Multiscale analysis of elastic waves in soft materials: From molecular chain networks to fiber composites

We provide a multiscale analysis of elastic waves in soft microstructured materials including the underlying molecular chain network mechanisms and micromechanics of hyperelastic fiber composites. First, we examine the interplay between the crosslinked and entangled polymer chains and elastic wave characteristics in finitely deformed materials. Next, we study the shear wave propagation in a class of heterogeneous hyperelastic composites. In particular, we consider the transversely isotropic fiber composites with phases characterized by the stiffening behavior stemming from the non-Gaussian statistics of polymer chains. By employing a micromechanics-based approach, we derive explicit expressions for phase velocities in terms of material properties and volume fraction of the phases. Our results indicate the significant influence of the variety of length-scales mechanisms on the elastic wave characteristics. We provide examples to illustrate the influence of the mechanisms under different loading conditions, wave propagation directionality, and material microstructure parameters.