论文标题
使用时间变化的应用字段确定2相复合材料和物体中的体积分数
Determining the volume fraction in 2-phase composites and bodies using time varying applied fields
论文作者
论文摘要
一个包含两个阶段的车身$θ$，可能形成一个周期性的复合材料，其微观结构比车身要小得多，或者可能在长度比例上具有与人体相当的结构，会受到缓慢的时间变化的边界条件，而边界条件将在$θ$中产生近似均匀的字段。在这里缓慢变化的时间意味着与时间变化相关的频率的波长和波的衰减长度大得多，大的尺寸要大于$θ$，因此我们可以进行准近似近似。这两个阶段中的至少一个没有瞬时响应，而是在前时间取决于字段。这些领域可能是与电力，磁性，多孔介质中的流体流或抗平移弹性相关的田地。我们发现，根据这些近似值，可以设计边界条件的时间变化，以便在特定时间$ t = t_0 $准确地产生相位的体积分数，而与相位的详细几何配置无关。此外，对于经过特殊量身定制的时间变化，可以在任何时候从$ t $中确定体积分数，而不仅仅是在特定时间$ t = t_0 $。我们还展示了如何在单个频率$ω_0$上振荡的时间变化的时间变化，以精确地检索响应在$ω_0$中。
A body $Θ$ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary conditions that would produce an approximate uniform field in $Θ$ were it filled with homogeneous material. Here slowly time varying means that the wavelengths and attenuation lengths of waves at the frequencies associated with the time variation are much larger than the size of $Θ$, so that we can make a quasistatic approximation. At least one of the two phase does not have an instantaneous response but rather depends on fields at prior times. The fields may be those associated with electricity, magnetism, fluid flow in porous media, or antiplane elasticity. We find, subject to these approximations, that the time variation of the boundary conditions can be designed so boundary measurements at a specific time $t=t_0$ exactly yield the volume fractions of the phases, independent of the detailed geometric configuration of the phases. Moreover, for specially tailored time variations, the volume fraction can be exactly determined frommeasurements at any time $t$, not just at the specific time $t=t_0$. We also show how time varying boundary conditions, not oscillating at the single frequency $ω_0$, can be designed to exactly retrieve the response at $ω_0$.
