Research About Numerical Modeling And Constitutive Modeling Of Magnetorheological Elastomers Under Finite Deformation

Magnetorheological elastomers (MREs) are a new kind of smart materials, whichmake micron-sized ferromagnetic particles being incorporated into polymer andsolidified under magnetic field. Anisotropic MREs consist of a chain or pillar structureand rubber matrix. If curing in the absence of a magnetic field, isotropicmagnetorheological elastomers can be obtained. As macro modulus of MREs can varywith the magnetic flux density, MREs can be widely used in variable stiffness apparatus.MREs not only have the characteristics of controllable, reversible and rapid response,but also have good stability. By means of theoretical analysis, finite element analysisand experimental methods, the basic mechanical properties of the MREs are studied andnew types of strain energy functions are developed. Main research contents and resultsare as follows:1) By using the Representative Volume Element (RVE) based on the PeriodicBoundary Condition (PBC), the macro Young’s modulus and shear modulus oforthotropic MREs under zero magnetic field are studied. The results of numericalmodeling are consistent with the results calculated from the analytical Mori-Tanalamodel and Double-Inclusions model, which are based on the Eshelby theory. The macromodulus obtained by using numerical modeling and Mori-Tanala model andDouble-Inclusions are more accurate than the Voigt model (homogeneous strain) andReuss model (homogeneous stress). The initial Young’s modulus and shear modulus ofthe particulates filler material have impact on the mechanical properties of rubber.2) By introducing a Maxwell stress tensor, the Young’s modulus and shear modulusof anisotropic MREs are studied under different magnetic flux density. By using theRVE approach, it is proved that the Young’s modulus induced by the magnetic fluxdensity is negative, while the magnitude of Young’s modulus of the whole MREsincreases with increasing magnetic flux density. The shear modulus of MREs is positiveand the magnitude of shear modulus increases with increasing magnetic flux density. Itis consistent with the conclusion derived by the dipole theory.3) Using an advanced three-dimensional (3-D) Digital Image Correlation(XJTUDIC) system for deformation measurement, a tensile test is carried out on therubber matrix. Several types of strain energy density function of hyperelastic materialare studied under large deformation. Commercial FEA software package ABAQES isused to implement the modeling taking advantage of the uniaxial test results. Yeoh, Neo-Hookean and Mooney-Rivlin hyperelastic models are chosen for the purose offitting with experiments data. It is found that simulation results from the Mooney-Rivlinmodel are in good agreemnet with experiments resilts.4) Based on the invariant theory of continuum mechanics for fiber reinforcecomposites by Spencer and taking into account the bending effect, an anisotropicnonlinear hyperelastic constitutive model for MREs without magnetic filed is developedfor rubber–cord reinforced composite material. Through theoretical and experimentalanalysis, it is demonstrated that the traditional finite deformation theory of thefiber-reinforced composite material is not suitable for bending deformation. Thebending stiffness should be taken into consideration and it is further verified by thebending simulation.5) A new type of strain energy density function for charactering the materialbehavior of anisotropic MREs working under the magnetic field is developed by addingtwo invariants with respect to the direction of magnetic field and direction of particleschains, respectively. The mechanical performances utilizing the new constitutive modelunder tensile and simple shear condition are investigated.