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Abstract
In this sequel to the first paper (Málek et al., 2014. International Journal of Pavement Engineering), in which we identified a generalisation of the model due to Burgers which was corroborated against two sets of experiments, including a challenging one showing distinctly different relaxation times for shear and normal stresses, we solve several time-dependent boundary value problems wherein the boundary of the material is deforming, that have relevance to applications involving asphalt. Problems wherein the boundary is subject to time-varying compressive loads such as those due to moving automobiles and the attendant rutting, and the compaction due to rollers are considered in additions to other problems.
Acknowledgements
K.R. Rajagopal thanks the Office of Naval Research and the National Science Foundation for its support.
Notes
1. Here the relaxation times and
are used instead of the ratios
and
that were used in the paper by Málek et al. (Citation2014).
2. Using the assumptions mentioned above the density is not presented in the simplified equations computed in Málek et al. (Citation2014) and so was not used.
3. Q2 stands for a continuous biquadratic element, for a discontinuous bilinear element.
4. We use a thick layer of viscoelastic material in order to capture the elastic response. Later, we shall use much thinner domains as the application we have in mind are pavements which are usually modelled as rate type viscoelastic fluids, which are much wider than thick.