Creep, recovery, and waves in a nonlinear fiber-reinforced viscoelastic solid

TL;DR

This paper develops a nonlinear viscoelastic model for fiber-reinforced biological tissues, revealing complex behaviors like persistent strains and non-standard wave solutions under various conditions.

Contribution

It introduces a novel constitutive model capturing nonlinear anisotropic viscoelasticity and derives equations showing unique creep, recovery, and wave phenomena.

Findings

Persistent nonzero strain in recovery

Strain growth during recovery

Traveling wave solutions that do not reach asymptotic limits

Abstract

We present a constitutive model capturing some of the experimentally observed features of soft biological tissues: nonlinear viscoelasticity, nonlinear elastic anisotropy, and nonlinear viscous anisotropy. For this model we derive the equation governing rectilinear shear motion in the plane of the fiber reinforcement; it is a nonlinear partial differential equation for the shear strain. Specializing the equation to the quasi-static processes of creep and recovery, we find that usual (exponential-like) time growth and decay exist in general, but that for certain ranges of values for the material parameters and for the angle between the shearing direction and the fiber direction, some anomalous behaviors emerge. These include persistence of a nonzero strain in the recovery experiment, strain growth in recovery, strain decay in creep, disappearance of the solution after a finite time, and similar odd comportments. For the full dynamical equation of motion, we find kink (traveling wave) solutions which cannot reach their assigned asymptotic limit.