On the independence of time and strain effects in the stress relaxation of ligaments and tendons

Abstract

The hypothesis of variables separation, namely the time and the strain separation in the relaxation function, is widely used in soft tissue biomechanics. Although this hypothesis is central to several biomechanical models, only few experimental works have tried to verify it. From these studies, contradictory results have been found. Moreover, it has recently been noted that no such experimental veri"cation has been performed for ligament tissues. In this paper, an experimental method is developed to test the hypothesis of variables separation. This method is then used with human cruciate ligaments and patellar tendons. It is shown that the use of the variables separation hypothesis is justi"ed at least for strain values lower than 16% for anterior cruciate ligament, lower than 12% for posterior cruciate ligament and lower than 6% for patellar tendon. The method presented in this paper could be used to verify the validity of variables separation for other tissues.

Non-linear viscoelastic laws for soft biological tissues

“…It has been shown that the relaxation modes showed only slight strain dependences for soft tissues (Soden and Kershaw, 1974). We confirmed this trend for the human patellar tendon specimens (Pioletti and Rakotomanana, 2000).…”

“…The hypothesis of variables separation was recently experimentally verified (Pioletti and Rakotomanana, 2000). In a relaxation stress identification, the integral part of equation (13) can be written as:…”

“…A custom made device has been elaborated to perform uniaxial static and dynamic tests on isolated ligaments and tendons at controlled temperature (37 • C) and humidity (100%) (Pioletti, 1997;Pioletti et al, 1996;Pioletti et al, 1999). The experimental situation corresponded to the isothermal situation assumed in the theory.…”

“…They also have an important viscous component in their behaviours (Fung, 1993). From an experimental point of view, mechanical tests performed on soft biological tissues illustrate that the stress depends on the strain rate (Danto and Woo, 1993;Haut, 1983;Pioletti et al, 1999) and that the stress decreases when specimens are subjected to a constant strain (Fung, 1993;Lyon et al, 1988;Pioletti, 1997).…”

Constitutive Equations

“…As for ligament, experiments by Provenzano et al (2001) showed creep rates (slope on a log-log plot of primary creep) to depend on load level, therefore QLV does not apply to ligament. Pioletti and Rakotomanana (2000) considered the QLV time-strain separability hypothesis but they did not deal directly with the viscoelastic functions. Figures of stress relaxation in Pioletti and Rakotomanana (2000) plotted clearly show that there is a strain dependence so a separable time-strain form as in the QLV model is only an approximation to the actual behavior.…”