Numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids
For quasistatic stress problems, two alternative constitutive relationships expressing the stress in a linear isotropic viscoelastic solid body 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 space domain using a finite element method, and semi-discrete error estimates are presented corresponding to each constitutive relationship. Through the use of quadrature rules and finite difference replacements, each semi-discrete scheme is fully discretized into the time domain so that two practical algorithms suitable for the numerical stress analysis of linear viscoelastic solids are produced. The semi-discrete estimates are then also extended into the time domain to give spatially \({\mathcal H}^1\) error estimates for each algorithm.
scientific article; zbMATH DE number 881012