Rheologically complex materials are described by function-valued properties with dependence on a timescale (linear viscoelasticity), input amplitude (nonlinear material behavior), or more generally both (nonlinear viscoelasticity). This complexity presents a difficulty when trying to utilize these material systems in engineering designs. Here, we focus on linear viscoelasticity and a methodolog...

In this paper, we rst study the abstract setting of linear vis-coelasticity and under reasonable conditions on the kernel we prove the exponential stability of the associated semigroup. Secondly, we study the general approximate schemes proposed by Banks and Burns, by Ito and Kappel, and by Fabiano and Ito, respectively. The uniformly exponential stability of semigroups associated with these ap...

A unifying theoretical framework for analyzing stochastic data from single-particle tracking (SPT) in viscoelastic materials is presented. A generalization of the bead-spring model for linear polymers is developed from a molecular point of view and from the standpoint of phenomenological linear viscoelasticity. The hydrodynamic interaction in the former is identiied as the dashpots in the latte...

We report here the first experimental measurements of nonlinear rheological material properties of hagfish slime, a hydrated biopolymer/biofiber network, and develop a microstructural constitutive model to explain the observed nonlinear viscoelastic behavior. The linear elastic modulus of the network is observed to be G′ ≈ 0.02 Pa for timescales 0.1 s ≤ t ≤ 10 s, making it one of the softest el...