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.

The nucleus of the eukaryotic cell contains a large pool of lipids together with structural proteins and genomic DNA. The project aim was to develop simple and robust lipid and DNA models that will allow for these complex molecules to be mixed together in order to elucidate the possible interactions. The large percentage of lipids found within the nucleus makes it likely that they exist in aggregates, although the actual role and structure in which they exist is unknown. While there has not been substantial work done to model such interactions between lipids and DNA in order to better understand the interactions within the nucleus, a substantial body of work exists on lipid/DNA complexes in relation to gene therapy. These simulations in many cases however, are too simple and the structures formed are pre-imposed to a certain degree. Our model would attempt to simulate these interactions without such pre-imposed conditions relying solely on interactions between the particles to drive the structures being formed. A coarse graining approach in which several groups of atoms are subsumed into single interaction sites was deemed suitable given the complexity of modelling a mixture of DNA and lipids, together with the solvent and ion environment. In this regard new models of lipids, DNA, ion and solvent models were developed in a purpose built molecular dynamics package called LANKA-Lipid And Nucleic acid Komputer Algorithm. The lipids in the model are represented as polar ellipsoids and the solvent as spheres with dipoles embedded within them. The interactions between the lipids and solvent are modelled using the Gay Berne potential. The developed lipid model was able to self assemble into a stable bilayer phase and reproduce many bilayer properties of a liquid crystal phase. The model was then extended to capture some of the other lipid phases seen in nature, including lyotropic phase transitions. A simple study of lipid mixtures has also been undertaken during this period. The importance of considering multicomponent lipid systems has increasingly been highlighted in the literature to make the lipid models more realistic. The developed lipid models are simple enough to extend and attempt to simulate the formation of lipid rafts and domain formation. Simulation of DNA in the past has largely focused on atomistic studies. While these have proved valuable they do not consider the macroscopic length scales of the molecule. Simplified models trying to capture long length scales have had to compromise on the molecular level detail. Coarse grain models while trying to bridge the gap have also remained largely idealistic in nature.