A new finite-element formulation for electromechanical boundary value problems

In this paper, a new nite-element formulation for the solution of electromechanical boundary value problems is presented. As opposed to the standard formulation that uses scalar electric potential as nodal variables, this new formulation implements a vector potential from which components of electric displacement are derived. For linear piezoelectric materials with positive de nite material moduli, the resulting nite-element sti ness matrix from the vector potential formulation is also positive de nite. If the material is non-linear in a fashion characteristic of ferroelectric materials, it is demonstrated that a straightforward iterative solution procedure is unstable for the standard scalar potential formulation, but stable for the new vector potential formulation. Finally, the method is used to compute elds around a crack tip in an idealized non-linear ferroelectric material, and results are compared to an analytical solution