Quasi-linear Viscoelastic Theory Research Articles

Stress relaxation of human ankles is only minimally affected by knee and ankle angle

Comprehensive characterization of stress relaxation in musculotendinous structures is needed to create robust models of viscoelastic behavior. The commonly used quasi-linear viscoelastic (QLV) theory requires that the relaxation response be independent of tissue strain (length). This study aims to characterize stress relaxation in the musculotendinous and ligamentous structures crossing the human ankle (ankle-only structures and the gastrocnemius muscle–tendon unit, which crosses the ankle and knee), and to determine whether stress relaxation is independent of the length of these structures. Two experiments were conducted on 8 healthy subjects. The first experiment compared stress relaxation over 10 min at different gastrocnemius muscle–tendon unit lengths keeping the length of ankle-joint only structures fixed. The second experiment compared stress relaxation at different lengths of ankle-joint only structures keeping gastrocnemius muscle–tendon unit length fixed. Stress relaxation data were fitted with a two-term exponential function ( T= G 0+ G 1 e − λ 1 t + G 2 e − λ 2 t ). The first experiment demonstrated a significant effect of gastrocnemius muscle–tendon unit length on G 1, and the second experiment demonstrated an effect of the length of ankle-joint only structures on G 2, λ 1 and λ 2 ( p<0.05). Nonetheless, the size of effects on stress relaxation was small (Δ G/ G<10%), similar to experimental variability. We conclude that stress relaxation in the relaxed human ankle is minimally affected by changing gastrocnemius muscle–tendon unit length or by changing the lengths of ankle-joint only structures. Consequently quasi-linear viscoelastic models of the relaxed human ankle can use a common stress relaxation modulus at different knee and ankle angles with minimal error.

Recruitment Viscoelasticity of the Tendon

There is still no agreement on the nature of tissues' viscoelasticity and on its reliable modeling. We speculate that disagreements between previous observations stem from difficulties of separating between viscoelastic and preconditioning effects, since both are manifested by similar response features. Here, this and related issues were studied in the tendon as a prototype for other soft tissues. Sheep digital tendons were preconditioned under strain that was higher by 1% than the one used in subsequent testing. Each specimen was then subjected to stress relaxation, and quick release or creep. A stochastic microstructural viscoelastic theory was developed based on the collagen fibers' properties and on their gradual recruitment with stretch. Model parameters were estimated from stress relaxation data and predictions were compared with the creep data. Following its validation, the new recruitment viscoelasticity (RVE) model was compared, both theoretically and experimentally, with the quasilinear viscoelastic (QLV) theory. The applied preconditioning protocol produced subsequent pure viscoelastic response. The proposed RVE model provided excellent fit to both stress relaxation and creep data. Both analytical and numerical comparisons showed that the new RVE theory and the popular QLV one are equivalent under deformation schemes at which no fibers buckle. Otherwise, the equivalence breaks down; QLV may predict negative stress, in contrast to data of the quick release tests, while RVE predicts no such negative stress. The results are consistent with the following conclusions: (1) fully preconditioned tendon exhibits pure viscoelastic response, (2) nonlinearity of the tendon viscoelasticity is induced by gradual recruitment of its fibers, (3) a new structure-based RVE theory is a reliable representation of the tendon viscoelastic properties under both stress relaxation and creep tests, and (4) the QLV theory is equivalent to the RVE one (and valid) only under deformations in which no fibers buckle. The results also suggest that the collagen fibers themselves are linear viscoelastic.

The Viscoelastic Properties of Passive Eye Muscle in Primates. II: Testing the Quasi-Linear Theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory.We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fung's model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition.While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.

Biomechanical and Biotribological Correlation of Induced Wear on Bovine Femoral Condyles

Characterizing the biomechanical and biotribological properties for articular surfaces in healthy, damaged, and repaired states will both elucidate the understanding of mechanical degradation and lubricating phenomena and enhance the development of functional tissue engineered cartilage and surgical repair techniques. In recent work, a new methodology involving concomitant linear translational and oscillating rotational motion was developed to determine the frictional and wear characteristics of articular cartilage. The impetus of this work was to further characterize the biomechanical characteristics from stress relaxation and dynamic cyclical indentation testing of normal and damaged articular cartilage and to correlate the biotribological characteristic findings with the biomechanical data. Quasilinear viscoelastic (QLV) theory was used to curve fit the stress-relaxation data, while the dynamic data were used both to determine the dynamic properties through fast Fourier transform analysis and to validate the dynamic behavior based on the properties obtained from the QLV theory. Comparisons of the curve-fit parameters showed a significant decrease in pre- versus postwear elastic response, A (p<0.04), and viscous response, c (p<0.01). In addition, the short term relaxation time, tau1 (p<0.0062), showed a significant decrease between surfaces with and without a defect. The magnitude of the complex modulus from dynamic tests revealed a decrease due to wear, lGlpostwearlGlprewear<1 (p<0.05). The loss factor, tan delta, was generally greater while lGl was less for those specimens experiencing rotation. A linear regression analysis was performed to correlate microstatic and microinitial with the curve-fit QLV parameters, A, B, c, tau1, and tau2. Increasing coefficients of friction correlated with decreases in the elastic response, A, viscous response, c, and the short term relaxation time constant, tau1, while B became increasingly nonlinear and tau2 became shorter postwear. Qualitatively, scanning electron microscopy photographs revealed the mechanical degradation of the tissue surface due to wear. Surfaces with a defect had an increased amount of wear debris, which ultimately contributed to third body wear. Surfaces without a defect had preferentially aligned abrasions, while those surfaces not within the wear path showed no signs of wear. The efficacy of various repair techniques and innovative repair tissue models in comparison to normal and worn articular surface tissue can be determined through experimental designs involving both biomechanical and biotribological parameter characterizations. The development of this comprehensive testing scenario involving both biotribological and biomechanical characteristics is essential to the continued development of potential articular repair tissue.

Temperature-dependent viscoelastic properties of the human supraspinatus tendon

Temperature effects on the viscoelastic properties of the human supraspinatus tendon were investigated using static stress-relaxation experiments and the quasi-linear viscoelastic (QLV) theory. Twelve supraspinatus tendons were randomly assigned to one of two test groups for tensile testing using the following sequence of temperatures: (1) 37, 27, and 17 °C (Group I, n=6), or (2) 42, 32, and 22 °C (Group II, n=6). QLV parameter C was found to increase at elevated temperatures, suggesting greater viscous mechanical behavior at higher temperatures. Elastic parameters A and B showed no significant difference among the six temperatures studied, implying that the viscoelastic stress response of the supraspinatus tendon is not sensitive to temperature over shorter testing durations. Using regression analysis, an exponential relationship between parameter C and test temperature was implemented into QLV theory to model temperature-dependent viscoelastic behavior. This modified approach facilitates the theoretical determination of the viscoelastic behavior of tendons at arbitrary temperatures.

Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries

Viscoelastic models can be used to better understand arterial wall mechanics in physiological and pathological conditions. The arterial wall reveals very slow time-dependent decays in uniaxial stress-relaxation experiments, coherent with weak power-law functions. Quasi-linear viscoelastic (QLV) theory was successfully applied to modeling such responses, but an accurate estimation of the reduced relaxation function parameters can be very difficult. In this work, an alternative relaxation function based on fractional calculus theory is proposed to describe stress relaxation experiments in strips cut from healthy human aortas. Stress relaxation (1 h) was registered at three incremental stress levels. The novel relaxation function with three parameters was integrated into the QLV theory to fit experimental data. It was based in a modified Voigt model, including a fractional element of order α, called spring–pot. The stress-relaxation prediction was accurate and fast. Sensitivity plots for each parameter presented a minimum near their optimal values. Least-squares errors remained below 2%. Values of order α = 0.1–0.3 confirmed a predominant elastic behavior. The other two parameters of the model can be associated to elastic and viscous constants that explain the time course of the observed relaxation function. The fractional-order model integrated into the QLV theory proved to capture the essential features of the arterial wall mechanical response.

On modelling nonlinear viscoelastic effects in ligaments

Experiments in human ligaments revealed that the rate of stress relaxation in such materials is strain dependent. This nonlinear behavior requires therefore a modified description of the standard quasilinear viscoelasticity theory commonly used in tissue biomechanics. The goal of this study is to characterize and demonstrate the importance of the nonlinear stress-relaxation behavior of ligaments undergoing finite deformation. The structural model presented herein is based on a local additive decomposition of the stress tensor into initial and non-equilibrium parts as resulted from the assumed structure of the free energy density function that generalizes Kelvin–Voigt nonlinear viscous models. We consider different viscoelastic behavior for the matrix and the fibers and the need of considering the strain dependency of this effect is clearly demonstrated. Model parameters were fit to experimental data obtained in specimens undergoing finite deformation in two directions: longitudinal and transversal with respect to the directions of the collagen fibers. The model was then tested against several multi-axial loading situations. The strain dependent relaxation and the strain rate dependent behavior of the human medial collateral ligament were accurately predicted.

Mechanical Characterization of Electrospun Polycaprolactone (PCL): A Potential Scaffold for Tissue Engineering

This paper investigates the mechanical behavior of electrospun polycaprolactone (PCL) under tensile loading. PCL in bulk form degrades slowly and is biocompatible, two properties that make it a viable option for tissue engineering applications in biomedicine. Of particular interest is the use of electrospun PCL tubes as scaffolds for tissue engineered blood vessel implants. Stress relaxation and tensile tests have been conducted with specimens at room temperature (21 degrees C) and 37 degrees C. Additionally, to probe the effects of moisture on mechanical behavior, specimens were tested either dry (in air) or submerged in water. In general, the electrospun PCL was found to exhibit rate dependence, as well as some dependence on the test temperature and on whether the sample was wet or dry. Two different models were investigated to describe the experimentally observed material behavior. The models used were Fung's theory of quasilinear viscoelasticity (QLV) and the eight-chain model developed for rubber elastomers by Arruda and Boyce (1993, "A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials," J. Mech. Phys. Solids, 41(2), pp. 389-412). The implementation and fitting results, as well as the advantages and disadvantages of each model, are presented. In general, it was found that the QLV theory provided a better fit.

Application of modified superposition model to viscoelastic behavior of periodontal ligament

The periodontal ligament (PDL) is a soft bio-logical tissue which shows a strongly nonlinear and time dependent mechanical behavior. Re-cent experiments on rabbit PDL revealed that the rate of stress relaxation is strain dependent. This nonlinear behavior of PDL cannot be de-scribed well by the separable quasi linear vis-coelasticity theory which is usually used in tis-sue biomechanics. Therefore, PDL requires a more general description which considers this nonlinearity and time dependency. The purpose of this study was to model strain dependent stress relaxation behavior of PDL using modi-fied superposition method. It is shown herein that modified superposition method describes viscoelastic nonlinearties well and shows a good compatibility with available experimental PDL data. Hence, the modified superposition model is suggested to describe periodontal ligament data, because it can suitably demon-strate both elastic nonlinearity and strain-dependent stress relaxation behavior of PDL.

Estimation of the quasi-linear viscoelastic parameters using a genetic algorithm

The quasi-linear viscoelastic (QLV) theory of Fung has been widely used for the modeling of viscoelastic properties of soft tissues. The essence of Fung’s approach is that the stress relaxation can be expressed in terms of the instantaneous elastic response and the reduced relaxation function. Using the Boltzmann superposition principle, the constitutive equation can be written as a convolution integral of the strain history and reduced relaxation function. In the appropriate models, QLV theory usually consists of five material parameters (two for the elastic response and three for the reduced relaxation function), which must be determined experimentally. However, to be consistent with the assumptions of QLV theory, the material functions should be obtained based on a step change in strain which is not possible to be performed experimentally. It is known that this may result in regression algorithms that converge poorly and yield non-unique solutions with highly variable constants, especially for long ramp times. In this paper, we use the genetic algorithm approach, which is an adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetics, and simultaneously fit the ramping and relaxation experimental data (on ligaments) to the QLV constitutive equation to obtain the material parameters.

PLANTAR PRESSURE REDISTRIBUTION AFTER A HIGH AND LOW UNLOAD

The plantar soft tissue is the primary means of physical interaction between a person and the ground during locomotion. Dynamic loads greater than body weight are borne across the entire plantar surface during each step. However, most testing of these tissues has concentrated on the structural properties of the heel pad. The purpose of this study was to determine the material properties of the plantar soft tissue from six locations beneath: the great toe (subhallucal), the 1st, 3rd and 5th metatarsal heads (submetatarsal), the lateral midfoot (lateral submidfoot) and the heel (subcalcaneal). We obtained specimens from these locations from 11 young, non-diabetic donors; the tissue was cut into 2 cm×2 cm blocks and the skin was removed. Stress relaxation experiments were conducted and the data were fit using the quasi-linear viscoelastic (QLV) theory. To determine tissue modulus, energy loss and the effect of test frequency, we also conducted displacement controlled triangle waves at five frequencies ranging from 0.005 to 10 Hz. The subcalcaneal tissue was found to have an increased relaxation time compared to the other areas. The subcalcaneal tissue was also found to have an increased modulus and decreased energy loss compared to the other areas. Across all areas, the modulus and energy loss increased for the 1 and 10 Hz tests compared to the other testing frequencies. This study is the first to generate material properties for all areas of the plantar soft tissue, demonstrating that the subcalcaneal tissue is different than the other plantar soft tissue areas. These data will have implications for foot computational modeling efforts and potentially for orthotic pressure reduction devices.

The compressive material properties of the plantar soft tissue

The plantar soft tissue is the primary means of physical interaction between a person and the ground during locomotion. Dynamic loads greater than body weight are borne across the entire plantar surface during each step. However, most testing of these tissues has concentrated on the structural properties of the heel pad. The purpose of this study was to determine the material properties of the plantar soft tissue from six locations beneath: the great toe (subhallucal), the 1st, 3rd and 5th metatarsal heads (submetatarsal), the lateral midfoot (lateral submidfoot) and the heel (subcalcaneal). We obtained specimens from these locations from 11 young, non-diabetic donors; the tissue was cut into 2 cm×2 cm blocks and the skin was removed. Stress relaxation experiments were conducted and the data were fit using the quasi-linear viscoelastic (QLV) theory. To determine tissue modulus, energy loss and the effect of test frequency, we also conducted displacement controlled triangle waves at five frequencies ranging from 0.005 to 10 Hz. The subcalcaneal tissue was found to have an increased relaxation time compared to the other areas. The subcalcaneal tissue was also found to have an increased modulus and decreased energy loss compared to the other areas. Across all areas, the modulus and energy loss increased for the 1 and 10 Hz tests compared to the other testing frequencies. This study is the first to generate material properties for all areas of the plantar soft tissue, demonstrating that the subcalcaneal tissue is different than the other plantar soft tissue areas. These data will have implications for foot computational modeling efforts and potentially for orthotic pressure reduction devices.

Nonlinear Viscoelastic Behavior of Human Knee Ligaments Subjected to Complex Loading Histories

The nonlinear viscoelastic structural response of the major human knee ligaments when subjected to complex loading histories is investigated, with emphasis on the collateral ligaments. Bone-ligament-bone specimens are tested in knee distraction loading, where the ligaments are in the anatomical position corresponding to a fully extended knee. Temporal nonlinearities for time scales in the range of 1<or=t <or=500 s are characterized with a dedicated series of loading histories. In particular, the response to several complex sequences of step-and-hold tests and loading-unloading cycles is investigated. The separability of the time and deformation dependent behavior, as assumed for the often used quasi linear viscoelastic (QLV) theory, is found to be insufficient for describing the response in the time range considered. Non-recoverable inelastic flow is observed in this time range. A phenomenological 1-dimensional nonlinear viscoelastic model that qualitatively describes the experimentally observed inelastic phenomena is presented.

Reduced Parameter Formulation for Incorporating Fiber Level Viscoelasticity into Tissue Level Biomechanical Models

Collagen is known to be a viscoelastic material and therefore is an important source of time dependent behavior in soft tissue. Though there are material models for soft tissue that rely on properties and structure of constituent collagen fibers, such models generally utilize only the elastic properties of collagen, and thus the resulting tissue level response does not possess any viscoelastic features. Here, the time dependent properties of collagen are directly incorporated into a fiber based hyperelastic model using the one dimensional theory of quasi-linear viscoelasticity within the context of a locally defined, anisotropic representation of extracellular matrix structure. The resulting model possesses seven material parameters and, using numerical and computational analysis, is shown to successfully predict many key features of soft tissue response including anisotropy, strain hardening, preconditioning, and rate independent hysteresis. A formulation is also introduced for incorporating fiber level viscoelasticity into structural models derived from a continuous representation of fiber structure.

A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67-76; Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306-312; Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908-214; Weiss et al., 2002, J. Biomech., 35, pp. 943-950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.

Pedestrian Injuries: Viscoelastic Properties of Human Knee Ligaments at High Loading Rates

Objective. Accidents involving pedestrians are very common, and often lead to severe injuries to the lower extremities. In a large portion of pedestrian-automobile collisions, knee ligament injuries are sustained. In this study, the viscoelastic properties of the four major human knee ligaments were investigated at loading rates representative for pedestrian-automobile collisions. Methods. Bone-ligament-bone specimens were tested in knee distraction loading. The collateral ligaments and the separate functional bundles of the cruciate ligaments were tested in the anatomical position corresponding to a fully extended knee. A series of step-and-hold tests and ramp tests at different rates were conducted to characterize the time-dependent behavior of the knee ligaments for deformation rates associated with the pedestrian impact loading environment. The quasi linear viscoelastic (QLV) theory was used to describe the structural response of the knee ligaments and averaged parameters for this model were determined. Results. The QLV theory was found to be applicable for the time range that is relevant for pedestrian-automobile collisions. The structural behavior of the knee ligaments was found to be particularly rate-sensitive for high elongation rates, as occur during these collisions. The ligament stiffness was found to increase with age for both the collateral ligaments and with weight for the medial collateral ligament. Conclusions. For the loading conditions that are relevant for pedestrian-automobile collisions, the use of the QLV model for the description of the mechanical behavior of knee ligaments is appropriate. The rate-sensitivity is particularly important for these extreme loading conditions. The relaxation behavior was found to be consistent between different ligament types and samples. Variations due to donor anthropometry were found predominantly for the instantaneous elastic behavior.

The effects of refreezing on the viscoelastic and tensile properties of ligaments

Biomechanical testing protocols for ligaments can be extensive and span two or more days. During this time, a specimen may have to undergo more than one cycle of freezing and thawing. Thus, the objective of this study was to evaluate the effects of refreezing on the viscoelastic and tensile properties of ligaments. The femur-medial collateral ligament-tibia complexes (FMTC) from six pairs of rabbit knees were used for this study. Following sacrifice, one leg in each pair was assigned to the fresh group and the FMTC was immediately dissected and prepared for testing. The contralateral knees were fresh-frozen at −20 °C for 3 weeks, thawed, dissected and then refrozen for one additional week before being tested as the refrozen group. The cross-sectional area and shape of the medial collateral ligament (MCL) was measured using a laser micrometer system. Stress relaxation and cyclic stress-relaxation tests in uniaxial tension were performed followed by a load to failure test. When the viscoelastic behavior of the MCL was described by the quasi-linear viscoelastic (QLV) theory, no statistically significant differences could be detected for the five constants ( A, B, C, τ 1 , and τ 2 ) between the fresh and refrozen groups ( p ⩾ 0.07 ) based on our sample size. In addition, the structural properties of the FMTCs and the mechanical properties of the MCLs were also found to be similar between the two groups ( p ⩾ 0.68 ). These results suggest that careful refreezing of the specimens had little or no effect on the biomechanical properties measured.

Fractional Order Viscoelasticity of the Aortic Valve Cusp: An Alternative to Quasilinear Viscoelasticity

Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however, particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. A one-dimensional (I-D) FOV reduced relaxation function was developed, replacing the QLV "box-spectrum" function with a fractional relaxation function. A direct-fit, global optimization method was used to estimate material parameters from stress relaxation tests on aortic valve tissue. We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV, particularly for the long time constant (tau2). The mean (n = 5) fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. RESULTS SUMMARY: mean QLV parameters were C = 0.079, tau1 = 0.004, tau2 = 76, and mean FOV parameters were beta = 0.29, tau = 0.076, and rho = 1.84. FOV can provide valuable new insights into tissue viscoelastic behavior Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.

A Quasi-Linear, Viscoelastic, Structural Model of the Plantar Soft Tissue With Frequency-Sensitive Damping Properties

Little is known about the structural properties of plantar soft-tissue areas other than the heel; nor is it known whether the structural properties vary depending on location. Furthermore, although the quasi-linear viscoelastic (QLV) theory has been used to model many soft-tissue types, it has not been employed to model the plantar soft tissue. The structural properties of the plantar soft tissue were quantified via stress relaxation experiments at seven regions (subcalcaneal, five submetatarsal, and subhallucal) across eight cadaveric feet. The cadaveric feet were 36.9 +/- 17.4 (mean +/- S.D.) years of age, all free from vascular diseases and orthopedics disorders. All tests were performed at a constant environmental temperature of 35 degrees C. Stress relaxation experiments were performed; different loads were employed for different areas based on normative gait data. A modification of the relaxation spectrum employed within the QLV theory allowed for the inclusion of frequency-sensitive relaxation properties in addition to nonlinear elastic behavior. The tissue demonstrated frequency-dependent damping properties that made the QLV theory ill suited to model the relaxation. There was a significant difference between the elastic structural properties (A) of the subcalcaneal tissue and all other areas (p = 0.004), and a trend (p = 0.067) for the fifth submetatarsal to have less viscous damping (c1) than the subhallucal, or first, second, or third submetatarsal areas. Thus, the data demonstrate that the structural properties of the foot can vary across regions, but careful consideration must be given to the applied loads and the manner in which the loads were applied.

Micromechanics-Based Modeling of Biological Tissues Using the High-Fidelity Generalized Method of Cells

ABSTRACTThe fundamental problem of micromechanics is the prediction of overall response of a composite material given the properties or response of the individual constituents and their internal geometric arrangement. The recently developed High-Fidelity Generalized Method of Cells is a promising micromechanics model whose predictive capability has been demonstrated for infinitesimal deformations in the presence of inelastic constituent behavior. The extension of this micromechanics model to the finite-deformation regime and incorporation of the quasi-linear viscoelasticity theory for the constituent response extends the range of this model's applicability to the bio-engineering area. Herein, an application involving the response of mitral valve chordae tendineae is presented that demonstrates the model's capability to mimic experimentally-observed response of this class of biological tissues rooted in their characteristic microstructures.