Solution strategies for FEM analysis with nonlinear viscoelastic polymers

The Schapery model is a very common model for nonlinear viscoelastic behaviour of polymers. Therefore this model has been implemented with a user subroutine into the FEM package MARC. Since explicit integration is relatively fast but is often accompanied by numerical instabilities and implicit integration is relatively slow but numerically stable, combined strategies have been programmed. Results show that the viscoelastic response of complex products can be calculated without numerical instabilities and with short calculation times. Full viscoelastic calculations and calculations using creep isochrones on dead weight loading of an HDPE bottle crate only differ from the onset of creep buckling.

[1]  Ian D. Moore,et al.  Finite Element Modelling of Inelastic Deformation of Ductile Polymers , 1997 .

[2]  W. Szyszkowski,et al.  An effective method for non-linear viscoelastic structural analysis , 1990 .

[3]  O. C. Zienkiewicz,et al.  A numerical method of visco-elastic stress analysis , 1968 .

[4]  C. Buckley,et al.  The onset of nonlinear viscoelasticity in multiaxial creep of glassy polymers: A constitutive model and its application to PMMA , 1998 .

[5]  Herbert Leaderman,et al.  Large longitudinal retarded elastic deformation of rubberlike network polymers , 1962 .

[6]  C. G. Broyden.  A Class of Methods for Solving Nonlinear Simultaneous Equations , 1965 .

[7]  Ashley F. Emery,et al.  Finite element modeling of the time‐dependent behavior of nonlinear ductile polymers , 1991 .

[8]  Herbert Leaderman,et al.  Elastic and creep properties of filamentous materials and other high polymers , 1943 .

[9]  J. Beijer,et al.  Modelling of creep behaviour in injection-moulded HDPE , 2000 .

[10]  Thomas J. R. Hughes,et al.  Unconditionally stable algorithms for quasi-static elasto/visco-plastic finite element analysis , 1978 .

[11]  O. C. Zienkiewicz,et al.  The finite element method, fourth edition; volume 2: solid and fluid mechanics, dynamics and non-linearity , 1991 .

[12]  C. Buckley,et al.  The relation between linear and non-linear viscoelasticity of polypropylene , 1974 .

[13]  D. R. Mears,et al.  Effects of Hydrostatic Pressure on the Mechanical Behavior of Polyethylene and Polypropylene , 1969 .

[14]  M. Henriksen,et al.  Nonlinear viscoelastic stress analysis—a finite element approach , 1984 .

[15]  O. C. Zienkiewicz,et al.  VISCO-PLASTICITY--PLASTICITY AND CREEP IN ELASTIC SOLIDS--A UNIFIED NUMERICAL SOLUTION APPROACH , 1974 .

[16]  M. F. Ahmad,et al.  A material point time integration procedure for anisotropic, thermo rheologically simple, viscoelastic solids , 1998 .

[17]  Richard Schapery.  On the characterization of nonlinear viscoelastic materials , 1969 .

[18]  A. Bakker,et al.  3-D schapery representation for non-linear viscoelasticity and finite element implementation , 1996 .

[19]  A. I. Leonov.  Nonequilibrium thermodynamics and rheology of viscoelastic polymer media , 1976 .

[20]  J. Z. Zhu,et al.  The finite element method , 1977 .

[21]  N. G. Mccrum,et al.  Principles Of Polymer Engineering , 1988 .

[22]  A. Ralston.  A first course in numerical analysis , 1965 .

[23]  I. Cormeau,et al.  Numerical stability in quasi‐static elasto/visco‐plasticity , 1975 .

[24]  P. R. Pinnock,et al.  The mechanical properties of solid polymers , 1966 .