Simulation of rate dependent plasticity for polymers with asymmetric effects

Abstract

Polycarbonate is an amorphous polymer which exhibits a pronounced strength-differential effect between compression and tension. Also strain rate and temperature influence the mechanical response of the polycarbonate. The concept of stress mode dependent weighting functions is used in the proposed model to simulate the asymmetric effects for different loading speeds. In this concept, an additive decomposition of the flow rule is assumed into a sum of weighted stress mode related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The resulting evolution equations are updated using a backward Euler scheme and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation of the resulting set of constitutive equations is used in a finite element program for parameter identification. The proposed model is verified by showing a good agreement with the experimental data. After that the model is used to simulate the laser transmission welding process.

Thermoviscoplastic modelling of asymmetric effects for polymers at large strains

“…The simulation of asymmetric material behaviour is formulated in Shaban et al (2007) on the basis of a stress mode related approach within a geometrically linear theory. The key idea is an additive decomposition of the inelastic strain rate into a sum of stress mode related quantities, which can be investigated individually in the laboratory.…”

“…The concept of stress mode dependent weighting functions has been introduced in Mahnken (2003) for simulation of asymmetric effects within a geometrically linear theory and is applied to glassy polymers in Shaban et al (2007). The key idea here consists in an additive decomposition of the inelastic strain rate tensor.…”

“…The main purpose of the present work is to extend the concept introduced in Shaban et al (2007) to the geometrically nonlinear case taking into consideration the thermomechanical effects. To this end a flow rule is postulated within a thermodynamic consistent framework in a mixed variant formulation, which preserves the volumetric and deviatoric properties for the pull-back and push-forward operations.…”

“…To this end a flow rule is postulated within a thermodynamic consistent framework in a mixed variant formulation, which preserves the volumetric and deviatoric properties for the pull-back and push-forward operations. Then, in accordance with the approach of Shaban et al (2007) an additive decomposition of the flow rule is assumed into a sum of weighted stress mode dependent quantities. Upon performing pull-back and push-forward operations, the flow rule is also formulated with respect to different configurations.…”

“…In a further part of the paper numerical aspects are addressed. In particular the mixed-variant flow-rule is integrated by an exponential integration scheme, thus leading to a formulation in principal directions and allowing the algorithm developed in Shaban et al (2007) for the geometrically nonlinear case. The proposed integration scheme can further be implemented into a finite element program such as the UMAT subroutine of the commercial finite element program (ABAQUS-Version 6.5, 2004).…”