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

TL;DR

This paper develops a hydrodynamic framework for (visco)elastic composite materials, introducing relative strains as a new macroscopic variable to better describe the dynamic behavior of inclusions and their environment.

Contribution

It presents a novel hydrodynamic model incorporating relative strains and other variables, advancing the understanding of composite material dynamics.

Findings

Identification of relative strains as a key macroscopic variable

Derivation of hydrodynamic equations including relative translations and rotations

Application to simplified geometries illustrating the model's relevance

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.