Advanced applications of the boundary element method to the analysis of polymers
The boundary element method was applied to polymer analysis. The comparison of two existing BEM approaches was carried out solving a benchmark viscoelastic problem numerically and comparing with the analytical solutions. The fundamental solutions due to both Heaviside and Dirac impulse were obtained for a generalised Maxwell SLS material model. A new time-domain BEM formulation for viscoelasticity was derived, and the computer program was implemented and validated. A mixed method for quasi-static viscoelasticity was proposed. Several viscoelastic problems were solved for the purpose of validating this formulation. Numerical results were compared with analytical solutions, and good agreement was achieved. The BEM was applied to viscoelastic fracture problems. The effectiveness of the adopted BEM modelling was tested on an elastic fracture problem. The time-dependent strain energy release rate and J-integral in viscoelasticity were evaluated under different loading conditions. The crack propagation velocity under constant strain loading was also obtained. Adopting BE methodology, an integral equation for nonlinear viscoelastic problems was derived. The method to remove the high singularity in the irreducible domain integral was proposed. A computer program for this nonlinear viscoelastic formulation was developed. A central-crack problem was solved and the expected effect of non-linearity on stress field was obtained.