Modeling inclusion problems in viscoelastic materials with the extended finite element method

Mechanical responses of viscoelastic materials with inclusions are studied. First, the incremental equations are formulated in time domain in the framework of the extended finite element method (XFEM), in which the enhancement functions are inserted in the approximation for representing inclusions. Next, the integration schemes are investigated for different type of elements in the extended finite element method. The full integration scheme is used for the low Poisson ratio (e.g. 0.3) problem, and the selective integration scheme treating the volumetric locking problem in the conventional finite element method (FEM) is extended in the present method for the high Poisson ratio (e.g. 0.49999) problem often encountered in viscoelastic materials. Numerical results show that the extended finite element method is efficient for complex problems involving viscoelastic materials even if nearly incompressible.