A micropolar shell model for hard‐magnetic soft materials

Abstract

Hard-magnetic soft materials (HMSMs) are particulate composites that particles with high coercivity are dispersed in a soft matrix. Since applying the magnetic loading induces a body couple in HMSMs, the resulting Cauchy stress is predicted to be asymmetric. Therefore, the micropolar continuum theory can be employed to capture the deformation of these materials. On the other hand, the geometries and structures made of HMSMs often possess small thickness compared to the overall dimensions of the body. Accordingly, in the present contribution, a 10-parameter micropolar shell formulation to model the finite elastic deformation of thin hard-magnetic soft structures under magnetic stimuli is developed. The proposed shell formulation allows for using three-dimensional constitutive laws without any need for modification to apply the plane stress assumption in thin structures. A nonlinear finite element formulation is also presented for the numerical solution of the governing equations. To alleviate the locking phenomenon, the enhanced assumed strain method is employed. Several examples are presented that demonstrate the performance and effectiveness of the proposed formulation.

Hard magnetics and soft materials—a synergy

“…A model based on micropolar continuum shell theory (where each material particle was coupled with a microstructure that can undergo micro-rotation) was proposed and verified with FE simulations [289,322]. Xing and Yong [323] investigated the viscoelastic effects of hMSMs in finite deformation and the instabilities they induce using a numerical model with a micro-mechanically motivated formulation.…”

“…The prevalent method in studying magneto-mechanical problems often assumes an ideal homogeneous magnetic field [272,289]. Yet, relying solely on this idealization might lead to significant disparities from observations in real setups.…”

The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

“…Their findings suggest that when modeling incompressible materials, the F-bar formulation can be computationally expensive, and the mixed displacementpotential formulation is somewhat sensitive to changes in the modulus. In the context of thin HMS materials, Dadgar-Rad and Hossain [329] developed a micro-based shell model for simulating their deformation. They extended the 7-degrees of freedom (DoF) formulation of Sansour [330] to a 10-DoF formulation scheme that accounted for the microrotation of the microstructure.…”

“…In the context of thin HMS materials, Dadgar–Rad and Hossain [ 329 ] developed a micro‐based shell model for simulating their deformation. They extended the 7‐degrees of freedom (DoF) formulation of Sansour [ 330 ] to a 10‐DoF formulation scheme that accounted for the microrotation of the microstructure.…”

Flutter analysis of laminated fiber-reinforced magnetorheological elastomer sandwich plate resting on an elastic foundation using an improved first-order shear deformation theory

“…Notably, Sun et al [12] have demonstrated that an augmentation in magnetic flux leads to smoother frequency response peaks, attributed to an amplified damping effect within the structure. Several other authors have investigated the viscoelastic modeling of MREs and their application [13][14][15][16][17][18].…”