a b s t r a c tThe paper outlines a new constitutive model and experimental results of rate-dependent finite elastic-plastic behavior of amorphous glassy polymers. In contrast to existing kinematical approaches to finite viscoplasticity of glassy polymers, the formulation proposed is constructed in the logarithmic strain space and related to a six-dimensional plastic metric. Therefore, it a priori avoids difficulties concerning with the uniqueness of a plastic rotation. The constitutive framework consists of three major steps: (i) A geometric pre-processing defines a total and a plastic logarithmic strain measures determined from the current and plastic metrics, respectively. (ii) The constitutive model describes the stresses and the consistent moduli work-conjugate to the logarithmic strain measures in an analogous structure to the geometrically linear theory. (iii) A geometric post-processing maps the stresses and the algorithmic tangent moduli computed in the logarithmic strain space to their nominal, material or spatial counterparts in the finite deformation space. The analogy between the formulation of finite plasticity in the logarithmic strain space and the geometrically linear theory of plasticity makes this framework very attractive, in particular regarding the algorithmic implementation. The flow rule for viscoplastic strains in the logarithmic strain space is adopted from the celebrated double-kink theory. The post-yield kinematic hardening is modeled by different network models. Here, we compare the response of the eight chain model with the newly proposed non-affine micro-sphere model. Apart from the constitutive model, experimental results obtained from both the homogeneous compression and inhomogeneous tension tests on polycarbonate are presented. Besides the load-displacement data acquired from inhomogeneous experiments, quantitative three-dimensional optical measurements of the surface strain fields are carried out. With regard to these experimental data, the excellent predictive quality of the theory proposed is demonstrated by means of representative numerical simulations.

a b s t r a c tThe 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.

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The non-linear inelastic response of glassy polymers is highly influenced by the three-dimensional deformation state, the temperature and the strain rate at which they are deformed. The contribution presents new experiments for different deformation modes which are carried out at different temperatures and rates on commercial bis-phenol A polycarbonate. Emphasis is put not only on the experimental results by themselves but also on the setup and the technique employed in the obtention of the data. The effect of temperature on the velocity with which the neck propagates along the gaged section of a flat specimen under tension is studied means a facility based on photogrammetry. From the homogeneous compression experiments a single set of material parameters appearing in a constitutive model based on the distributed free volume theory under the frame work of additive kinematics will be identified. The inhomogeneous experimental results serve then as a validation for 3-D simulations since the non-uniform strain distribution on the surfaces of both, simulations and experiments, can be compared. , show strong dependence on the temperature and the force under which they are deformed. Thus, the experimental procedure has to be regulated and strictly followed to deform the material always under the same conditions. For the uniaxial compression experiments, cylindrical specimens as shown in Fig.1a were employed. Barreling and shearing effects are common undesired phenomena appearing in compression experiments, leading to a softer response of the material. However, they can be avoided by placing a piece of teflon film on top and bottom of the specimen. In addition to that, a small amount of commercial liquid lubricant is placed between each teflon film and the metal plate. A convex spherical selfadjustable seat, which improves the alignment of the upper and lower metal plates as suggested by Arruda et al. [1], is placed on the lower concave plate. A picture of this arrangement is illustrated in Fig.1a. In the case of homogeneous plane strain experiments additional challenges arise due to a higher constraint in the deformation. It is a well documented fact that frictional effects in such an experiment can drastically influence the results. For this purpose the cubic specimen shown in Fig.1b was wrapped using two layers of teflon film with commercial liquid lubricant between the layers. This considerably alleviated the friction between the piece and the die. The upper punch against which the piece was compressed was not attached to the testing machine but left free for better alignment of the die and the punch (Fig.1c). All the experiments presented here have been performed using a servo-hydraulic MTS 810 Material Test System together with a MTS 651 Environmental Chamber. Care was taken on placing the necessary hardware as well as the specimens inside the environmental chamber prior to the experiment until they reached the desired temperature in order to avoid temperature differences between the test piece and the dies.