Unconfined Compression of Articular Cartilage: Nonlinear Behavior and Comparison With a Fibril-Reinforced Biphasic Model

1999 ◽  
Vol 122 (2) ◽  
pp. 189-195 ◽  
Author(s):  
M. Fortin ◽  
J. Soulhat ◽  
A. Shirazi-Adl ◽  
E. B. Hunziker ◽  
M. D. Buschmann
Keyword(s):  
Articular Cartilage ◽  
Mechanical Behavior ◽  
Small Amplitude ◽  
Dynamic Stiffness ◽  
Scaling Law ◽  
Nonlinear Behavior ◽  
Hydraulic Permeability ◽  
Unconfined Compression ◽  
Biphasic Model ◽  
Strain Dependent

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample’s radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models. [S0148-0731(00)00702-0]

A Fibril-Network-Reinforced Biphasic Model of Cartilage in Unconfined Compression

1999 ◽  
Vol 121 (3) ◽  
pp. 340-347 ◽  
Author(s):  
J. Soulhat ◽  
M. D. Buschmann ◽  
A. Shirazi-Adl
Keyword(s):  
Stress Relaxation ◽  
Composite Structure ◽  
Solid Phase ◽  
Constitutive Law ◽  
Published Data ◽  
Hydraulic Permeability ◽  
Unconfined Compression ◽  
Model Calculations ◽  
Biphasic Model ◽  
Reinforced Composite

Cartilage mechanical function relies on a composite structure of a collagen fibrillar network entrapping a proteoglycan matrix. Previous biphasic or poroelastic models of this tissue, which have approximated its composite structure using a homogeneous solid phase, have experienced difficulties in describing measured material responses. Progress to date in resolving these difficulties has demonstrated that a constitutive law that is successful for one test geometry (confined compression) is not necessarily successful for another (unconfined compression). In this study, we hypothesize that an alternative fibril-reinforced composite biphasic representation of cartilage can predict measured material responses and explore this hypothesis by developing and solving analytically a fibril-reinforced biphasic model for the case of uniaxial unconfined compression with frictionless compressing platens. The fibrils were considered to provide stiffness in tension only. The lateral stiffening provided by the fibril network dramatically increased the frequency dependence of disk rigidity in dynamic sinusoidal compression and the magnitude of the stress relaxation transient, in qualitative agreement with previously published data. Fitting newly obtained experimental stress relaxation data to the composite model allowed extraction of mechanical parameters from these tests, such as the rigidity of the fibril network, in addition to the elastic constants and the hydraulic permeability of the remaining matrix. Model calculations further highlight a potentially important difference between homogeneous and fibril-reinforced composite models. In the latter type of model, the stresses carried by different constituents can be dissimilar, even in sign (compression versus tension) even though strains can be identical. Such behavior, resulting only from a structurally physiological description, could have consequences in the efforts to understand the mechanical signals that determine cellular and extracellular biological responses to mechanical loads in cartilage.

The Asymmetry of Transient Response in Compression Versus Release for Cartilage in Unconfined Compression

2001 ◽  
Vol 123 (5) ◽  
pp. 519-522 ◽  
Author(s):  
L. P. Li ◽  
M. D. Buschmann ◽  
A. Shirazi-Adl
Keyword(s):  
Articular Cartilage ◽  
Large Deformation ◽  
Transient Response ◽  
Tensile Strain ◽  
Hydraulic Permeability ◽  
Compression Tests ◽  
Unconfined Compression ◽  
The Asymmetry

Observations in compression tests of articular cartilage have revealed unequal load increments for compression and release of the same amplitude applied to a disk with an identical previously imposed compression (in equilibrium). The mechanism of this asymmetric transient response is investigated here using a nonlinear fibril-reinforced model. It is found that the asymmetry is predominantly produced by the fibril stiffening with its tensile strain. In addition, allowing the hydraulic permeability to decrease significantly with compressive dilatation of cartilage increases the transient fibril strain, resulting in a stronger asymmetry. Large deformation also enhances the asymmetry as a consequence of stronger fibril stiffening.

Effect of Anisotropic Permeability of the Superficial Layer on the Frictional Property in Articular Cartilage

2013 ◽  
Author(s):  
Kyuichiro Imade ◽  
Hiromichi Fujie
Keyword(s):  
Articular Cartilage ◽  
Hydrodynamic Lubrication ◽  
Articular Surface ◽  
Compressive Strain ◽  
Electron Microscopic Observation ◽  
Superficial Layer ◽  
Frictional Property ◽  
Hydraulic Permeability ◽  
Electron Microscopic ◽  
Biphasic Model

Articular cartilage has a significant lubrication property that has been explained in previous studies by many theories including mixed lubrication, hydrodynamic lubrication, surface gel hydration lubrication, biphasic theory, and so on. However the mechanism of continuously low friction in articular cartilage still remains unclear. Reynaud and Quinn indicated that the hydraulic permeability was significantly anisotropic under compressive strain; the tangential permeability becomes lower than the normal permeability under compression [1]. Meanwhile scanning electron microscopic observation indicated that the superficial layer of articular surface was consisted of close-packed collagen fibers aligning parallel with articular surface and tangling each other in normal cartilage (Fig. 1). It is, therefore, suggested that the permeability is extremely low in the tangential direction when subjected to compressive strain. We have a hypothesis that the unique structure and properties in the articular cartilage superficial layer may improve the lubrication properties [2]. Therefore, we performed an analytical study using a fiber-reinforced poroelastic biphasic model to determine the effect of lateral permeability reduction in the superficial layer on the frictional property of articular cartilage.

Biphasic Poroviscoelastic Model Simultaneously Predicts Axial Reaction Force and Lateral Displacement of Articular Cartilage During an Unconfined Compression-Stress Relaxation Experiment

1999 ◽  
Author(s):  
Mark R. DiSilvestro ◽  
Qiliang Zhu ◽  
Marcy Wong ◽  
Jukka Jurvelin ◽  
Jun-Kyo Suh
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Stress Relaxation ◽  
Mechanical Behavior ◽  
Lateral Displacement ◽  
Reaction Force ◽  
Simple Extension ◽  
Unconfined Compression ◽  
Relaxation Experiment ◽  
Diarthrodial Joints

Abstract Articular cartilage lining the articulating surfaces in diarthrodial joints is composed of an extracellular matrix and interstitial fluid. The complex mechanical behavior of this tissue has been successfully modeled by the linear biphasic poroviscoelastic (BPVE) model first introduced by Mak (1986). This model, a simple extension of the well-known biphasic theory first proposed by Mow et al. (1980), accounts for both fluid flow-dependent and fluid flow-independent viscoelastic mechanisms which contribute to the overall mechanical behavior exhibited by the tissue. Despite the success of the linear BPVE model for indentation (Suh and Bai, 1997), as well as that described for unconfined compression (Suh and DiSilvestro, 1997, 1998), the model’s ability to account for more than one measurable variable with a single parameter set has not been established. Therefore, the objective, of this study was to assess the ability of the linear BPVE model to account for both the axial reaction force and lateral deformation of a cylindrical plug of articular cartilage subjected to unconfined compression under a stress relaxation protocol.

Articular Cartilage Biomechanics Modeled via an Intrinsically Compressible Biphasic Model: Implications and Deviations From an Incompressible Biphasic Approach

2013 ◽  
Author(s):  
Francesco Travascio ◽  
Roberto Serpieri ◽  
Shihab Asfour
Keyword(s):  
Articular Cartilage ◽  
Experimental Testing ◽  
Solid Matrix ◽  
Hydraulic Permeability ◽  
Theoretical Frameworks ◽  
Theoretical Formulation ◽  
New Model ◽  
Biphasic Model ◽  
Testing Procedures ◽  
Cartilage Biomechanics

Biphasic continuum models have been extensively deployed for modeling macroscopic articular cartilage biomechanics [1,2]. This consolidated theoretical approach schematizes tissue as a mixture of an elastic solid matrix embedded in a fluid phase. In physiological conditions, intrinsic compressibility of each phase is very limited when compared to the whole tissue macroscopic counterpart. Based on such experimental evidence, intrinsic phase compressibility is generally reasonably neglected [3]. Hence, traditionally, cartilage biomechanics models have been developed on the basis of incompressible biphasic formulations [3–5], often referred to as Incompressible Theories of Mixtures (ITM). Alternatively, a more general biphasic model for cartilage biomechanics, accounting for full intrinsic compressibility of phases, may be considered. A consistent theoretical formulation of this type has been recently made available [6,7], hereby referred to as Theory of Microscopically Compressible Porous Media (TMCPM). In the present contribution, a new model for articular cartilage biomechanics, based on TMCPM, was developed. Predictions of this new model, and its deviations from a traditional ITM approach were studied. In particular, deviations between compressible and incompressible theoretical frameworks were investigated with a specific focus on the repercussions on models’ capability of characterizing fundamental tissue properties, such as hydraulic permeability, via established experimental testing procedures.

Numerical Dynamic Analysis of a Single Link Soft Robot Finger

2013 ◽  
Vol 459 ◽  
pp. 449-454 ◽  
Author(s):  
Elango Natarajan ◽  
Ahmad Athif Mohd Faudzi ◽  
Viknesh Malliga Jeevanantham ◽  
Muhammad Rusydi Muhammad Razif ◽  
Ili Najaa Aimi Mohd Nordin
Keyword(s):  
Room Temperature ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Mode Shapes ◽  
Soft Robot ◽  
Fundamental Frequencies ◽  
Single Link ◽  
Hyper Elastic ◽  
Finger Model ◽  
Strain Dependent

In this paper, a solid, single link soft robot finger was modeled with SILASTIC P-1 Silicone, supplied by Dow Corning®. The material is anon-linear hyper elastic, strain dependent, room temperature vulcanized (RTV) rubber. When the fingers are actuated for grasping and object manipulation, they vibrate with excessive amplitudes, which will disturb the precise positioning of the fingers. Vibration analysis through numerical simulation was conducted in ANSYS®V12. The first ten fundamental frequencies and their mode shapes were numerically computed and presented from modal analysis. The lowest natural frequency of the finger model was found to be 2.14 Hz. The dynamic stiffness of the finger model was then computed from the natural frequencies. It was found to be nonlinear in nature. The dynamic characteristics of the finger model during the excitation between 1 Hz and 1000 Hz were studied in transient analysis. The peak acceleration occurred at 9.3 Hz, while the peak velocity occurs at 3.75 Hz and 4.8 Hz with the magnitude of 0.013 mm/s.

scholarly journals Vibration analysis of hard-coating laminated plate considering strain-dependent characteristic

2018 ◽  
Vol 37 (4) ◽  
pp. 789-800 ◽  
Author(s):  
Wei Sun ◽  
Xiaozhou Liu ◽  
Jixiang Jiang
Keyword(s):  
Composite Plate ◽  
Nonlinear Behavior ◽  
Coating Material ◽  
Hard Coating ◽  
Nonlinear Phenomenon ◽  
Laminated Plate ◽  
Lagrange’S Equation ◽  
Calculation Results ◽  
Material Nonlinear ◽  
Strain Dependent

An analytical modeling method of hard-coating laminated plate under base excitation was studied considering strain-dependent characteristic of coating material (i.e. a kind of material nonlinear behavior). For convenience, the strain-dependent characteristic of hard-coating material was characterized by polynomial, and the material parameters were divided into two parts: linearity and nonlinearity. Hard coating was regarded as a special layer in the analysis and Lagrange’s equation was used to acquire nonlinear equation of motion of the hard-coating laminated plate. Based on Newton–Raphson method, the procedure of solving resonant response and resonant frequency of composite plate was presented. Finally, a T300/QY89l1 laminated plate with NiCoCrAlY + YSZ hard coating was chosen to demonstrate the proposed method, the linear and nonlinear vibrations of the composite plate were solved, and only the linear results were validated by ANSYS software. The results reveal that there is a big difference between the calculation results considering the nonlinearity of coating material and the linear results, which means the laminated plate displays soft nonlinear phenomenon because of depositing coating.

ANTICYTOSKELETAL DRUGS AND TIME CULTURE EFFECTS UPON THE MECHANICAL BEHAVIOR OF DERMAL EQUIVALENT TISSUE SUBMITTED TO UNCONFINED COMPRESSION LOADING

2008 ◽  
Vol 08 (03) ◽  
pp. 339-352 ◽  
Author(s):  
S. RAMTANI ◽  
D. GEIGER
Keyword(s):  
Mechanical Behavior ◽  
Internal State ◽  
Skin Grafting ◽  
Biological Tissues ◽  
Matrix Remodeling ◽  
Unconfined Compression ◽  
Compression Loading ◽  
Dermal Equivalent ◽  
Variable Approach ◽  
Time Culture

The dermal equivalent (DE), a dermis substitute consisting of human skin fibroblasts growing into a three-dimensional collagen matrix, is extensively used in many applications: wound-healing response, pharmacological studies, skin grafting, fibroblast proliferation and migration, extracellular matrix remodeling, and efficacy of cosmetic products. The widespread growth of numerical modeling in biomechanical research has placed a heightened emphasis on accurate material property data for soft biological tissues, in particular for equivalent dermis which has not been so thoroughly investigated. Under unconfined compression loading, the effects of the strain rate, time culture, and cytoskeleton-disrupting agents are experimentally investigated. In order to model the observed mechanical behavior of the DE under the above conditions, the internal state variable approach is adopted for finite deformation viscoelasticity and the optimized material parameters are identified with respect to the stated thermodynamic restriction (i.e. positive viscous dissipation).

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