NUMERICAL TECHNIQUES FOR THE TREATMENT OF QUASI-STATIC VISCOELASTIC STRESS PROBLEMS IN LINEAR ISOTROPIC SOLIDS

For quasistatic stress problems two alternative constitutive relations hips expressing the stress in a linear isotropic viscoelastic solid bo dy as a linear functional of the strain are available. In conjunction with the equations of equilibrium, these form the mathematical models for the stress problems. These models are first discretized in the spa ce domain using a finite element method and semi-discrete error estima tes are presented corresponding to each constitutive relationship. Thr ough the use respectively of quadrature rules and finite difference re placements each semi-discrete scheme is fully discretized into the tim e domain so that two practical algorithms suitable for the numerical s tress analysis of linear viscoelastic solids are produced. The semi-di screte estimates are then also extended into the time domain to give s patially H-1 error estimates for each algorithm. The numerical schemes are predicted on exact analytical solutions for a simple model proble m, and finally on design data for a real polymeric material.