A boundary value problem arising from nonlinear viscoelasticity: Mathematical analysis and numerical simulations

The large deformations of solid structures are necessarily described by nonlinear constitutive equations and its effective calculation leads to nonlinear boundary value problems. In this article we apply the successive linear approximation method by considering the relative Lagrangian formulation to describe the deformations of a nearly incompressible viscoelastic material. We prove the existence, uniqueness and regularity of weak solutions for the boundary value problem associated with each step of the method and we perform numerical simulations for the problem of borehole closing in well drilling.