中文摘要：

磁流变弹性体是一种在不同磁场条件下力学性能可控的智能材料。磁流变弹性体的模量为无磁场下材料的模量和磁场诱导产生的模量之和。运用基于周期性边界条件的代表性体积单元法，用理论和有限元两种方法对比研究了无磁场下磁流变弹性体的宏观弹性模量和剪切模量。通过引入 Maxwell 应力张量，研究了磁流变弹性体在不同磁感应强度下对磁场诱导产生的弹性模量和剪切模量的影响。用 RVE 的方法证明了，磁流变弹性体由于磁场诱导产生的弹性模量是负数，但总的弹性模量是正数，且其大小随磁感应强度的增大而增大。而其初始剪切模量则始终为正数，其大小随着磁场强度的增大而增大，这与偶极子理论推导得到的结论一致。

英文摘要：

Magnetorheological elastomers （MREs）are a class of smart materials whose mechanical properties can be changed under different magnetic field.The modulus of MREs is divided into the modulus under no mag-netic field and the modulus induced by the magnetic field.Based on the Periodic Boundary Condition （PBC）,a representative volume element （RVE）was proposed to calculate the macroscopic elastic modulus and shear modulus without a magnetic field.By introducing the Maxwell stress tensor,the elastic modulus and shear modulus induced by different magnetic flux induction of MREs were studied.By using the RVE approach it is proved that the elastic modulus induced by the magnetic flux density is negative,while the magnitude of elastic modulus of the whole MREs increases with increasing magnetic flux density.The shear modulus of MREs is positive and the magnitude of shear modulus increases with increasing magnetic flux density.The dipole theory is consistent with the conclusion.