Quasi-linear Viscoelastic Theory Research Articles

Micromechanical modeling of rate-dependent behavior of Connective tissues

In this paper, a constitutive and micromechanical model for prediction of rate-dependent behavior of connective tissues (CTs) is presented. Connective tissues are considered as nonlinear viscoelastic material. The rate-dependent behavior of CTs is incorporated into model using the well-known quasi-linear viscoelasticity (QLV) theory. A planar wavy representative volume element (RVE) is considered based on the tissue microstructure histological evidences. The presented model parameters are identified based on the available experiments in the literature. The presented constitutive model introduced to ABAQUS by means of UMAT subroutine. Results show that, monotonic uniaxial test predictions of the presented model at different strain rates for rat tail tendon (RTT) and human patellar tendon (HPT) are in good agreement with experimental data. Results of incremental stress-relaxation test are also presented to investigate both instantaneous and viscoelastic behavior of connective tissues.

STUDY ON MECHANICAL CHARACTERIZATION OF LIVER TISSUE BASED ON HAPTIC DEVICES FOR VIRTUAL SURGICAL SIMULATION

In recent years, virtual surgical simulation has been one of the hot direction of digital medical research, it is mainly used in teaching, training, diagnosis, preoperative planning, rehabilitation and modeling and analysis of surgical instruments. The modeling of soft tissue of human organs is the basis to realize the virtual surgical simulation. The quasi-linear viscoelastic (QLV) theory has been proposed by Fung, and it was widely used for modeling the constitutive equation of soft tissues. The purpose of this study is to determine the mechanical characterization of the liver soft tissue based on the PHANTOM Omni Haptic devices. Five parameters are included in the constitutive equation with QLV theory, which must be determined experimentally. The specimens were obtained from fresh porcine liver tissues in vitro. The liver tissues were cut into 14[Formula: see text]mm[Formula: see text][Formula: see text][Formula: see text]14[Formula: see text]mm[Formula: see text][Formula: see text][Formula: see text]14[Formula: see text]mm cubes. Two types of unconfined compression tests were performed on cube liver specimens. Puncture tests were performed on the complete liver. The material parameters of the QLV constitutive equation were obtained by fitting the experimental data. These parameters will provide the references for the computational modeling of the liver in the virtual surgical simulation.

Biaxial Properties of the Left and Right Pulmonary Arteries in a Monocrotaline Rat Animal Model of Pulmonary Arterial Hypertension.

In a monocrotaline (MCT) induced-pulmonary arterial hypertension (PAH) rat animal model, the dynamic stress-strain relation was investigated in the circumferential and axial directions using a linear elastic response model within the quasi-linear viscoelasticity theory framework. Right and left pulmonary arterial segments (RPA and LPA) were mechanically tested in a tubular biaxial device at the early stage (1 week post-MCT treatment) and at the advanced stage of the disease (4 weeks post-MCT treatment). The vessels were tested circumferentially at the in vivo axial length with matching in vivo measured pressure ranges. Subsequently, the vessels were tested axially at the mean pulmonary arterial pressure by stretching them from in vivo plus 5% of their length. Parameter estimation showed that the LPA and RPA remodel at different rates: axially, both vessels decreased in Young's modulus at the early stage of the disease, and increased at the advanced disease stage. Circumferentially, the Young's modulus increased in advanced PAH, but it was only significant in the RPA. The damping properties also changed in PAH; in the LPA relaxation times decreased continuously as the disease progressed, while in the RPA they initially increased and then decreased. Our modeling efforts were corroborated by the restructuring organization of the fibers imaged under multiphoton microscopy, where the collagen fibers become strongly aligned to the 45 deg angle in the RPA from an uncrimped and randomly organized state. Additionally, collagen content increased almost 10% in the RPA from the placebo to advanced PAH.

Multi-material 3-D viscoelastic model of a transtibial residuum from in-vivo indentation and MRI data

Although the socket is critical in a prosthetic system for a person with limb amputation, the methods of its design are largely artisanal. A roadblock for a repeatable and quantitative socket design process is the lack of predictive and patient specific biomechanical models of the residuum. This study presents the evaluation of such a model using a combined experimental–numerical approach. The model geometry and tissue boundaries are derived from magnetic resonance imaging (MRI). The soft tissue non-linear elastic and viscoelastic mechanical behavior was evaluated using inverse finite element analysis (FEA) of in-vivo indentation experiments. A custom designed robotic in-vivo indentation system was used to provide a rich experimental data set of force versus time at 18 sites across a limb. During FEA, the tissues were represented by two layers, namely the skin-adipose layer and an underlying muscle-soft tissue complex. The non-linear elastic behavior was modeled using 2nd order Ogden hyperelastic formulations, and viscoelasticity was modeled using the quasi-linear theory of viscoelasticity. To determine the material parameters for each tissue, an inverse FEA based optimization routine was used that minimizes the combined mean of the squared force differences between the numerical and experimental force-time curves for indentations at 4 distinct anatomical regions on the residuum. The optimization provided the following material parameters for the skin-adipose layer: [c=5.22kPam=4.79γ=3.57MPaτ=0.32s] and for the muscle-soft tissue complex [c=5.20kPam=4.78γ=3.47MPaτ=0.34s]. These parameters were evaluated to predict the force–time curves for the remaining 14 anatomical locations. The mean percentage error (mean absolute error/ maximum experimental force) for these predictions was 7±3%. The mean percentage error at the 4 sites used for the optimization was 4%.

Quasi-linear viscoelastic properties of the human medial patello-femoral ligament

The evaluation of viscoelastic properties of human medial patello-femoral ligament is fundamental to understand its physiological function and contribution as stabilizer for the selection of the methods of repair and reconstruction and for the development of scaffolds with adequate mechanical properties. In this work, 12 human specimens were tested to evaluate the time- and history-dependent non linear viscoelastic properties of human medial patello-femoral ligament using the quasi-linear viscoelastic (QLV) theory formulated by Fung et al. (1972) and modified by Abramowitch and Woo (2004). The five constant of the QLV theory, used to describe the instantaneous elastic response and the reduced relaxation function on stress relaxation experiments, were successfully evaluated. It was found that the constant A was 1.21±0.96MPa and the dimensionless constant B was 26.03±4.16. The magnitude of viscous response, the constant C, was 0.11±0.02 and the initial and late relaxation time constants τ1 and τ2 were 6.32±1.76s and 903.47±504.73s respectively. The total stress relaxation was 32.7±4.7%. To validate our results, the obtained constants were used to evaluate peak stresses from a cyclic stress relaxation test on three different specimens. The theoretically predicted values fit the experimental ones demonstrating that the QLV theory could be used to evaluate the viscoelastic properties of the human medial patello-femoral ligament.

Simple shear of a compressible quasilinear viscoelastic material

Fung’s theory of quasilinear viscoelasticity (QLV) was recently reappraised by the authors [Proc. R. Soc. A 479 (2014), 20140058] in light of discussions in the literature of its apparent deficiencies. Due to the utility of the deformation of simple shear in a variety of applications, especially in experiment to deduce material properties, here QLV is employed to solve the problem of the simple shear of a nonlinear compressible quasilinear viscoelastic material. The effects of compressibility on the subsequent deformation and stress fields that result in this isochoric deformation are highlighted, and calculations of the dissipated energy associated with both a ‘ramp’ simple shear profile and oscillatory shear are given.

Is the time-dependent behaviour of the aortic valve intrinsically quasi-linear?

The widely popular quasi-linear viscoelasticity (QLV) theory has been employed extensively in the literature for characterising the time-dependent behaviour of many biological tissues, including the aortic valve (AV). However, in contrast to other tissues, application of QLV to AV data has been met with varying success, with studies reporting discrepancies in the values of the associated quantified parameters for data collected from different timescales in experiments. Furthermore, some studies investigating the stress-relaxation phenomenon in valvular tissues have suggested discrete relaxation spectra, as an alternative to the continuous spectrum proposed by the QLV. These indications put forward a more fundamental question: Is the time-dependent behaviour of the aortic valve intrinsically quasi-linear? In other words, can the inherent characteristics of the tissue that govern its biomechanical behaviour facilitate a quasi-linear time-dependent behaviour? This paper attempts to address these questions by presenting a mathematical analysis to derive the expressions for the stress-relaxation G(t) and creep J(t) functions for the AV tissue within the QLV theory. The principal inherent characteristic of the tissue is incorporated into the QLV formulation in the form of the well-established gradual fibre recruitment model, and the corresponding expressions for G(t) and J(t) are derived. The outcomes indicate that the resulting stress-relaxation and creep functions do not appear to voluntarily follow the observed experimental trends reported in previous studies. These results highlight that the time-dependent behaviour of the AV may not be quasi-linear, and more suitable theoretical criteria and models may be required to explain the phenomenon based on tissue’s microstructure, and for more accurate estimation of the associated material parameters. In general, these results may further be applicable to other planar soft tissues of the same class, i.e. with the same representation for fibre recruitment mechanism and discrete time-dependent spectra.

An Approach to Determine Pressure Profile Generated by Compression Bandage Using Quasi-Linear Viscoelastic Model

Understanding the stress relaxation behavior of the compression bandage could be very useful in determining the behavior of the interface pressure exerted by the bandage on a limb during the course of the compression treatment. There has been no comprehensive study in the literature to investigate the pressure profile (interface pressure with time) generated by a compression bandage when applied at different levels of strain. The present study attempts to describe the pressure profile, with the use of a quasi-linear viscoelastic model, generated by a compression bandage during compression therapy. The quasi-linear viscoelastic (QLV) theory proposed by Fung (Fung, 1972, "Stress Strain History Relations of Soft Tissues in Simple Elongation," Biomechanics: Its Foundations and Objectives, Y. C. Fung, N. Perrone, and M. Anliker, eds., Prentice-Hall, Englewood Cliffs, NJ, pp. 181-207). was used to model the nonlinear time- and history-dependent relaxation behavior of the bandage using the ramp strain approach. The regression analysis was done to find the correlation between the pressure profile and the relaxation behavior of the bandage. The parameters of the QLV model, describing the relaxation behavior of the bandage, were used to determine the pressure profile generated by the bandage at different levels of strain. The relaxation behaviors of the bandage at different levels of strain were well described by the QLV model parameters. A high correlation coefficient (nearly 0.98) shows a good correlation of the pressure profile with the stress relaxation behavior of the bandage.The prediction of the pressure profile using the QLV model parameters were in agreement with the experimental data. The pressure profile generated by a compression bandage could be predicted using the QLV model describing the nonlinear relaxation behavior of the bandage. This new application of the QLV theory helps in evaluating the bandage performance during compression therapy as scientific wound care management.

Interdependency of stress relaxation and afferent nerve discharge in rat small intestine

Background and aimsTo be able to characterize intestinal mechano-electrical transduction, i.e. the mechanoreceptor behaviour, quantitative nerve studies with controlled and quantified stimulus are needed. This study aimed to determine the relationship between mechanical stress relaxation and afferent discharge adaptation evoked by fast isovolumetric bag distensions in the rat jejunum. MethodsMultiunit afferent activity was recorded in vivo from jejunum afferents from five male Wistar rats. The jejunum was distended via a bag at a distension speed of 0.5ml/s to volumes of 0.2, 0.25, 0.3 and 0.4ml, respectively. The distension was stopped and the volume was kept constant for 2min to induce stress relaxation. The pressure in the bag, the afferent discharge (spike rate) and the diameter of the segment during the relaxation time were recorded simultaneously. ResultsThe afferent discharge responses to distension showed a pattern with a peak during the sudden loading followed by decreasing activity with time. At distension volumes of 0.2, 0.25, 0.3 and 0.4ml, the afferent discharge declined faster and to a greater extent (94%, 91%,96% and 87%) than the stress decreased (55%, 45%, 59% and 56%) during stress relaxation (p<0.001). Both the stress and the afferent discharge during the constant volume distension were independent of the distension volumes (p>0.5). The stress and the afferent discharge during the distension can be described mathematically on the basis of the quasi-linear theory of viscoelasticity. The association between the stress and the afferent discharge during the constant volume distension is linear with the same slope under various distension volumes. ConclusionsIntestinal mechanoreceptors were sensitive to the stress stimulus and a linear association between the stress relaxation and afferent discharge adaptation was found. The quasi-linear theory of visco-elasticity can be transferred to analysis of mechanical stimulus evoked afferent discharge.

A QUASI-LINEAR VISCOELASTIC MODEL FOR THE PASSIVE PROPERTIES OF THE HUMAN HIP JOINT

Properties of passive elastic structures constituting the human hip joint can be exploited to increase efficiency of human locomotion. As studies estimating the passive contributions to the net joint moment often disregard damping properties of the joint such contributions overestimate the energy gained during leg retraction within swing and stance phase. We built an experimental apparatus to measure moment-angle-relations during motor guided cyclic movements over a wide range of angular velocities and step-like changes in hip angle. On the basis of the experimentally gained data set the objective of this study was to model the elastic as well as the damping characteristics of the joint in the sagittal plane utilizing the Quasi-Linear Viscoelastic theory (QLV). A double exponential function was conveniently employed to describe the elastic response. The dependency of the hip joint stiffness on biarticular muscles was incorporated by repeating the measurement protocol for different knee angles. Due to the fact that the stiffness characteristics of the elastic response were merely shifted over knee angles we introduced an equilibrium angle at the hip joint as exponential function of the knee angle eventually yielding an elastic response as a function of hip and knee angle. In order to cover the damping characteristics the reduced relaxation function comprising a continuous spectrum of relaxation was utilized. We exemplify the applicability of the QLV model on published kinematic data on human walking and estimated that approximately 27% of the energy passively stored at the hip dissipates during the gait cycle.

THE EFFECT OF PREGNANCY AND POSTPARTUM RECOVERY ON THE VISCOELASTIC BEHAVIOR OF THE RAT CERVIX

The objective of this study was to elucidate the normal functional adaptations of the cervix in pregnancy. Utilizing a Long-Evans rodent model, the cervix was divided into distal and proximal portions for virgin, mid-pregnant, and four weeks postpartum animals. The quasi-linear viscoelastic theory describes the elastic and viscous behavior of the cervix. A hydroxyproline assay was used to measure collagen content. The nonlinearity of the elastic response significantly increased throughout the entire cervix during pregnancy when compared to virgin samples (p < 0.05) and was similar to virgin samples postpartum. All viscous behavior, except for the short-term relaxation of the proximal cervix, significantly differed for pregnant specimens (p < 0.05) and remained similar to pregnant samples postpartum. Collagen content was found to increase by mid-pregnancy only in the proximal cervix when compared to virgin. Distal and proximal portions, however, were found to differ in collagen content at all time points (p < 0.05). This study finds that the cervix becomes elastically stiffer with increasing strain and exhibits increased viscous behavior during pregnancy, with incomplete recovery postpartum. These alterations allow for quick dissipation of loads, and are likely related to altered matrix organization and porosity reported by others.

Estimates Dynamic Material Properties of Ligaments under the Fast Strain Rate

The cyclic mechanical property of ligament plays an important role in biomechanics. If the microstructural volume fractions, orientations, and interactions among components for different ligament types are understood, it is conceivable to develop a general ligament model that is based on microstructural properties. But the cycle loading experiment is very difficult to operate, for convenience we can use the relationship between the complex modulus and relaxation modulus. Thus, in order to characterize the comprehensive viscoelastic behavior of cervical spine ligaments within their physiological range, the mechanical response of three types of human cervical spines: the anterior longitudinal ligament, the posterior longitudinal ligament and the ligamentum flavum and a porcine posterior longitudinal ligament collagen fascicles were simulated using quasi-linear viscoelastic theory model using the data from stress relaxation experiments at fast strain rate. A seven parameter model was investigated, which is sufficient to characterize the ligament dynamic material properties. Such model used the instantaneous elastic functions approximated as linear under fast strain rate. Dynamic material properties including storage modulus, loss modulus, the dynamic modulus of elasticity and the internal damping were investigated by transforming the stress relaxation data into frequency domain by Laplace transformation.

Dynamic, Regional Mechanical Properties of the Porcine Brain: Indentation in the Coronal Plane

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ∼10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.

Modified constitutive equation for quasi-linear theory of viscoelasticity

The constitutive equation of the quasi-linear theory of viscoelasticity is modified with the view to simplify our understanding of the physical meaning of numerous kernel functions. In the resulting equation, the instantaneous and the regular parts have the same structure, and the instantaneous part coincides with the well-known constitutive equation of the nonlinear theory of elasticity.

Quasi-linear viscoelastic properties of PC-12 neuron-like cells measured using atomic force microscopy

Atomic force microscopy has been widely used to measure the mechanical properties of living cells. Models based on Hertz theory are often utilized to estimate the Young's modulus of cells. In practice, the nonlinear viscoelastic behavior of cells can often be observed in indentation experiments. In this article, the quasi-linear viscoelasticity (QLV) theory, which has been successfully applied to many biological tissues, was employed to construct the constitutive equation of neuron-like PC-12 cells. The values of Young's modulus obtained via our proposed method were one or two orders of magnitude, depending on the indenting rate, less than those obtained using methods based on the modified Hertzian model. The Kelvin model was also introduced to describe the solid and liquid behavior of cells. The prediction error of the Kelvin model was larger than that of the proposed QLV model, especially at the peak force and the toe portion of the force response. The results revealed that the Young's modulus estimated by the QLV model was less affected by indenting rates than that estimated by the modified Hertzian model or the Kelvin model. The proposed QLV model accounting for the indenting conditions was capable of describing both the nonlinear elastic response and relaxation behavior and, therefore, was more appropriate for modeling the biomechanical behaviors of PC-12 cells than the nonlinear elastic model or the linear viscoelastic model.

The Quasi-Linear Viscoelastic Properties of Diabetic and Non-Diabetic Plantar Soft Tissue

The purpose of this study was to characterize the viscoelastic behavior of diabetic and non-diabetic plantar soft tissue at six ulcer-prone/load-bearing locations beneath the foot to determine any changes that may play a role in diabetic ulcer formation and subsequent amputation in this predisposed population. Four older diabetic and four control fresh frozen cadaveric feet were each dissected to isolate plantar tissue specimens from the hallux, first, third, and fifth metatarsals, lateral midfoot, and calcaneus. Stress relaxation experiments were used to quantify the viscoelastic tissue properties by fitting the data to the quasi-linear viscoelastic (QLV) theory using two methods, a traditional frequency-insensitive approach and an indirect frequency-sensitive approach, and by measuring several additional parameters from the raw data including the rate and amount of overall relaxation. The stress relaxation response of both diabetic and non-diabetic specimens was unexpectedly similar and accordingly few of the QLV parameters for either fit approach and none of raw data parameters differed. Likewise, no differences were found between plantar locations. The accuracy of both fit methods was comparable, however, neither approach predicted the ramp behavior. Further, fit coefficients varied considerably from one method to the other, making it hard to discern meaningful trends. Future testing using alternate loading modes and intact feet may provide more insight into the role that time-dependent properties play in diabetic foot ulceration.

Matrix Deposition Modulates the Viscoelastic Shear Properties of Hydrogel-Based Cartilage Grafts

Hydrogel-based scaffolds such as alginate have been extensively investigated for cartilage tissue engineering, largely due to their biocompatibility, ambient gelling conditions, and the ability to support chondrocyte phenotype. While it is well established that the viscoelastic response of articular cartilage is essential for articulation and load bearing, the time-dependent mechanical properties of hydrogel-based cartilage scaffolds have not been extensively studied. Therefore, the objective of this study was to characterize the intrinsic viscoelastic shear properties of chondrocyte-laden alginate scaffolds and determine the effects of seeding density and culturing time on these properties. Specifically, the viscoelastic properties (equilibrium and dynamic shear moduli and dynamic phase shift angle) of these engineered cartilage grafts were measured under torsional shear. In addition, the rapid ramp-step shear stress relaxation of the alginate-based cartilage scaffolds was modeled using the quasi-linear viscoelastic (QLV) theory. It was found that scaffold stiffness increased with both culturing time and cell density, whereas viscosity did not change significantly with cell density (30 vs. 60 million/mL). Similar to native cartilage, the energy dissipation of engineered scaffolds under pure shear is highly correlated to the glycosaminoglycan content. In contrast, collagen content was not strongly correlated to scaffold shear modulus, especially the instantaneous shear modulus predicted by the quasi-linear viscoelastic model. The findings of this study provide new insights into the structure-function relationship of engineered cartilage and design of functional grafts for cartilage repair.

Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure–Area Dynamics Under In Vivo and Ex Vivo Conditions

A better understanding of the biomechanical properties of the arterial wall provides important insight into arterial vascular biology under normal (healthy) and pathological conditions. This insight has potential to improve tracking of disease progression and to aid in vascular graft design and implementation. In this study, we use linear and nonlinear viscoelastic models to predict biomechanical properties of the thoracic descending aorta and the carotid artery under ex vivo and in vivo conditions in ovine and human arteries. Models analyzed include a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (an arctangent and a sigmoid model) that relate changes in arterial blood pressure to the vessel cross-sectional area (via estimation of vessel strain). These models were developed using the framework of Quasilinear Viscoelasticity (QLV) theory and were validated using measurements from the thoracic descending aorta and the carotid artery obtained from human and ovine arteries. In vivo measurements were obtained from 10 ovine aortas and 10 human carotid arteries. Ex vivo measurements (from both locations) were made in 11 male Merino sheep. Biomechanical properties were obtained through constrained estimation of model parameters. To further investigate the parameter estimates, we computed standard errors and confidence intervals and we used analysis of variance to compare results within and between groups. Overall, our results indicate that optimal model selection depends on the artery type. Results showed that for the thoracic descending aorta (under both experimental conditions), the best predictions were obtained with the nonlinear sigmoid model, while under healthy physiological pressure loading the carotid arteries nonlinear stiffening with increasing pressure is negligible, and consequently, the linear (Kelvin) viscoelastic model better describes the pressure-area dynamics in this vessel. Results comparing biomechanical properties show that the Kelvin and sigmoid models were able to predict the zero-pressure vessel radius; that under ex vivo conditions vessels are more rigid, and comparatively, that the carotid artery is stiffer than the thoracic descending aorta; and that the viscoelastic gain and relaxation parameters do not differ significantly between vessels or experimental conditions. In conclusion, our study demonstrates that the proposed models can predict pressure-area dynamics and that model parameters can be extracted for further interpretation of biomechanical properties.

Predicting Arterial Flow and Pressure Dynamics Using a 1D Fluid Dynamics Model with a Viscoelastic Wall

This paper combines a generalized viscoelastic model with a one-dimensional (1D) fluid dynamics model for the prediction of blood flow, pressure, and vessel area in systemic arteries. The 1D fluid dynamics model is derived from the Navier–Stokes equations for an incompressible Newtonian flow through a network of cylindrical vessels. This model predicts pressure and flow and is combined with a viscoelastic constitutive equation derived using the quasilinear viscoelasticity theory that relates pressure and vessel area. This formulation allows for inclusion of an elastic response as well as an appropriate creep function allowing for the description of the viscoelastic deformation of the arterial wall. Three constitutive models were investigated: a linear elastic model and two viscoelastic models. The Kelvin and sigmoidal viscoelastic models provide linear and nonlinear elastic responses, respectively. For the fluid domain, the model assumes that a given flow profile is prescribed at the inlet, that flow is c...

A comparison of the quasi-static mechanical and non-linear viscoelastic properties of the human semitendinosus and gracilis tendons

Background Over 50-% of anterior cruciate ligament reconstructions are performed using semitendinosus and gracilis tendon autografts. Despite their increased use, there remains little quantitative data on their mechanical behavior. Therefore, the objective of this study was to investigate the quasi-static mechanical and non-linear viscoelastic properties of human semitendinosus and gracilis tendons, as well as the variation of these properties along their length. Methods Specimens were subjected to a series of uniaxial tensile tests: 1-h static stress-relaxation test, 30 cycle cyclic stress-relaxation test and load to failure test. To describe the non-linear viscoelastic behavior, the quasi-linear viscoelastic theory was utilized to model data from the static stress-relaxation experiment. Findings The constants describing the viscoelastic behavior were similar between the proximal and distal halves of the gracilis tendon. The proximal half of the semitendinosus tendon, however, had a greater viscous response than its distal half, which was also significantly higher than the proximal gracilis tendon. In terms of the quasi-static mechanical properties, the properties were similar between the proximal and distal halves of the semitendinosus tendon. However, the distal gracilis tendon showed a significantly higher tangent modulus and ultimate stress compared to its proximal half, which was also significantly higher than the distal semitendinosus tendon. Interpretation The results of this study demonstrate differences between the semitendinosus and gracilis tendons in terms of their quasi-static mechanical and non-linear viscoelastic properties. These results are important for establishing surgical preconditioning protocols and graft selection.