The concept of material forces in nonlinear electro-elastostatics

In this work we review the application of material forces in electro-elastostatics, especially in the computation of the so-called vectorial J-integral in crack problems. The formulations of material forces take into account the contribution of the outer space surrounding the body under consideration. It is shown that the contribution of the outer space is of importance when the polarization is relatively weak, for example in the case of electronic electro-active polymers, and that this contribution can be ignored if the polarization is much higher than that of the surrounding space like in most piezoelectric materials