Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence

Residual stress due to shrinkage of polymethylmethacrylate bone cement after polymerisation is possibly one factor capable of initiating cracks in the mantle of cemented hip replacements. No relationship between residual stress and observed cracking of cement has yet been demonstrated. To investigate if any relationship exists, a physical model has been developed which allows direct observation of damage in the cement layer on the femoral side of total hip replacement. The model contains medial and lateral cement layers between a bony surface and a metal stem; the tubular nature of the cement mantle is ignored. Five specimens were prepared and examined for cracking using manual tracing of stained cracks, observed by transmission microscopy; cracks were located and measured using image analysis. A mathematical approach for the prediction of residual stress due to shrinkage was developed which uses the thermal history of the material to predict when stress-locking occurs, and estimates subsequent thermal stress. The residual stress distribution of the cement layer in the physical model was then calculated using finite element analysis. Results show maximum tensile stresses normal to the observed crack directions, suggesting a link between residual stress and pre-load cracking. The residual stress predicted depends strongly on the definition of the reference temperature for stress-locking. The highest residual stresses (4-7 MPa) are predicted for shrinkage from maximum temperature; in this case, magnitudes are sufficiently high to initiate cracks when the influence of stress raisers such as pores or interdigitation at the bone/cement interface are taken into account (up to 24 MPa when calculating stress around a pore according to the method of Harrigan and Harris (J. Biomech. 24(11) (1991) 1047-1058). We conclude that the damage accumulation failure scenario begins before weight-bearing due to cracking induced by residual stress around pores or stress raisers.     

Cement mantle fatigue failure in total hip replacement: experimental and computational testing

One possible loosening mechanism of the femoral component in total hip replacement is fatigue cracking of the cement mantle. A computational method capable of simulating this process may therefore be a useful tool in the preclinical evaluation of prospective implants. In this study, we investigated the ability of a computational method to predict fatigue cracking in experimental models of the implanted femur construct. Experimental specimens were fabricated such that cement mantle visualisation was possible throughout the test. Two different implant surface finishes were considered: grit blasted and polished. Loading was applied to represent level gait for two million cycles. Computational (finite element) models were generated to the same geometry as the experimental specimens, with residual stress and porosity simulated in the cement mantle. Cement fatigue and creep were modelled over a simulated two million cycles. For the polished stem surface finish, the predicted fracture locations in the finite element models closely matched those on the experimental specimens, and the recorded stem displacements were also comparable. For the grit blasted stem surface finish, no cement mantle fractures were predicted by the computational method, which was again in agreement with the experimental results. It was concluded that the computational method was capable of predicting cement mantle fracture and subsequent stem displacement for the structure considered.     

Finite element and experimental models of cemented hip joint reconstructions can produce similar bone and cement strains in pre-clinical tests

Finite element (FE) models could be used for pre-clinical testing of cemented hip replacement implants against the damage accumulation failure scenario. To accurately predict mechanical failure, the models should accurately predict stresses and strains. This should be the case for various implants. In the current study, two FE models of composite hip reconstructions with two different implants were validated relative to experimental bone and cement strains. The objective was an overall agreement within 10% between experimental and FE strains. Two stem types with different clinical results were analyzed: the Lubinus SPII and the Mueller Curved with loosening rates of 4% and 16% after 10 yr, respectively (Prognosis of total hip replacement. 63rd Annual Meeting of the American Academy of orthopaedic surgeons, Atlanta, USA). For both implant types, six stems were implanted in composite femurs. All specimens were subjected to bending. The Mueller Curved specimens were additionally subjected to torsion. Bone strains were recorded at 10 locations on the cortex and cement strains at three locations within the cement mantle. An FE model was built for both stem types and the experiments were simulated. Bone and cement strains were calculated at the experimental gauge locations. Most FE bone strains corresponded to the mean experimental strains within two standard deviations; most FE cement strains within one standard deviation. Linear regression between the FE and mean experimental strains produced slopes between 0.82 and 1.03, and R(2) values above 0.98. Particularly for the Mueller Curved, agreement improved considerably when FE strains were compared to the strains from the experimental specimen used to build the FE model. The objective of overall agreement within 10% was achieved, indicating that both FE models were successfully validated. This prerequisite for accurately predicting long-term failure has been satisfied.     

Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure.

Failure of articular cartilage has been investigated experimentally and theoretically, but there is only partial agreement between observed failure and predicted regions of peak stresses. Since trauma and repetitive stress are implicated in the etiopathogenesis of osteoarthritis, it is important to develop cartilage models which correctly predict sites of high stresses. Cartilage is anisotropic and inhomogeneous, though it has been difficult to incorporate these complexities into engineering analyses. The objectives of this study are to demonstrate that a transversely isotropic, biphasic model of cartilage can provide agreement between predicted regions of high stresses and observed regions of cartilage failure and that with transverse isotropy cartilage stresses are more sensitive to convexity and concavity of the surfaces than with isotropy. These objectives are achieved by solving problems of diarthrodial joint contact by the finite-element method. Results demonstrate that transversely isotropic models predict peak stresses at the cartilage surface and the cartilage-bone interface, in agreement with sites of fissures following impact loading; isotropic models predict peak stresses only at the cartilage-bone interface. Also, when convex cartilage layers contacted concave layers in this study, the highest tensile stresses occur in the convex layer for transversely isotropic models; no such differences are found with isotropic models. The significance of this study is that it establishes a threshold of modeling complexity for articular cartilage that provides good agreement with experimental observations under impact loading and that surface curvatures significantly affect stress and strain within cartilage when using a biphasic transversely isotropic model.     

On the importance of considering porosity when simulating the fatigue of bone cement

Fatigue cracking in the cement mantle of total hip replacement has been identified as a possible cause of implant loosening. Retrieval studies and in vitro tests have found porosity in the cement may facilitate fatigue cracking of the mantle. The fatigue process has been simulated computationally using a finite element/continuum damage mechanics (FE/CDM) method and used as a preclinical testing tool, but has not considered the effects of porosity. In this study, experimental tensile and four-point bend fatigue tests were performed. The tensile fatigue S-N data were used to drive the computational simulation (FE/CDM) of fatigue in finite element models of the tensile and four-point bend specimens. Porosity was simulated in the finite element models according to the theory of elasticity and using Monte Carlo methods. The computational fatigue simulations generated variability in the fatigue life at any given stress level, due to each model having a unique porosity distribution. The fracture site also varied between specimens. Experimental validation was achieved for four-point bend loading, but only when porosity was included. This demonstrates that the computational simulation of fatigue, driven by uniaxial S-N data can be used to simulate nonuniaxial loadcases. Further simulations of bone cement fatigue should include porosity to better represent the realities of experimental models.     

Stress analysis of cemented glenoid prostheses in total shoulder arthroplasty

Glenoid component loosening is the most-frequently encountered problem in the total shoulder arthroplasty. The purpose of the study was to investigate whether failure of the glenoid component is caused by stresses generated within the cement mantle, implant materials and at the various interfaces during humeral abduction, using 3-D FE analyses of implanted glenoid structures. FE models, one total polyethylene and the other, metal backed polyethylene, were developed using CT-scan data and submodelling technique, which was based on an overall solution of a natural scapula model acted upon by all the muscles, ligaments and joint reaction forces. Material interfaces were assumed to be fully bonded. Based on the FE stress analysis, the following observations were made. (1) The submodelling technique, which required a large-size submodel and the use of prescribed displacements at cut-boundaries located far away from the glenoid, was crucial for evaluations on glenoid component. (2) Total polyethylene results in lower-peak stresses (tensile: 10 MPa, Von-Mises: 8.31 MPa) in the cement as compared to a metal-backed design (tensile: 11.5 MPa, Von-Mises: 9.81 MPa). The maximum principal (tensile) stresses generated in the cement mantle for both the designs were below its failure strength, but might evoke crack initiation. (3) The cement-bone interface adjacent to the tip of the keel seemed very likely to fail for both the designs. In case of metal-backed design, this interface adjacent to the tip of the keel appears even more likely to fail. (4) High metal-cement interface stresses for a moderate load might indicate failure at higher load. (5) It appears that both the designs were vulnerable to failure in some ways or the other. A part of the subchondral bone along the longitudinal axis of the glenoid cavity should be preserved to strengthen the glenoid structure and to reduce the use of cement.     

Pre-clinical validation of a new partially cemented femoral prosthesis by synergetic use of numerical and experimental methods

The present work reports the pre-clinical validation of an innovative partially cemented femoral prosthesis called cement-locked uncemented (CLU) prosthesis. The inventors of the device under investigation claimed that, when compared to a comparable fully cemented stem, the new stem would present various advantages. Two previous experimental studies confirmed that primary stability and stress shielding were comparable to those of cemented stems. Aim of the present study was to investigate if the remaining claims were confirmed as well. A complete finite element model of the bone-implant complex was created from CT data. The model was validated against in vitro measurements of bone surface strains as well as against primary stability measurements. The peak stresses predicted in the CLU cement mantle were not found significantly lower than those reported in other studies on fully cemented stems. However, once the cement inlet geometry is optimised and the associated stress risers are eliminated, the CLU cement mantle should be subjected to much lower stresses. The stress induced in the stems by both load cases was well below the fatigue limit of the Ti6Al4V alloy. Finite element models predicted for all load cases relative motion between cement and metal lower than 60 microm. This amplitude may be fully accommodated by elastic deformations of the cement micro-ridges. The experimental and numerical results showed the validity of the new fixation concept, although a further optimisation of the geometry of the cement pockets is needed in order to further reduce the stresses in the cement.     

Microstructural residual stress in particle-filled dental composite

The main goal of this study is to develop a micromechanical model of a particle-filled dental composite focused on the residual stress (RS) field developed during the curing process in its microstructure. A finite element model of a representative volume element of filler and resin was developed, and volumetric shrinkage was simulated during the curing process. Four material models (von Mises plasticity model, Drucker–Prager plasticity model, von Mises plasticity model with stress relaxation and Drucker–Prager plasticity with stress relaxation) of the polymer resin were built to assess the influence of the material model on the resulting internal stress. The relationship between the curing process and the magnitude of the stress components will be described, and an analysis of the post-curing state of the material in particular microstructure locations will be conducted in this study. Obtained RS is comparable to the stresses developed in the material under the external load. The substantial dependence on the choice of material model for resin is to be observed, and the suitability of particular models is discussed.     

Measurement of transient and residual stresses during polymerization of bone cement for cemented hip implants

The initial fixation of a cemented hip implant relies on the strength of the interface between the stem, bone cement and adjacent bone. Bone cement is used as grouting material to fix the prosthesis to the bone. The curing process of bone cement is an exothermic reaction where bone cement undergoes volumetric changes that will generate transient stresses resulting in residual stresses once polymerization is completed. However, the precise magnitude of these stresses is still not well documented in the literature. The objective of this study is to develop an experiment for the direct measurement of the transient and residual radial stresses at the stem-cement interface generated during cement polymerization. The idealized femoral-cemented implant consists of a stem placed inside a hollow cylindrical bone filled with bone cement. A sub-miniature load cell is inserted inside the stem to make a direct measurement of the radial compressive forces at the stem-cement interface, which are then converted to radial stresses. A thermocouple measures the temperature evolution during the polymerization process. The results show the evolution of stress generation corresponding to volumetric changes in the cement. The effect of initial temperature of the stem and bone as well as the cement-bone interface condition (adhesion or no adhesion) on residual radial stresses is investigated. A maximum peak temperature of 70 degrees C corresponds to a peak in transient stress during cement curing. Maximum radial residual stresses of 0.6MPa in compression are measured for the preheated stem.     

Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus.

Accurate tissue stress predictions for the annulus fibrosus are essential for understanding the factors that cause or contribute to disc degeneration and mechanical failure. Current computational models used to predict in vivo disc stresses utilize material laws for annular tissue that are not rigorously validated against experimental data. Consequently, predictions of disc stress resulting from physical activities may be inaccurate and therefore unreliable as a basis for defining mechanical-biologic injury criteria. To address this need we present a model for the annulus as an isotropic ground substance reinforced with two families of collagen fibers, and an approach for determining the material constants by simultaneous consideration of multiple experimental data sets. Two strain energy functions for the annulus are proposed and used in the theory to derive the constitutive equations relating the stress to pure stretch deformations. These equations are applied to four distinct experimental protocols and the material constants are determined from a simultaneous, nonlinear regression analysis. Good agreement between theory and experiment is achieved when the invariants are included within multiple, separate exponentials in the strain energy function.     

The influence of cement mantle thickness and stem geometry on fatigue damage in two different cemented hip femoral prostheses

Experimental models can be used for pre-clinical testing of cemented and other type of hip replacements. Total hip replacement (THR) failure scenarios include, among others, cement damage accumulation and the assessment of accurate stress and strain magnitudes at the cement mantle interfaces (stem-cement and cement-bone) can be used to predict mechanical failure. The aseptic loosening scenario in cemented hip replacements is currently not fully understood, and methods of evaluating medical devices must be developed to improve clinical performance. Different results and conclusions concerning the cement micro-cracking mechanism have been reported.The aim of this study was to verify the in vitro behavior of two cemented femoral stems with respect to fatigue crack formation. Fatigue crack damage was assessed at the medial, lateral, anterior and posterior sides of the Lubinus SPII and Charnley stems. All stems were loaded and tested in stair climbing fatigue loading during one million cycles at 2 Hz. After the experiments each implanted synthetic femur was sectioned and analyzed. We observed more damage (cracks per area) for the Lubinus SPII stem, mainly on the proximal part of the cement mantle. The micro-cracking formation initiated in the stem–cement interface and grew towards the direction of cortical bone of the femur.Overall, the cement–bone interface seems to be crucial for the success of the hip replacement. The Charnley stem provoked more damage on the cement–bone interface. A failure index (maximum length of crack/maximum thickness of cement) considered was higher for the cement–stem interface of the Lubinus SPII stem. For a cement mantle thickness higher than 5 mm, cracking initiated at the cement–bone interface and depended on the opening canal process (reaming procedure and instrumentation). The analysis also showed that fatigue-induced damage on the cement mantle, increasing proximally, and depended on the axial position of the stem. The cement thickness is an important factor for the success of THR and this study evidenced that cement thickness higher than 2 mm apparently does not affect the mechanical behavior of the cement mantel and induce more crack formation on the cement–bone interface.     

Thermal analysis of bone cement polymerisation at the cement-bone interface

The two major problems that have been reported with the use of polymethylmethacrylate (PMMA) cement are thermal necrosis of surrounding bone due to the high heat generation during polymerisation and chemical necrosis due to unreacted monomer release. Computer models have been used to study the temperature and monomer distribution after cementation. In most of these models, however, polymerisation is modelled as temperature independent and cancellous bone is modelled as a continuum. Such models thus cannot account for the expected important role of the trabecular bone micro-structure. The aim of this study is to investigate the distribution of temperature and monomer leftover at the cancellous bone–cement interface during polymerisation for a realistic trabecular bone—cement micro-structure and realistic temperature-dependent polymerisation kinetics behaviour.

A 3-D computer model of a piece of bovine cancellous bone that underwent pressurization with bone–cement was generated using a micro-computed tomography scanner. This geometry was used as the basis for a finite element model and a temperature-dependent problem for bone cement polymerisation kinetics was solved to simulate the bone cement polymerisation process in the vicinity of the interface. The transient temperature field throughout the interface was calculated, along with the polymerisation fraction distribution in the cement domain.

The calculations revealed that the tips of the bone trabeculae that are embedded in the cement attain temperatures much higher than the average temperature of the bone volume. A small fraction of the bone (10%) is exposed to temperatures exceeding 70°C, but the exposure time to these high temperatures is limited to 50 s. In the region near the bone, the cement polymerisation fraction (about 84%) is less than that in the centre (where it is reaching values of over 96%). An important finding of this study thus is the fact that the bone tissue that is subjected to the highest temperatures is also subjected to high leftover monomer concentration. Furthermore the maximum bone temperature is reached relatively early, when monomer content in the neighbouring cement is still quite high.     

Stem surface roughness alters creep induced subsidence and 'taper-lock' in a cemented femoral hip prosthesis

The clinical success of polished tapered stems has been widely reported in numerous long term studies. The mechanical environment that exists for polished tapered stems, however, is not fully understood. In this investigation, a collarless, tapered femoral total hip stem with an unsupported distal tip was evaluated using a 'physiological' three-dimensional (3D) finite element analysis. It was hypothesized that stem-cement interface friction, which alters the magnitude and orientation of the cement mantle stress, would subsequently influence stem 'taper-lock' and viscoelastic relaxation of bone cement stresses. The hypothesis that creep-induced subsidence would result in increases to stem-cement normal (radial) interface stresses was also examined. Utilizing a viscoelastic material model for the bone cement in the analysis, three different stem-cement interface conditions were considered: debonded stem with zero friction coefficient (mu=0) (frictionless), debonded stem with stem-cement interface friction (mu=0.22) ('smooth' or polished) and a completely bonded stem ('rough'). Stem roughness had a profound influence on cement mantle stress, stem subsidence and cement mantle stress relaxation over the 24-h test period. The frictionless and smooth tapered stems generated compressive normal stress at the stem-cement interface creating a mechanical environment indicative of 'taper-lock'. The normal stress increased with decreasing stem-cement interface friction but decreased proximally with time and stem subsidence. Stem subsidence also increased with decreasing stem-cement interface friction. We conclude that polished stems have a greater potential to develop 'taper-lock' fixation than do rough stems. However, subsidence is not an important determinant of the maintenance of 'taper-lock'. Rather subsidence is a function of stem-cement interface friction and bone cement creep.     

The behavior of the micro-mechanical cement-bone interface affects the cement failure in total hip replacement

In the current study, the effects of different ways to implement the complex micro-mechanical behavior of the cement-bone interface on the fatigue failure of the cement mantle were investigated. In an FEA-model of a cemented hip reconstruction the cement-bone interface was modeled and numerically implemented in four different ways: (I) as infinitely stiff, (II) as infinitely strong with a constant stiffness, (III) a mixed-mode failure response with failure in tension and shear, and (IV) realistic mixed mode behavior obtained from micro-FEA models. Case II, III, and IV were analyzed using data from a stiff and a compliant micro-FEA model and their effects on cement failure were analyzed. The data used for Case IV was derived from experimental specimens that were tested previously. Although the total number of cement cracks was low for all cases, the compliant Case II resulted in twice as many cracks as Case I. All cases caused similar stress distributions at the interface. In all cases, the interface did not display interfacial softening; all stayed the elastic zone. Fatigue failure of the cement mantle resulted in a more favorable stress distribution at the cement-bone interface in terms of less tension and lower shear tractions. We conclude that immediate cement-bone interface failure is not likely to occur, but its local compliancy does affect the formation of cement cracks. This means that at a macro-level the cement-bone interface should be modeled as a compliant layer. However, implementation of interfacial post-yield softening does seems to be necessary.     

Using in vivo Cine and 3D multi-contrast MRI to determine human atherosclerotic carotid artery material properties and circumferential shrinkage rate and their impact on stress/strain predictions

In vivo magnetic resonance image (MRI)-based computational models have been introduced to calculate atherosclerotic plaque stress and strain conditions for possible rupture predictions. However, patient-specific vessel material properties are lacking in those models, which affects the accuracy of their stress/strain predictions. A noninvasive approach of combining in vivo Cine MRI, multicontrast 3D MRI, and computational modeling was introduced to quantify patient-specific carotid artery material properties and the circumferential shrinkage rate between vessel in vivo and zero-pressure geometries. In vivo Cine and 3D multicontrast MRI carotid plaque data were acquired from 12 patients after informed consent. For each patient, one nearly-circular slice and an iterative procedure were used to quantify parameter values in the modified Mooney-Rivlin model for the vessel and the vessel circumferential shrinkage rate. A sample artery slice with and without a lipid core and three material parameter sets representing stiff, median, and soft materials from our patient data were used to demonstrate the effect of material stiffness and circumferential shrinkage process on stress/strain predictions. Parameter values of the Mooney-Rivlin models for the 12 patients were quantified. The effective Young's modulus (YM, unit: kPa) values varied from 137 (soft), 431 (median), to 1435 (stiff), and corresponding circumferential shrinkages were 32%, 12.6%, and 6%, respectively. Using the sample slice without the lipid core, the maximum plaque stress values (unit: kPa) from the soft and median materials were 153.3 and 96.2, which are 67.7% and 5% higher than that (91.4) from the stiff material, while the maximum plaque strain values from the soft and median materials were 0.71 and 0.293, which are about 700% and 230% higher than that (0.089) from the stiff material, respectively. Without circumferential shrinkages, the maximum plaque stress values (unit: kPa) from the soft, median, and stiff models were inflated to 330.7, 159.2, and 103.6, which were 116%, 65%, and 13% higher than those from models with proper shrinkage. The effective Young's modulus from the 12 human carotid arteries studied varied from 137 kPa to 1435 kPa. The vessel circumferential shrinkage to the zero-pressure condition varied from 6% to 32%. The inclusion of proper shrinkage in models based on in vivo geometry is necessary to avoid over-estimating the stresses and strains by up 100%. Material stiffness had a greater impact on strain (up to 700%) than on stress (up to 70%) predictions. Accurate patient-specific material properties and circumferential shrinkage could considerably improve the accuracy of in vivo MRI-based computational stress/strain predictions.     

Residual stresses at the stem-cement interface of an idealized cemented hip stem

During the operation of total hip arthroplasty, when the cement polymerizes between the stem implant and the bone, residual stresses are generated in the cement. The purpose of this study was to determine whether including residual stresses at the stem-cement interface of cemented hip implants affected the cement stress distributions due to externally applied loads. An idealized cemented hip implant subjected to bending was numerically investigated for an early post-operative situation. The finite element analysis was three-dimensional and used non-linear contact elements to represent the debonded stem-cement interface. The results showed that the inclusion of the residual stresses at the interface had up to a 4-fold increase in the von Mises cement stresses compared to the case without residual stresses.     

Three-dimensional finite element analysis of glenoid replacement prostheses: a comparison of keeled and pegged anchorage systems

Glenoid component loosening is the dominant cause of failure in total shoulder arthroplasty. It is presumed that loosening in the glenoid is caused by high stresses in the cement layer. Several anchorage systems have been designed with the aim of reducing the loosening rate, the two major categories being "keeled" fixation and "pegged" fixation. However, no three-dimensional finite element analysis has been performed to quantify the stresses in the cement or to compare the different glenoid prosthesis anchorage systems. The objective of this study was to determine the stresses in the cement layer and surrounding bone for glenoid replacement components. A three-dimensional model of the scapula was generated using CT data for geometry and material property definition. Keeled and pegged designs were inserted into the glenoid, surrounded by a 1-mm layer of bone cement. A 90 deg arm abduction load with a full muscle and joint load was applied, following van der Helm (1994). Deformations of the prosthesis, stresses in the cement, and stresses in the bone were calculated. Stresses were also calculated for a simulated case of rheumatoid arthritis (RA) in which bone properties were modified to reflect that condition. A maximum principal stress-based failure model was used to predict what quantity of the cement is at risk of failure at the levels of stress computed. The prediction is that 94 percent (pegged prosthesis) and 68 percent (keeled prosthesis) of the cement has a greater than 95 percent probability of survival in normal bone. In RA bone, however, the situation is reversed where 86 percent (pegged prosthesis) and 99 percent (keeled prosthesis) of the cement has a greater than 95 percent probability of survival. Bone stresses are shown to be not much affected by the prosthesis design, except at the tip of the central peg or keel. It is concluded that a "pegged" anchorage system is superior for normal bone, whereas a "keeled" anchorage system is superior for RA bone.     

A 3-D constrained mixture model for mechanically mediated vascular growth and remodeling

In contrast to the widely applied approach to model soft tissue remodeling employing the concept of volumetric growth, microstructurally motivated models are capable of capturing many of the underlying mechanisms of growth and remodeling; i.e., the production, removal, and remodeling of individual constituents at different rates and to different extents. A 3-dimensional constrained mixture computational framework has been developed for vascular growth and remodeling, considering new, microstructurally motivated kinematics and constitutive equations and new stress and muscle activation mediated evolution equations. Our computational results for alterations in flow and pressure, using reasonable physiological values for rates of constituent growth and turnover, concur with findings in the literature. For example, for flow-induced remodeling, our simulations predict that, although the wall shear stress is restored completely, the circumferential stress is not restored employing realistic physiological rate parameters. Also, our simulations predict different levels of thickening on inner versus outer wall locations, as shown in numerous reports of pressure-induced remodeling. Whereas the simulations are meant to be illustrative, they serve to highlight the experimental data currently lacking to fully quantify mechanically mediated adaptations in the vasculature.     

The prediction of stress-relaxation of ligaments and tendons using the quasi-linear viscoelastic model

Recent studies have questioned the ability of the quasi-linear viscoelastic (QLV) model to predict stresses and strains in response to loading conditions other than those used to fit the model. The objective of this study was to evaluate the ability of several models in the literature to predict the elastic stress response of ligament and tendon at strain levels higher than the levels used to fit the model. The constitutive models were then used to evaluate the ability of the QLV model to predict the overall stress response during stress relaxation. The models expressing stress as an exponential function of strain significantly overestimated stress when used at higher strain levels. The polynomial formulation of the Mooney–Rivlin model more accurately predicted the stress–strain behavior of ligament and tendon. The results demonstrate that the ability of the QLV model to accurately predict the stress-relaxation response is dependent in part on the accuracy of the function used to model the elastic response of the soft tissue.