Discrete schemes for treating hereditary problems of viscoelasticity and applications

Mathematical models for treating problems of linear viscoelasticity involving hereditary constitutive relations for compressible solids are presented, and their discretisation using finite element methods in space together with quadrature rules in time to treat the hereditary integrals is described. Theoretical error estimates in appropriate Sobolev space settings are given, both as they arise as a result of using a Gronwall inequality, and also from employing a more sensitive comparison theorem which (for the quasistatic problem, and under physically reasonable assumptions on the relaxation function) yields much sharper constants in the estimates. nge of applicability of the mathematical models, and hence the numerical schemes and error estimates are discussed in the context of various materials, primarily polymeric materials, and extensions of the techniques to the modelling of manufacturing processes such as thermoforming are presented.