Experimental Verification of the Roles of Intrinsic Matrix Viscoelasticity and Tension-Compression Nonlinearity in the Biphasic Response of Cartilage

2003 ◽  
Vol 125 (1) ◽  
pp. 84-93 ◽  
Author(s):  
Chun-Yuh Huang ◽  
Michael A. Soltz ◽  
Monika Kopacz ◽  
Van C. Mow ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Strain Rate ◽  
Dynamic Loading ◽  
Dynamic Compression ◽  
Solid Matrix ◽  
Supporting Evidence ◽  
Compression Stress ◽  
Unconfined Compression ◽  
Support Mechanism

A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410–417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73–84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1–38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r2=0.966±0.032 for testing at slow strain rate; r2=0.998±0.002 for testing at fast strain rate) and predictions of the dynamic response r2=0.91±0.06. This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.

A Biphasic Transversely Isotropic Poroviscoelastic Model for the Unconfined Compression of Hydrated Soft Tissue

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
H. Hatami-Marbini ◽  
R. Maulik
Keyword(s):  
Articular Cartilage ◽  
Soft Tissue ◽  
Stress Relaxation ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Viscoelastic Model ◽  
Transversely Isotropic ◽  
Solid Matrix ◽  
Unconfined Compression ◽  
Material Parameters

The unconfined compression experiments are commonly used for characterizing the mechanical behavior of hydrated soft tissues such as articular cartilage. Several analytical constitutive models have been proposed over the years to analyze the unconfined compression experimental data and subsequently estimate the material parameters. Nevertheless, new mathematical models are still required to obtain more accurate numerical estimates. The present study aims at developing a linear transversely isotropic poroviscoelastic theory by combining a viscoelastic material law with the transversely isotropic biphasic model. In particular, an integral type viscoelastic model is used to describe the intrinsic viscoelastic properties of a transversely isotropic solid matrix. The proposed constitutive theory incorporates viscoelastic contributions from both the fluid flow and the intrinsic viscoelasticity to the overall stress-relaxation behavior. Moreover, this new material model allows investigating the biomechanical properties of tissues whose extracellular matrix exhibits transverse isotropy. In the present work, a comprehensive parametric study was conducted to determine the influence of various material parameters on the stress–relaxation history. Furthermore, the efficacy of the proposed theory in representing the unconfined compression experiments was assessed by comparing its theoretical predictions with those obtained from other versions of the biphasic theory such as the isotropic, transversely isotropic, and viscoelastic models. The unconfined compression behavior of articular cartilage as well as corneal stroma was used for this purpose. It is concluded that while the proposed model is capable of accurately representing the viscoelastic behavior of any hydrated soft tissue in unconfined compression, it is particularly useful in modeling the behavior of those with a transversely isotropic skeleton.

scholarly journals Experimental Research on Mechanical and Energy Characteristics of Reinforced Rock under Dynamic Loading

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Xinxi Liu ◽  
Yu Li ◽  
Fujun Zhao ◽  
Yanming Zhou ◽  
Weiwei Wang ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Strain Rate ◽  
Dynamic Loading ◽  
Split Hopkinson Pressure Bar ◽  
Dynamic Compression ◽  
Surrounding Rock ◽  
Absorbed Energy ◽  
Energy Characteristics ◽  
Deep Mining ◽  
The Stability

The properties of anchored surrounding rock may vary considerably under complex geological and stress conditions, especially dynamic loading in deep mining. Therefore, comprehensive study of the reinforced mechanism is required to prevent failures associated with deep mining. In this paper, with sandstone as matrix and steel bar as bolt, the dynamic compression test of reinforced rock was carried out by using a 50 mm rod diameter split Hopkinson pressure bar (SHPB) test device. The mechanical and energy characteristics of reinforced rock under dynamic loading were analyzed. The results show that the dynamic strength of reinforced sample is greater than that of unreinforced sample and increases with the increase of the strain rate. The reflected energy and absorbed energy increase with the increase of incident energy, while the transmitted energy increases slightly. The higher the strain rate, the larger the energy dissipation rate and the higher the degree of fragmentation. It shows that the energy dissipation characteristic reflects the internal damage process to some extent. Compared with the results of unreinforced samples, the reflected energy of reinforced samples significantly increases and the absorbed energy will significantly decrease. It can be seen that the bolt can reduce absorbed energy of surrounding rock, thereby improving the stability of roadway surrounding rock. The results may provide reference for the stability of deep roadway and support design.

Experimental and Numerical Analysis of Qinling Mountain Engineered Rocks during Pulse-Shaped SHPB Test

2015 ◽  
Vol 16 (3-4) ◽  
pp. 165-171
Author(s):  
Shi Liu ◽  
Jinyu Xu
Keyword(s):  
Compressive Strength ◽  
Elastic Modulus ◽  
Strain Rate ◽  
Energy Absorption ◽  
Absorption Rate ◽  
Failure Modes ◽  
Dynamic Compression ◽  
Peak Strain ◽  
Compression Stress ◽  
Dynamic Compressive Strength

AbstractIn order to study the dynamic compression mechanical properties of engineering rock under high strain rate （100~102 S−1）loads, dynamic compression tests of three common engineering rocks (marble, sandstone and granite) taken from the Qinling Mountain are studied subjected to five different kinds of shock air pressure using Φ 100 mm split Hopkinson pressure bar test system improved with purple copper waveform shaper. The dynamic compression stress-strain curves, dynamic compressive strength, peak strain, energy absorption rate and elastic modulus of three rocks variation with strain rate are researched. The dynamic compression failure modes under different strain rates are analyzed. Then the three-dimensional numerical simulations of waveform shaper shaping effects and stress wave propagation in the SHPB tests are carried out to reproduce the test results. The research results show that the dynamic compression stress-strain curves show certain discreteness, and there is an obvious rebound phenomenon after the peak. With the increase in strain rate, the dynamic compressive strength, peak strain and energy absorption rate are all in a certain degree of increase, but the elastic modulus have no obvious change trend. Under the same strain rate, the dynamic compressive strength of granite is greatest while of sandstone is least. With the increase in strain rate, the margin of increase in peak strain and energy absorption rate of granite is greatest while of sandstone is least. The failure modes of the sample experience a developing process from outside to inside with the increase of strain rate.

scholarly journals Modeling of Neutral Solute Transport in a Dynamically Loaded Porous Permeable Gel: Implications for Articular Cartilage Biosynthesis and Tissue Engineering

2003 ◽  
Vol 125 (5) ◽  
pp. 602-614 ◽  
Author(s):  
Robert L. Mauck ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Solute Transport ◽  
Dynamic Loading ◽  
Interstitial Fluid ◽  
Articular Surface ◽  
Compressive Strain ◽  
Convective Transport ◽  
Solid Matrix ◽  
Bathing Solution ◽  
Loading Frequency

A primary mechanism of solute transport in articular cartilage is believed to occur through passive diffusion across the articular surface, but cyclical loading has been shown experimentally to enhance the transport of large solutes. The objective of this study is to examine the effect of dynamic loading within a theoretical context, and to investigate the circumstances under which convective transport induced by dynamic loading might supplement diffusive transport. The theory of incompressible mixtures was used to model the tissue (gel) as a mixture of a gel solid matrix (extracellular matrix/scaffold), and two fluid phases (interstitial fluid solvent and neutral solute), to solve the problem of solute transport through the lateral surface of a cylindrical sample loaded dynamically in unconfined compression with frictionless impermeable platens in a bathing solution containing an excess of solute. The resulting equations are governed by nondimensional parameters, the most significant of which are the ratio of the diffusive velocity of the interstitial fluid in the gel to the solute diffusivity in the gel Rg, the ratio of actual to ideal solute diffusive velocities inside the gel Rd, the ratio of loading frequency to the characteristic frequency of the gel f^, and the compressive strain amplitude ε0. Results show that when Rg>1,Rd<1, and f^>1, dynamic loading can significantly enhance solute transport into the gel, and that this effect is enhanced as ε0 increases. Based on representative material properties of cartilage and agarose gels, and diffusivities of various solutes in these gels, it is found that the ranges Rg>1,Rd<1 correspond to large solutes, whereas f^>1 is in the range of physiological loading frequencies. These theoretical predictions are thus in agreement with the limited experimental data available in the literature. The results of this study apply to any porous hydrated tissue or material, and it is therefore plausible to hypothesize that dynamic loading may serve to enhance solute transport in a variety of physiological processes.

An in Situ Dual Indentation and Optimization Method to Determine Mechanical Properties of Articular Cartilage

2007 ◽  
Author(s):  
Jonathan E. Pottle ◽  
J.-K. Francis Suh
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Structural Integrity ◽  
Reaction Force ◽  
Model Parameters ◽  
Unconfined Compression ◽  
Confined Compression ◽  
Practical Applications

The efficacy of the biphasic poroviscoelastic (BPVE) theory [1] in constitutive modeling of articular cartilage biomechanics is well-established [2–4]. Indeed, this model has been used to simultaneously predict stress relaxation force across confined compression, unconfined compression, and indentation protocols [2,3]. Previous works have also demonstrated success in simultaneously curve-fitting the BPVE model to reaction force and lateral deformation data gathered from stress relaxation tests of articular cartilage in unconfined compression [4]. However, a potential limitation of practical applications of such a successful model is seen in some commonly-employed mechanical testing methods for articular cartilage, such as confined compression and unconfined compression. These methods require the excision of a disk of cartilage from its underlying subchondral base, which likely would compromise the structural integrity of the tissue, causing swelling and curling artifacts of the sample [5]. Indentation represents a testing protocol that can be used with an intact cartilage layer. This results in a specimen more closely resembling cartilage in vivo. Using an agarose gel construct, our previous study [6] has demonstrated that a unique set of the six BPVE model parameters of a soft tissue can be determined readily from in situ dual indentation method using stress relaxation and creep viscoelastic protocols. The objective of the current study is to validate the efficacy of this technique as a means to determine the BPVE material parameters of articular cartilage.

scholarly journals Dynamic Response of Immature Bovine Articular Cartilage in Tension and Compression, and Nonlinear Viscoelastic Modeling of the Tensile Response

2006 ◽  
Vol 128 (4) ◽  
pp. 623-630 ◽  
Author(s):  
Seonghun Park ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Tensile Stress ◽  
Dynamic Modulus ◽  
Relaxation Function ◽  
Tensile Modulus ◽  
Relaxation Response ◽  
Unconfined Compression ◽  
Tensile Response ◽  
Cyclical Loading

Very limited information is currently available on the constitutive modeling of the tensile response of articular cartilage and its dynamic modulus at various loading frequencies. The objectives of this study were to (1) formulate and experimentally validate a constitutive model for the intrinsic viscoelasticity of cartilage in tension, (2) confirm the hypothesis that energy dissipation in tension is less than in compression at various loading frequencies, and (3) test the hypothesis that the dynamic modulus of cartilage in unconfined compression is dependent upon the dynamic tensile modulus. Experiment 1: Immature bovine articular cartilage samples were tested in tensile stress relaxation and cyclical loading. A proposed reduced relaxation function was fitted to the stress-relaxation response and the resulting material coefficients were used to predict the response to cyclical loading. Adjoining tissue samples were tested in unconfined compression stress relaxation and cyclical loading. Experiment 2: Tensile stress relaxation experiments were performed at varying strains to explore the strain-dependence of the viscoelastic response. The proposed relaxation function successfully fit the experimental tensile stress-relaxation response, with R2=0.970±0.019 at 1% strain and R2=0.992±0.007 at 2% strain. The predicted cyclical response agreed well with experimental measurements, particularly for the dynamic modulus at various frequencies. The relaxation function, measured from 2% to 10% strain, was found to be strain dependent, indicating that cartilage is nonlinearly viscoelastic in tension. Under dynamic loading, the tensile modulus at 10Hz was ∼2.3 times the value of the equilibrium modulus. In contrast, the dynamic stiffening ratio in unconfined compression was ∼24. The energy dissipation in tension was found to be significantly smaller than in compression (dynamic phase angle of 16.7±7.4deg versus 53.5±12.8deg at 10−3Hz). A very strong linear correlation was observed between the dynamic tensile and dynamic compressive moduli at various frequencies (R2=0.908±0.100). The tensile response of cartilage is nonlinearly viscoelastic, with the relaxation response varying with strain. A proposed constitutive relation for the tensile response was successfully validated. The frequency response of the tensile modulus of cartilage was reported for the first time. Results emphasize that fluid-flow dependent viscoelasticity dominates the compressive response of cartilage, whereas intrinsic solid matrix viscoelasticity dominates the tensile response. Yet the dynamic compressive modulus of cartilage is critically dependent upon elevated values of the dynamic tensile modulus.

An Analysis of the Unconfined Compression of Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 165-173 ◽  
Author(s):  
C. G. Armstrong ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Fluid Pressure ◽  
Constant Strain Rate ◽  
Elastic Solid ◽  
Solid Matrix ◽  
Unconfined Compression ◽  
Creep Stress ◽  
Internal Fluid ◽  
Equilibrium Response

Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates. Instantaneously, the “biphasic” continuum deforms without change in volume and behaves like an incompressible elastic solid of the same shear modulus. Radial fluid flow then allows the internal fluid pressure to equilibrate with the external environment. The equilibrium response is controlled by the Young’s modulus and Poisson’s ratio of the solid matrix.

Strain-rate Dependent Stiffness of Articular Cartilage in Unconfined Compression

2003 ◽  
Vol 125 (2) ◽  
pp. 161-168 ◽  
Author(s):  
L. P. Li ◽  
M. D. Buschmann ◽  
A. Shirazi-Adl
Keyword(s):  
Articular Cartilage ◽  
Strain Rate ◽  
Compressive Strain ◽  
Fluid Pressure ◽  
Nonlinear Function ◽  
Protective Mechanism ◽  
Unconfined Compression ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Elastic Loading

The stiffness of articular cartilage is a nonlinear function of the strain amplitude and strain rate as well as the loading history, as a consequence of the flow of interstitial water and the stiffening of the collagen fibril network. This paper presents a full investigation of the interplay between the fluid kinetics and fibril stiffening of unconfined cartilage disks by analyzing over 200 cases with diverse material properties. The lower and upper elastic limits of the stress (under a given strain) are uniquely established by the instantaneous and equilibrium stiffness (obtained numerically for finite deformations and analytically for small deformations). These limits could be used to determine safe loading protocols in order that the stress in each solid constituent remains within its own elastic limit. For a given compressive strain applied at a low rate, the loading is close to the lower limit and is mostly borne directly by the solid constituents (with little contribution from the fluid). In contrast, however in case of faster compression, the extra loading is predominantly transported to the fibrillar matrix via rising fluid pressure with little increase of stress in the nonfibrillar matrix. The fibrillar matrix absorbs the loading increment by self-stiffening: the quicker the loading the faster the fibril stiffening until the upper elastic loading limit is reached. This self-protective mechanism prevents cartilage from damage since the fibrils are strong in tension. The present work demonstrates the ability of the fibril reinforced poroelastic models to describe the strain rate dependent behavior of articular cartilage in unconfined compression using a mechanism of fibril stiffening mainly induced by the fluid flow.

Glycosaminoglycan and Collagen Remodeling During In Vitro Dynamic Compression of Articular Cartilage: Experiments and Finite Element Modeling

2013 ◽  
Author(s):  
Kevin A. Yamauchi ◽  
Christopher B. Raub ◽  
Albert C. Chen ◽  
Robert L. Sah ◽  
Scott J. Hazelwood ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Dynamic Compression ◽  
Fluid Velocity ◽  
Biomechanical Properties ◽  
Mechanical Stimuli ◽  
Unconfined Compression ◽  
Growth Data ◽  
Collagen Remodeling ◽  
Continuum Mixture Model

The biomechanical properties of articular cartilage (AC) can be altered by chemical and mechanical stimuli. Dynamic unconfined compression (UCC) has been shown to increase biosynthesis at moderate strain amplitudes (1–4%) and frequencies from 0.01Hz. to 0.1Hz [1]. Furthermore, interstitial fluid velocity and maximum principle strain have been proposed as candidates for controlling glycosaminoglycan (GAG) and collagen (COL) remodeling, respectively [2,3]. The goal of this study was to integrate in vitro growth data, including biochemical and microstructural properties, into a computational continuum mixture model to elucidate potential mechanical triggers for AC tissue remodeling.

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