Coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory

The paper outlines a constitutive model for finite thermo-visco-plastic behavior of amorphous glassy polymers and considers details of its numerical implementation. In contrast to existing kinematical approaches to finite plasticity of glassy polymers, the formulation applies a plastic metric theory based on an additive split of Lagrangian Hencky-type strains into elastic and plastic parts. The analogy between the proposed formulation in the logarithmic strain space and the geometrically linear theory of plasticity, makes this constitutive framework very transparent and attractive with regard to its numerical formulation. The characteristic strain hardening of the model is derived from a polymer network model. We consider the particularly simple eight chain model, but also comment on the recently developed microsphere model. The viscoplastic flow rule in the logarithmic strain space uses structures of the free volume flow theory, which provides a highly predictive modeling capacity at the onset of viscoplastic flow. The integration of this micromechanically motivated approach into a three-dimensional computational model is a key concern of this work. We outline details of the numerical implementation of this model, including elements such as geometric pre- and post-transformations to/from the logarithmic strain space, a thermomechanical operator split algorithm consisting of an isothermal mechanical predictor followed by a heat conduction corrector and finally, the consistent linearization of the local update algorithm for the dissipative variables as well as its relationship to the global tangent operator. The performance of the proposed formulation is demonstrated by means of a spectrum of numerical examples, which we compare with our experimental findings.