The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid. For some applications, such as modeling biological materials, capturing internal boundary viscosity is important. We present numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow. We find that t...

We deal with initial-boundary value problems describing vertical vibrations of viscoelastic von Kármán-Donnell shells with a rigid inner obstacle. The short memory (Kelvin-Voigt) material is considered. A weak formulation of the problem is in the form of the hyperbolic variational inequality. We solve the problem using the penalization method.

In this paper, a nonlinear axially moving string with the Kelvin-Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a certain critical value. The proof is established by showing that a Lyapunov function corresponding to the string decays to zero exponentially. It is also shown ...

In this paper, the classic Kelvin-Voigt model coupled thermo-viscoelasticity model of hollow and solid spheres under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general fo...

Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The...

Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The...