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arXiv 1607.08736cond-mat.softcond-mat.mtrl-sciphysics.flu-dyn
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(粘)弹性复合材料的流体力学描述及相对应变作为新的宏观变量

Hydrodynamic description of (visco)elastic composite materials and relative strains as a new macroscopic variable

Andreas M. Menzel

摘要:

根据特定需要调整材料特性的一种可能性是将一种物质的单元嵌入另一种物质的基质中。甚至在操作期间容易调节的材料也可以以这种方式产生。在(粘)弹性物质中,基质材料以及内含物和/或它们的直接环境都可以动态变形。如果夹杂物及其周围环境的典型动态响应时间接近宏观响应时间,则需要将其变形过程纳入动态宏观表征。沿着这些路线,我们提出了(粘)弹性复合材料的流体动力学描述。为此,额外的应变变量反映了夹杂物的状态及其直接环境。这些额外的应变变量一般不设置由粗粒度的宏观位移场。除此之外,在我们的推导过程中,我们还包括以前在不同背景下引入的相对平移和相对旋转的宏观变量。作为一个中心点,我们的方法揭示了一个新的宏观变量的重要性:相对应变。我们分析了两个简化的最小示例几何作为说明。

英文摘要:

One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a new macroscopic variable: relative strains. We analyze two simplified minimal example geometries as an illustration.

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