Hard-magnetic soft materials belong to the class of active materials that undergo finite deformation and alter their material properties when subjected to magnetic loading. Because of these characteristics, the periodic composites/phononic crystals made up of hard-magnetic soft materials can be promising candidates for filtering acoustic/elastic waves across frequency bands that can be tuned in real-time by applying external magnetic loading. In this work, the nonlinear finite deformation, and the superimposed small-amplitude longitudinal elastic wave band gap characteristics of an infinite periodic hard-magnetic soft material laminate under the applied magnetic flux density are investigated. The compressible Gent hyperelastic model in conjunction with the ideal hard-magnetic soft material model is used for characterizing the constitutive response of laminate phases. The band structure of an infinite periodic hard-magnetic soft material laminate subjected to magnetic load is extracted by developing an in-house finite element model with Bloch’s periodic boundary conditions. The influence of some factors such as material properties, volume fractions, and applied magnetic flux density on the tunability of the longitudinal wave band gaps is explored. The numerical findings demonstrate that the width and the position of band gaps can be tuned by varying the applied magnetic flux density. The volume fraction and the material properties of laminate phases also play significant roles in the generation of band gaps. The numerical results and inferences reported here should provide the guidelines for designing futuristic remotely and actively controlled wave-manipulating devices.

硬磁软材料属于一类活性材料，在受到磁负载时会发生有限变形并改变其材料特性。由于这些特性，由硬磁软材料制成的周期性复合材料/声子晶体可以成为过滤跨频带的声波/弹性波的有前途的候选者，这些频带可以通过施加外部磁负载进行实时调谐。在这项工作中，研究了无限周期硬磁软材料层合板在外加磁通密度下的非线性有限变形和叠加小振幅纵向弹性波带隙特性。可压缩的 Gent 超弹性模型与理想的硬磁软材料模型相结合，用于表征层压相的本构响应。通过开发具有 Bloch 周期性边界条件的内部有限元模型，提取了承受磁载荷的无限周期性硬磁软材料层压板的能带结构。探讨了材料特性、体积分数和外加磁通密度等因素对纵波带隙可调谐性的影响。数值结果表明，可以通过改变施加的磁通密度来调整带隙的宽度和位置。层压相的体积分数和材料特性在带隙的产生中也起着重要作用。