A simultaneous solution procedure for strong interactions of generalized Newtonian fluids and viscoelastic solids at large strains

The paper presents a methodology for numerical analyses of coupled systems exhibiting strong interactions of viscoelastic solids and generalized Newtonian fluids. In the monolithic approach, velocity variables are used for both solid and fluid, and the entire set of model equations is discretized with stabilized space–time finite elements. A viscoelastic material model for finite deformations, which is based on the concept of internal variables, describes the stress-deformation behaviour of the solid. In the generalized Newtonian approach for the fluid, the viscosity depends on the shear strain rate, leading to common non-Newtonian fluid models like the power-law. The consideration of non-linear constitutive equations for solid and fluid documents the capability of the monolithic space–time finite element formulation to deal with complex material models. The methodology is applied to fluidconveying cantilevered pipes in order to determine the influence of material non-linearities on stability characteristics of coupled systems