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.