A Comparison of Hereditary Integral and Internal Variable Approaches to Numerical Linear Solid Viscoelasticity

abstract This article rst compares the mathematical models obtained when a problem of linear quasistatic solid viscoelasticity is modelled by: (i) a hereditary integral with Prony series; and, (ii) an evolution equation for internal strain variables. We then connrm that while the models are the same, the numerical approximations arising from them will, in general, be diierent. This suggests the need for a posteriori error estimates for the internal variable formulation so that viscoelasticity problems may be eeciently and reliably simulated. Acknowledgement The authors are pleased to acknowledge the stimulation of their interest in internal variable methods in the viscoelasticity context derived from conversations with Dr A R Johnson.