Modelling of the post yield response of amorphous polymers under different stress states

- This work proposes new constitutive laws for the post yield response of amorphous polymers under different stress states.
- An efficient numerical integration algorithm is presented.
- A closed-form analytical expression is derived for the consistent tangent operator.
- The experimental response of the polycarbonate is captured in the numerical results.

In this contribution, an elasto-viscoplastic constitutive model based on the single mode EGP (Eindhoven Glassy Polymer) model is proposed to describe the deformation behaviour of solid polymers subjected to finite deformations under different stress states. The polymeric material examined in this work is a specific commercial grade of Bisphenol, a polycarbonate called Makrolon 2607, for which there were experimental results available in the open literature for: uniaxial compression, plane strain compression and tensile test on a dumbbell shape specimen. The material properties of the original model are determined and calibrated from a uniaxial compression-loading test. Then, several numerical examples under different stress states are presented to illustrate the limitations of the single mode EGP model. A more general elasto-viscoplastic model is proposed, which preserves the isotropy of the original model, using the lode angle parameter to distinguish shear-dominated stress states and capture the material post yield response. The numerical treatment of the model, including the state update procedure and also the consistent tangent operator, required for the finite implementation of the model within an implicit finite element scheme, is presented. A comprehensive set of numerical examples is employed to compare the predictions of the original and new models against experimental results and to investigate the effect of the proposed modifications. The numerical results show that the proposed model provides a closer agreement with experimental evidence and opens the possibility for computational simulations of amorphous polymers under different stress states.