The numerical determination of dispersion relations in periodic materials via the finite element method is a difficult task in most standard codes. Here, we propose a novel technique which allows the computation of these band structures from local elemental subroutines in contrast with existing methods which impose Bloch boundary conditions on the global arrays. The proposed local approach is thus readily applicable to several physical contexts and space dimensionalities. Here we present the details of this element-based algorithm and provide verification results for three different kinematic assumptions applied to phononic crystals in a classical and a micropolar elastic medium. The paper also includes in the form of supplementary material, a fully-coded user subroutine and a test-problem to be used in a commercial finite element code.

中文翻译：

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一种通用的基于元素的方法来计算具有现有有限元代码的周期性材料中的色散关系

在大多数标准代码中，通过有限元方法数值确定周期性材料中的色散关系是一项艰巨的任务。在这里，我们提出了一种新技术，该技术允许从局部元素子程序计算这些能带结构，这与将 Bloch 边界条件施加到全局阵列上的现有方法形成对比。因此，所提出的局部方法很容易适用于几个物理环境和空间维度。在这里，我们介绍了这种基于元素的算法的细节，并为应用于经典和微极弹性介质中的声子晶体的三种不同运动学假设提供了验证结果。该论文还以补充材料的形式包括一个完全编码的用户子程序和一个用于商业有限元代码的测试问题。