A superstable time-discrete scheme for the numerical integration of viscous constitutive equations

The general framework of the paper deals with the finite element modelling of mechanical problems involving viscous materials such as bitumen or bituminous concrete. Its aim is to present a second-order-accurate discrete scheme which remains unconditionally superstable when used for the time discretization of the linear and non-linear viscoelastic constitutive equations considered. After stating the space- and time-continuous mechanical problem we focus on the time discretization of these equations, considering three different schemes. For both of them sufficiently small values of the time step are required in order to ensure the superstability, whereas the third remains unconditionally superstable. Eventually, some numerical results are presented. © 1998 John Wiley & Sons, Ltd.