XFEM modeling and homogenization of magnetoactive composites

This paper addresses the application of the extended finite element method (XFEM) to the modeling of two-dimensional coupled magneto-mechanical field problems. Continuum formulations of the stationary magnetic and the coupled magneto-mechanical boundary problem are outlined, and the corresponding weak forms are derived. The XFEM is applied to generate numerical models of a representative volume element, characterizing a magnetoactive composite material. Weak discontinuities occurring at material interfaces are modeled numerically by an enriched approximation of the primary field variables. In order to reduce the complexity of the representation of curved interfaces, an element local approach is proposed which allows an automated computation of the level set values. The composite's effective behavior and its coupled magneto-mechanical response are computed numerically by a homogenization procedure. The scale transition process is based on the energy equivalence condition, which is satisfied by using periodic boundary conditions.