Saxena Prashant, Hossain Mokarram, Steinmann Paul
Chair of Applied Mechanics , University of Erlangen-Nuremberg , Paul-Gordan Strasse 3, Erlangen 91052, Germany.
Proc Math Phys Eng Sci. 2014 Jun 8;470(2166):20140082. doi: 10.1098/rspa.2014.0082.
Iron-filled magnetorheological polymers, when cured in the presence of a magnetic field, result in having a transversely isotropic structure with iron particles forming chains along the direction of applied magnetic induction. In this work, we model the magneto-viscoelastic deformation (and magnetization) process of such polymers. Components of the deformation gradient and the applied magnetic induction in the direction of anisotropy are considered to be additional arguments of the energy density function. The existence of internal damping mechanisms is considered by performing a multiplicative decomposition of the deformation gradient and an additive decomposition of the magnetic induction into equilibrium and non-equilibrium parts. Energy density functions and evolution laws of the internal variables are proposed that agree with the laws of thermodynamics. In the end, we present solutions of some standard deformation cases to illustrate the theory. In particular, it is shown that the orientation of resultant magnetic field and principal stress directions change with time owing to viscoelastic evolution.
填充铁的磁流变聚合物在磁场存在下固化时，会形成横向各向同性结构，其中铁颗粒沿外加磁感应方向形成链状。在这项工作中，我们对这类聚合物的磁粘弹性变形（和磁化）过程进行建模。变形梯度的分量以及外加磁感应在各向异性方向上的分量被视为能量密度函数的附加自变量。通过对变形梯度进行乘法分解以及将磁感应分解为平衡部分和非平衡部分的加法分解，来考虑内部阻尼机制的存在。提出了与热力学定律相符的能量密度函数和内部变量的演化规律。最后，我们给出一些标准变形情况的解以说明该理论。特别地，结果表明由于粘弹性演化，合成磁场的方向和主应力方向会随时间变化。
