Flow of a Burgers fluid due to time varying loads on deforming boundaries

•We compare the properties of the solution for four standard viscoelastic models.•We present and test monolithic FEM solver for ALE formulation of viscoelastic model.•Simulations of technological problems like “rutting” of roadways or rolling.

In this paper we study three boundary-initial value problems within the context of four rate type viscoelastic constitutive models, the Maxwell model, the Oldroyd-B model, Burgers model and the generalized Burgers model. We consider challenging problems wherein the boundary is deforming with time. The flows lead to a complex system of partial differential equations that require the development of a robust numerical procedure based on the arbitrary Lagrangian–Eulerian method.