The discretized equations of motion are integrated using a Newmark algorithm. Three illustrative benchmark problems are used to evaluate the proposed implementation: dynamic shear band formation and propagation in a polymer under compression, dynamic response of a polymer under impact and quasi-static response of a polymer composite plate with a hole under uniaxial tension along fibers. 2008 Elsevier B.V. All rights reserved.