Nonlinear Viscoelastic Behavior of Human Knee Ligaments Subjected to Complex Loading Histories

The nonlinear viscoelastic structural response of the major human knee ligaments when subjected to complex loading histories is investigated, with emphasis on the collateral ligaments. Bone-ligament-bone specimens are tested in knee distraction loading, where the ligaments are in the anatomical position corresponding to a fully extended knee. Temporal nonlinearities for time scales in the range of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 \le t \le 500\,$$\end{document}s are characterized with a dedicated series of loading histories. In particular, the response to several complex sequences of step-and-hold tests and loading-unloading cycles is investigated. The separability of the time and deformation dependent behavior, as assumed for the often used quasi linear viscoelastic (QLV) theory, is found to be insufficient for describing the response in the time range considered. Non-recoverable inelastic flow is observed in this time range. A phenomenological 1-dimensional nonlinear viscoelastic model that qualitatively describes the experimentally observed inelastic phenomena is presented.