11 July 2002 New finite element formulation for electromechanics
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Abstract
A new finite element formulation for the solution of electromechanical boundary value problems is presented. As opposed to the standard formulation that utilizes a 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 definite material moduli, the resulting finite element stiffness matrix from the vector potential formulation is also positive definite. If the material is nonlinear 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 fields around a crack tip in an idealized non-linear ferroelectric material, and results are compared to an analytical solution.
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Chad M. Landis, "New finite element formulation for electromechanics", Proc. SPIE 4699, Smart Structures and Materials 2002: Active Materials: Behavior and Mechanics, (11 July 2002); doi: 10.1117/12.475012; https://doi.org/10.1117/12.475012
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