Numerical finite element formulation of the Schapery non-linear viscoelastic material model

Rami M. Haj-Ali*, Anastasia H. Muliana

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This study presents a numerical integration method for the non-linear viscoelastic behaviour of isotropic materials and structures. The Schapery's three-dimensional (3D) non-linear viscoelastic material model is integrated within a displacement-based finite element (FE) environment. The deviatoric and volumetric responses are decoupled and the strain vector is decomposed into instantaneous and hereditary parts. The hereditary strains are updated at the end of each time increment using a recursive formulation. The constitutive equations are expressed in an incremental form for each time step, assuming a constant incremental strain rate. A new iterative procedure with predictor-corrector type steps is combined with the recursive integration method. A general polynomial form for the parameters of the non-linear Schapery model is proposed. The consistent algorithmic tangent stiffness matrix is realized and used to enhance convergence and help achieve a correct convergent state. Verifications of the proposed numerical formulation are performed and compared with a previous work using experimental data for a glassy amorphous polymer PMMA.

Original languageEnglish
Pages (from-to)25-45
Number of pages21
JournalInternational Journal for Numerical Methods in Engineering
Issue number1
StatePublished - 7 Jan 2004
Externally publishedYes


  • Finite element
  • Iterative
  • Non-linear
  • Recursive
  • Schapery
  • Viscoelastic


Dive into the research topics of 'Numerical finite element formulation of the Schapery non-linear viscoelastic material model'. Together they form a unique fingerprint.

Cite this