Two new variational principles for nonlinear magnetoelastostatics are derived. Each is based on use of two independent variables: the deformation function and, in one case the scalar magnetostatic potential, in the other the magnetostatic vector potential. The derivations are facilitated by use of Lagrangian magnetic field variables and constitutive laws expressed in terms of these variables. In each case all the relevant governing equations, boundary and continuity conditions emerge. These principles have a relatively simple structure and therefore offer the prospect of leading to finite-element formulations that can be used in the solution of realistic boundary-value problems.
- nonlinear elasticity
- variational principles
- smart materials
Bustamante, R., Dorfmann, A., & Ogden, R. W. (2008). On variational formulations in nonlinear magnetoelastostatics. Mathematics and Mechanics of Solids, 13(8), 725-745. https://doi.org/10.1177/1081286507079832