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.
Dual Cross-Linked Hydrogels: Linear Rheology and Fractional Calculus Modeling
NanoEngineering Group, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology（以色列理工学院机械工程学院纳米工程组）；Department of Chemical Engineering and Materials Science, Michigan State University（密歇根州立大学化学工程与材料科学系）
