Xfem modeling and the effective behavior of magnetorheological elastomers

TLDR: In this paper, an extended finite element method (XFEM) is applied to the modeling of coupled magneto-mechanical field problems under the aspects of finite deformations and physical nonlinearities.

Abstract: The present contribution addresses the application of the extended finite element method (XFEM) to the modeling of coupled magneto-mechanical field problems under the aspects of finite deformations and physical nonlinearities. Based on experiments model parameters are identified and used to simulate the effective behavior of magnetorheological elastomers (MRE) under characteristic magnetic and mechanical loadings. 1. Motivation This study is motivated by the need to develop a multiscale modeling approach for novel composite materials with magnetically switchable properties. On the microscale the proposed composite material consists of a polymeric matrix with embedded magnetizable particles. Such materials are called MRE. The rheological properties of the MRE can be altered by the application of an external magnetic stimulus. This so called magnetorheological effect is caused by magnetic and mechanical interactions between the micron sized particles. 2. Field equations The problem is described in the framework of finite deformations. For the stationary magnetic field the Maxwell equations are presented in the current confi- guration of deformable media together with appropriate transformation relations of the magnetic field variables linking them to a reference configuration. The particles of the MRE exhibit a nonlinear magnetization behavior with saturation at high values of the magnetic field but negligible hysteresis effects. Beside a linear approach a phenomenological model is used to describe this magnetic nonlinearity. Based on a microscopically motivated model for the electrodynamics of conti- nua (1) the balance of momentum is expressed in terms of the total stress tensor. It consists of a mechanical and a magnetic part. However, this decomposition is not unique. A crucial task is the formulation of thermodynamically consistent consti- tutive equations for the finite deformations framework which should coincide in the limit case with the geometric linear model used in (2,3). The nonmagnetic polymeric matrix of the MRE is modeled by a compressible neo-Hookean material. The magneto-mechanical coupling is considered to be weak. Therefore, the stationary magnetic and the mechanical problem are solved consecutively and are coupled by the deformation, magnetic loads and the material. 3. Numerical solution strategy and it's validation Generating numerical models is a problem in particular if complex local material structures are considered. In this case, the application of the standard FEM tends to result in an extensive modeling and meshing effort including problems related to distorted elements. The XFEM (2,4) offers the possibility to use