INCREMENTAL VISCOELASTIC THREE-DIMENSIONAL FEM BASED ON HERRMANN VARIATIONAL PRINCIPLE AND ITS APPLICATION

Incremental FEM is developed for incompressible and nearly incompressible viscoelastic problems and the three-dimensional analysis of SRM grain is presented. Firstly the constitutive relation of incompressible and nearly incompressible viscoelastic material is derived based on the Herrmann functional and correspondence principle. Afterwards three-dimensional finite element formulations are obtained using the principle of virtual work. Finally incompressible and nearly incompressible analysis of a hollow cylindrical grain with elastic restraint is presented. The results illustrate that the proposed method is valid for viscoelastic problems whose Poisson’s ratio is close or equal to 0.5, especially suitable for the structural analysis of solid propellant grain.