On 3-D coupled BEM–FEM simulation of nonlinear electro-elastostatics

In this work the numerical simulation of nonlinear electro-elastostatics is considered with a special focus on the influence of the free space surrounding an electro-sensitive body. The influence of the free space on the electric field and on the deformation field inside an electro-sensitive body can become highly important for many materials and can change profoundly the simulation results. In order to take into account this influence, the free space must be simulated by using, for example, the finite element method (FEM) or the boundary element method (BEM). A coupled BEM–FEM approach is employed here to exploit the advantage of the finite element method in solving nonlinear problems and the advantage of the boundary element method in dealing with infinite domains. Numerical studies using this approach show that for materials with low electric permittivity, the free space can have a huge impact on the simulated electric and deformation fields. The same observation is expected for the general case of nonlinear electro-elasticity and nonlinear electro-viscoelasticity and constitutes the direction for future works.