Hydrodynamic description of elastic or viscoelastic composite materials: Relative strains as macroscopic variables

Abstract

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.

Dynamic elastic moduli in magnetic gels: Normal modes and linear response

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“…Also the chains do not need to be as perfectly straight as considered here but could for example be weakly wiggled [8]. On the theoretical side, a connection to continuum descriptions on the macroscopic scale shall be established in the future [4,36,92].…”

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