Viscoelastic Relaxation and Recovery of Tendon

Abstract

Abstract-Tendons exhibit complex viscoelastic behaviors during relaxation and recovery. Recovery is critical to predicting behavior in subsequent loading, yet is not well studied. Our goal is to explore time-dependent recovery of these tendons after loading. As a prerequisite, their straindependent viscoelastic behaviors during relaxation were also characterized. The porcine digital flexor tendon was used as a model of tendon behavior. Strain-dependent relaxation was observed in tests at 1, 2, 3, 4, 5, and 6% strain. Recovery behavior of the tendon was examined by performing relaxation tests at 6%, then dropping to a low but nonzero strain level. Results show that the rate of relaxation in tendon is indeed a function of strain. Unlike previously reported tests on the medial collateral ligament (MCL), the relaxation rate of tendons increased with increased levels of strain. This strain-dependent relaxation contrasts with quasilinear viscoelasticity (QLV), which predicts equal time dependence across various strains. Also, the tendons did not recover to predicted levels by nonlinear superposition models or QLV, though they did recover partially. This recovery behavior and behavior during subsequent loadings will then become problematic for both quasilinear and nonlinear models to correctly predict.

Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels

“…Indeed, a study of preconditioning found it to be associated with enhanced collagen fiber alignment (42). There are some studies that have reported strainenhanced stress relaxation in tissues such as ligaments and tendon (43,44), although the mechanism of strain-enhanced relaxation underlying this tissue-scale behavior was not established.…”

Biaxial mechanical properties of swine uterosacral and cardinal ligaments

“…Constitutive theories such as nonlinear superposition (Findley et al 1976) and Schapery theory (Schapery 1969) have been successfully employed to describe the onedimensional dependency of the stress relaxation rate (or creep rate) on strain (or stress) in articular ligaments and tendons (Provenzano et al 2002;Hingorani et al 2004;Duenwald et al 2009Duenwald et al , 2010. QLV generalizations have been also presented to capture such dependency in collagen (Pryse et al 2003;Nekouzadeh et al 2007).…”

Modelling approaches for evaluating multiscale tendon mechanics

“…Furthermore, tendon mechanical behaviour should be characterized in three dimensions, but simplification to two-dimensional models is beneficial to both successfully characterize tendon behaviour under uniaxial loading and eliminate material constants during the fitting process. Based on these assumptions, Duenwald et al evaluated the accuracy of a modified QLV model with nonlinear superposition and a Schapery nonlinear viscoelastic model to interpret strain-dependent relaxation behaviour of biological tissues by including rise time and ramp strain history during loading [61,70]. Nonlinear superposition of this model failed to address recovery behaviour, but Schapery's model matched experimental curves and was able to predict both recovery and reloading behaviour [61][62][63]71] rsfs.royalsocietypublishing.org Interface Focus 6: 20150044…”

“…Although this model has the potential to be extended and generalized to describe a variety of nonlinear anisotropic materials in three dimensions, its limitation is to assume an instantaneous material response after strain is applied [57]. More accurate mathematical models should be developed to fully interpret the complex nonlinear experimental results of the strain-dependent stress relaxation and stress-dependent creep behaviour of ligaments [58,59] and tendons [60]. To better capture complex nonlinear properties, significant advancements on viscoelastic models have been made (table 1).…”