The design of band gap metamaterials, i.e., metamaterials with the capability to inhibit wave propagation of a specific frequency range, has numerous potential engineering applications, such as acoustic filters and vibration isolation control. In order to describe the behavior of such materials, a novel integral micromorphic elastic continuum is introduced, and its ability to describe band gaps is studied in the one-dimensional setting. The nonlocal formulation is based on a modification of two terms in the expression for potential energy density. The corresponding dispersion equation is derived and converted to a dimensionless format, so that the effect of individual parameters can be described in the most efficient way. The results indicate that both suggested nonlocal modifications play an important role. The original local micromorphic model reproduces a band gap only in the special, somewhat artificial case, when the stiffness coefficient associated with the gradient of the micromorphic variable vanishes. On the other hand, the nonlocal formulation can provide band gaps even for nonzero values of this coefficient, provided that the penalty coefficient that enforces coupling between the micromorphic variable and nonlocal strain is sufficiently high and the micromorphic stiffness is sufficiently low.

带隙超材料的设计，即具有抑制特定频率范围的波传播能力的超材料，具有许多潜在的工程应用，例如声学滤波器和隔振控制。为了描述此类材料的行为，引入了一种新颖的积分微形弹性连续体，并在一维环境下研究了其描述带隙的能力。非局部公式基于势能密度表达式中两项的修改。推导相应的色散方程并将其转换为无量纲格式，以便可以以最有效的方式描述各个参数的影响。结果表明，两种建议的非局部修饰都发挥着重要作用。原始的局部微形态模型仅在特殊的、有些人为的情况下再现带隙，此时与微形态变量的梯度相关的刚度系数消失。另一方面，即使对于该系数的非零值，非局部公式也可以提供带隙，只要强制微形态变量和非局部应变之间的耦合的惩罚系数足够高并且微形态刚度足够低。