This work investigates the primary sinusoidal bifurcation wrinkling response of single- and multi-layered magnetorheological elastomer (MRE) film–substrate systems subjected to combined transverse applied magnetic fields and in-plane biaxial pre-compression. A recently proposed continuum model that includes the volume fraction of soft-magnetic particles is employed to analyze the effect of the magnetic properties upon the bifurcation response of the system. The analysis is built in a highly versatile manner using a finite-element discretization approach along the direction of the applied magnetic field and Fourier expansions along the infinite in-plane layer directions. This allows for a seamless investigation of various multi-layered structures. First, we analyze the effect of biaxial pre-compression upon the critical magnetic field for a film–substrate system and for various mechanical stiffness ratios. We observe a kink in the critical magnetic curves and a reflection in the corresponding wave numbers as they cross the equi-biaxial pre-compression regime. Subsequently, we consider a MRE film bonded to a MRE substrate and study the effect of the particle volume fraction ratios in those two parts. As a result, we obtain sharp pattern transitions, i.e., long-to-short wavelength changes with only minor perturbations of the applied pre-compression. The presence of a magnetic substrate changes qualitatively and quantitatively the bifurcation response of the film–substrate system. Finally, we carry out a data-mining exercise to minimize the critical magnetic field at bifurcation by using three different topologies, i.e., a monolayer, a bilayer and a sandwich film. We find that the topologies resembling closely the monolayer one lead to the lowest critical magnetic fields for a given biaxial pre-compression.

这项工作研究了单层和多层磁流变弹性体（MRE）膜-基底系统在组合的横向施加磁场和面内双轴预压缩作用下的主要正弦分叉起皱反应。使用最近提出的包括软磁性颗粒的体积分数的连续模型，来分析磁性对系统的分叉响应的影响。使用有限元离散方法（沿施加磁场的方向）和傅里叶展开（沿无限平面内层的方向），以高度通用的方式进行分析。这允许无缝研究各种多层结构。第一，我们分析了双轴预压缩对薄膜-基底系统和各种机械刚度比的临界磁场的影响。当它们穿过等双轴预压缩状态时，我们在临界磁曲线中观察到一个扭结，并在相应的波数中观察到一个反射。随后，我们考虑将MRE膜粘结到MRE基底上，并研究这两个部分中颗粒体积分数比率的影响。结果，我们获得了尖锐的图案过渡，即，从长到短的波长变化，所施加的预压缩只有很小的扰动。磁性基板的存在在质量和数量上都会改变膜-基板系统的分叉响应。最后，我们通过使用三种不同的拓扑结构（即单层，双层和三明治膜）进行数据挖掘活动，以最大程度地减小分叉处的临界磁场。我们发现，对于给定的双轴预压缩，非常类似于单层拓扑的拓扑导致最低的临界磁场。