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One possibility to adjust material properties to a specific need is to embedunits of one substance into a matrix of another substance. Even materials thatare readily tunable during operation can be generated in this way. In(visco)elastic substances, both the matrix material as well as the inclusionsand/or their immediate environment can be dynamically deformed. If the typicaldynamic response time of the inclusions and their surroundings approach themacroscopic response time, their deformation processes need to be included intoa dynamic macroscopic characterization. Along these lines, we present ahydrodynamic description of (visco)elastic composite materials. For thispurpose, additional strain variables reflect the state of the inclusions andtheir immediate environment. These additional strain variables in general arenot set by a coarse-grained macroscopic displacement field. Apart from that,during our derivation, we also include the macroscopic variables of relativetranslations and relative rotations that were previously introduced indifferent contexts. As a central point, our approach reveals and classifies theimportance of a new macroscopic variable: relative strains. We analyze twosimplified minimal example geometries as an illustration.

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