A coupled BEM-FEM method for finite strain magneto-elastic boundary-value problems

International audienceThe first objective of this contribution is the formulation of nonlinear problems in magneto-elasticity involving finite geometry of the surrounding free space. More specifically for the magnetic part of the problem, the surrounding free space is described by means of a boundary integral equation for which boundary elements are used that are appropriately coupled with the finite element discretization used inside the material. The second objective is to develop a numerical strategy to solve the strongly coupled magneto-mechanics problem at hand. Herein we provide a staggered scheme consisting of a magnetostatic resolution employing the above coupled BEM-FEM procedure at fixed deformation, followed by a mechanical resolution at fixed magnetic fields. This decoupled method renders the whole solution strategy very appealing since, among others, the first BEM-FEM resolution is linear for some prototype models, and the remaining mechanical resolution is analogous to nowadays classical nonlinear elastostatic problems in the finite strain range. Some nonlinear boundary-value problems are simulated to demonstrate the applicability of the proposed framework