Viscoelastic multiscaling in immersed networks

Abstract

Rheological responses are the most relevant features to describe soft matter. So far, such constitutive relations are still not well understood in terms of small scale properties, although this knowledge would help the design of synthetic and biomaterials. Here, we investigate, computational and analytically, how mesoscopic-scale interactions influence the macroscopic behavior of viscoelastic materials. We design a coarse-grained approach where the local elastic and viscous contributions can be controlled. Applying molecular dynamics simulations, we mimic real indentation assays. When elastic forces are dominant, our model reproduces the Hertzian behavior of contact. However, when friction increases, it restores the standard linear solid model. We show how the response parameters depend on the microscopic elastic and viscous contributions. Besides, we show that the contact Hertz model is equivalent to the virial stress, an atomistic approach of the continuum Cauchy stress tensor. In addition, relaxation experiments were performed on polyacrylamide gels with an atomic force microscopic in order to validate our numerical relaxation curves. The bisacrylamide concentration in the gel has a clear impact on the equivalent elastic and viscous contributions of the sample. Moreover, our findings also suggest that the relaxation times, obtained in relaxation and oscillatory experiments, obey a universal behavior in viscoelastic materials.