On the contribution of solid and fluid behavior to the modeling of the time-dependent mechanics of tendons under semi-confined compression.

The present work aims to investigate whether it is possible to identify and quantify the contributions of the interstitial fluid and the solid skeleton to the overall time-dependent behavior of tendons based on a single mechanical test. For this purpose, the capabilities of three different time-dependent models (a viscoelastic, a poroelastic and a poroviscoelastic) were investigated in the modeling of the experimental behavior obtained from semi-confined compression with stress relaxation tests transverse to collagen fibers. The main achieved result points out that the poroviscoelastic model was the only one capable to characterize both the experimental responses of the force and volume changes of the tissue samples. Moreover, further analysis of this model shows that while the kinematics of the sample are mainly governed by the fluid flow (pore pressure contribution of the model), the behavior intrinsically associated with the viscoelastic solid skeleton makes a significant contribution to the experimental force response. This study reinforces the importance of taking both the experimental kinematics and kinetics of tendon tissues into account during the constitutive characterization procedure.

Is the fluid volume fraction equal to the water content in tendons? Insights on biphasic modeling.

The mass density of highly hydrated soft tissues is generally assumed to be very close to that of the water, resulting that the fluid mass fraction (water content) being equal to the fluid volume fraction. Within this context, the present study aims to investigate whether such an assumption actually holds for tendon tissues and to what extent it may affect the constitutive characterizations based on biphasic (poroelastic) models. Once the water content was assessed by a classical drying assay, the fluid volume fraction was obtained based on an image segmentation approach. The main achieved results point out that the fluid volume fraction is ∼20% higher than the water content in the studied tendons (flexor digitorum profundus bovine tendons). Based on this, it is shown that the use of the water content instead of the fluid volume fraction may considerably bias the results drawn by biphasic modeling of tendons. Accordingly, a proper measurement of the fluid volume fraction is then required.

An experimental and numerical study on the transverse deformations in tensile test of tendons.

The transverse deformations of tendons assessed in tensile tests seems to constitute a controversial issue in literature. On the one hand, large positive variations of the Poisson's ratio have been reported, indicating volume reduction under tensile states. On the other hand, negative values were also observed, pointing out an auxetic material response. Based on these experimental observations, the following question is raised: Are these large and discrepant transverse deformations intrinsically related to the constitutive response of tendons or they result from artifacts of the mechanical test setup? In order to provide further insights to this question, an experimental and numerical study on the transverse kinematics of tendons was carried out. Tensile experiments were performed in branches of deep digital flexor tendons of domestic porcine, where the transverse displacements were measured by two high-speed, high-accuracy optical digital micrometers placed transversely to one another. Aiming at a better understanding of the effects of the mechanical test setup in the transverse measurements, a three-dimensional finite element model is proposed to resemble the tensile experiment. The main achieved results strongly support the following hypotheses regarding tensile tests of tendons: the clamping region considerably affects the kinematics of the specimen even at a large distance from the clamps; the transverse deformations are mainly ruled by stiff fibers embedded in a soft matrix; the generalization of the Poisson's ratio to draw conclusions about changes in volume of tendons may lead to misinterpretations.

On multiscale boundary conditions in the computational homogenization of an RVE of tendon fascicles.

Present study provides a numerical investigation on multiscale boundary conditions in the computational homogenization of a representative volume element (RVE) of tendon fascicles. A three-dimensional hexagonal-helicoidal finite element RVE composed of two material phases (collagen fibers and cells) and three finite strain viscoelastic models (collagen fibrils, matrix of fibers and cells) compose the multiscale model. Due to the unusual helical geometry of the RVE, the performance of four multiscale boundary conditions is evaluated: the linear boundary displacements model, the minimally constrained model and two mixed boundary conditions allying characteristics of both, linear and minimal models. Numerical results concerning microscopic kinematic fields and macroscopic stress-strain curves point out that one of the mixed models is able to predict the expected multiscale mechanics of the RVE, presenting sound agreement with experimental facts reported in literature, for example: characteristic non-linear shape of the stress-strain curves; macroscopic energy loss by hysteresis; axial rotation of fascicles observed in tensile tests; collagen fibrils are the main load-bearing components of tendons; cells contribute neither to the stiffness nor to the macroscopic energy loss. Moreover, the multiscale model provides important insights on the micromechanics of tendon fascicles, predicting a non-homogeneous and relevant strain localization on cells, even under physiological macroscopic strain amplitudes.