A time‐integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation
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The present study introduces a time-integration algorithm for solving a non-linear viscoelastic-viscoplastic (VE-VP) constitutive equation of isotropic polymers. The material parameters in the constitutive models are stress dependent. The algorithm is derived based on an implicit time-integration method (Computational Inelasticity. Springer: New York, 1998) within a general displacement-based finite element (FE) analysis and suitable for small deformation gradient problems. Schapery's integral model is used for the VE responses, while the VP component follows the Perzyna model having an overstress function. A recursive- iterative method (Int. J. Numer. Meth. Engng 2004; 59:25-45) is employed and modified to solve the VE-VP constitutive equation. An iterative procedure with predictor-corrector steps is added to the recursive integration method. A residual vector is defined for the incremental total strain and the magnitude of the incremental VP strain. A consistent tangent stiffness matrix, as previously discussed in Ju (J. Eng. Mech. 1990; 116:1764-1779) and Simo and Hughes (Computational Inelasticity. Springer: New York, 1998), is also formulated to improve convergence and avoid divergence. Available experimental data on time-dependent and inelastic responses of high-density polyethylene are used to verify the current numerical algorithm. The time-integration scheme is examined in terms of its computational efficiency and accuracy. Numerical FE analyses of microstructural responses of polyethylene reinforced with elastic particle are also presented. © 2009 John Wiley & Sons, Ltd.
author list (cited authors)
Kim, J. S., & Muliana, A. H.