Vector potential formulation for the three-dimensional finite element analysis of nonlinear electromechanical problems

Artem S. Semenov; Albrecht C. Liskowsky; Herbert Balke

doi:10.1117/12.715144

9 April 2007 Vector potential formulation for the three-dimensional finite element analysis of nonlinear electromechanical problems

Artem S. Semenov, Albrecht C. Liskowsky, Herbert Balke

Author Affiliations +

Proceedings Volume 6526, Behavior and Mechanics of Multifunctional and Composite Materials 2007; 65260A (2007) https://doi.org/10.1117/12.715144
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2007, San Diego, California, United States

Abstract

Ferroelectroelastic materials exhibit nonlinear behavior when they are subjected to high electromechanical loadings. Using the standard formulation with the scalar potential as electric nodal variable in the nonlinear finite element analysis can lead to a low convergence of the iteration procedures. Therefore the formulation with a vector potential as electric nodal variable is developed, which ensures a positive definite stiffness matrix. Solutions of boundary value problems using the scalar potential formulation lie on a saddle point in the space of the nodal degrees of freedom, whereas solutions for the vector potential formulation are in a minimum. Unfortunately, the latter solutions involving the "curlcurl" operator are non-unique in the three-dimensional case. A Coulomb gauge condition imposed on the electric vector potential improves the convergence behavior of nonlinear problems, and in combination with appropriate boundary conditions, it can enforce unique vector potential solutions. A penalized version of the weak vector potential formulation with the Coulomb gauge is proposed and tested on some numerical examples in ferroelectricity.

Citation Download Citation

Artem S. Semenov, Albrecht C. Liskowsky, and Herbert Balke "Vector potential formulation for the three-dimensional finite element analysis of nonlinear electromechanical problems", Proc. SPIE 6526, Behavior and Mechanics of Multifunctional and Composite Materials 2007, 65260A (9 April 2007); https://doi.org/10.1117/12.715144

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