A Tensor‐Based Approach for Coupled Magneto‐Mechanical Modeling of Magneto‐Active Elastomers

Magneto‐active elastomers (MAEs) are smart composite materials whose mechanical response can be controlled by external magnetic fields, which makes them attractive for applications such as adaptive actuators, tunable vibration isolators, and sensing devices. In this contribution, a tensor‐based constitutive framework for the coupled magneto‐mechanical modeling of anisotropic soft MAEs is proposed. The formulation is developed for materials with chain‐like particle structures and provides a unified description of isotropic, transversely isotropic, and orthotropic material behavior. In contrast to invariant‐based approaches, where isotropic and anisotropic coupling effects are introduced through separate scalar terms, the present framework employs second‐order constitutive tensors to represent directional magnetic and magneto‐mechanical properties in the energy function. The model is formulated within finite‐strain magneto‐elasticity and is evaluated by comparison with an invariant‐based anisotropic formulation. Numerical examples for a bilayer cantilever beam and a cylindrical MAE sample demonstrate that the proposed tensor‐based approach reproduces the response of the invariant‐based formulation with high accuracy, while providing a more general representation of anisotropic coupling effects. The results further illustrate the influence of particle‐chain orientation, anisotropic stiffness, and buckling on the magnetostriction behavior of MAEs.