Load Sharing Between Solid and Fluid Phases in Articular Cartilage: II — Comparison of Experimental Results and u-p Finite Element Predictions

1998 ◽  
Vol 120 (5) ◽  
pp. 620-624 ◽  
Author(s):  
N. Mukherjee ◽  
J. S. Wayne
Keyword(s):  
Finite Element ◽  
Applied Load ◽  
Solid Phase ◽  
Articular Surface ◽  
Femoral Condyle ◽  
Fluid Phase ◽  
Actual Surface ◽  
Surface Deformations ◽  
Cartilage Layer ◽  
Fluid Phases

Experimental measurements in conjunction with theoretical predictions were used to determine the extent of load supported by the fluid phase of cartilage at the articular surface. The u-p finite element model was used to simulate the loading of six separate porcine knee joints and to predict surface deformations of the cartilage layer on the lateral femoral condyle. Representative geometry for the condyle, contact pressures, and intrinsic material properties of the cartilage layer were supplied from experimental measures (see Part I). The u-p finite element predictions for surface deformations of the cartilage layer were obtained for several load partitioning states between the solid and fluid phases of cartilage at the articular surface. These were then compared to actual surface deformations obtained experimentally. It appeared from the comparison that approximately 75 percent of the applied load was borne by the fluid phase at the articular surface under this loading regime. This was qualitatively in agreement with the hypothesis that an applied load to articular joints is partitioned at the surface to the two phases according to the surface area ratios of the solid and fluid phases. It appeared that the solid phase was shielded from the total applied stress on the articular surface by the fluid and could be a reason for the excellent durability of the tissue under the demanding conditions in a diarthrodial joint.

Contact Creep of Biphasic Cartilage Layers

1999 ◽  
Vol 66 (1) ◽  
pp. 137-145 ◽  
Author(s):  
R. Kelkar ◽  
G. A. Ateshian
Keyword(s):  
Material Properties ◽  
Applied Load ◽  
Interstitial Fluid ◽  
Integral Transform ◽  
Solid Phase ◽  
Fluid Phase ◽  
Biphasic Model ◽  
Physiological Loading ◽  
Fluid Pressurization ◽  
Creep Problem

Integral transform methods are used to solve the contact creep problem between two identical cylindrical biphasic cartilage layers bonded to rigid impermeable subchondral bone substrates. The biphasic model employed for cartilage consists of a binary mixture of an incompressible porous-permeable solid phase and an incompressible fluid phase. Solutions are obtained as a function of time, from the instantaneous to the equilibrium responses of the tissue. A significant result of this analysis is that under application of a step load, fluid pressurization may support upward of 96 percent of the total applied load for more congruent joints, shielding the solid collagen-proteoglycan matrix of the tissue from excessive stresses during physiological loading durations. The protection imparted by interstitial fluid pressurization to the solid collagen-proteoglycan matrix of cartilage is investigated, and the influence of material properties and osteoarthritic changes on the potential loss of this protective effect is discussed.

Effects of Friction on the Unconfined Compressive Response of Articular Cartilage: A Finite Element Analysis

1990 ◽  
Vol 112 (2) ◽  
pp. 138-146 ◽  
Author(s):  
Robert L. Spilker ◽  
Jun-Kyo Suh ◽  
Van C. Mow
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Articular Cartilage ◽  
Soft Tissues ◽  
Solid Phase ◽  
Mechanical Test ◽  
Fluid Phase ◽  
Element Formulation ◽  
Unconfined Compression ◽  
Element Analysis

A finite element analysis is used to study a previously unresolved issue of the effects of platen-specimen friction on the response of the unconfined compression test; effects of platen permeability are also determined. The finite element formulation is based on the linear KLM biphasic model for articular cartilage and other hydrated soft tissues. A Galerkin weighted residual method is applied to both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via a penalty method. The solid phase displacements and fluid phase velocities are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problem of a cylindrical specimen of soft tissue in unconfined compression. These studies show that interfacial friction plays a major role in the unconfined compression response of articular cartilage specimens with small thickness to diameter ratios.

Load Sharing Between Solid and Fluid Phases in Articular Cartilage: I — Experimental Determination of in Situ Mechanical Conditions in a Porcine Knee

1998 ◽  
Vol 120 (5) ◽  
pp. 614-619 ◽  
Author(s):  
N. Mukherjee ◽  
J. S. Wayne
Keyword(s):  
Articular Cartilage ◽  
Articular Surface ◽  
Femoral Condyle ◽  
Compressive Load ◽  
Lateral Femoral Condyle ◽  
Lateral Condyle ◽  
Medial Side ◽  
Contact Pressures ◽  
Fluid Phases

The in situ mechanical conditions of cartilage in the articulated knee were quantified during joint loading. Six porcine knees were subjected to a 445 N compressive load while cartilage deformations and contact pressures were measured. From roentgenograms, cartilage thickness before and during loading allowed the calculation of tissue deformation on the lateral femoral condyle at different times during the loading process. Contact pressures on the articular surface were measured with miniature fiber-optic pressure transducers. Results showed that the medial side of the lateral femoral condyle had higher contact pressures, as well as deformations. To begin to correlate the pressures and resulting deformations, the intrinsic material properties of the cartilage on the lateral condyle were obtained from indentation tests. Data from four normal control specimens indicated that the aggregate modulus of the medial side was significantly higher than in other areas of the condyle. These experimental measures of the in situ mechanical conditions of articular cartilage can be combined with theoretical modeling to obtain valuable information about the relative contributions of the solid and fluid phases to supporting the applied load on the cartilage surface (see Part II).

Analysis of the system precipitation reactor-separation unit. Porosity of the filtration cake as a function of properties of the solid phase

1981 ◽  
Vol 46 (11) ◽  
pp. 2640-2649 ◽  
Author(s):  
Otakar Söhnel
Keyword(s):  
Linear Function ◽  
Surface Area ◽  
Granulometric Composition ◽  
Solid Phase ◽  
Separation Unit ◽  
Initial Concentration ◽  
Actual Surface ◽  
Suspension Concentration

Porosity of the filtration cake, formed at filtration of model suspensions of CaCO3, BaCrO4 and ZnO is not a function of suspension concentration as long as the solid phase forming the suspension is of the same granulometric composition. The calculated surface area of the solid phase, effective as concerns filtration at ΔP = 30 kPa, is smaller than the actual surface area determined by absorption of nitrogen. Porosity of the filtration cake formed at filtration of suspensions of Mg(OH)2, CaCO3, SrCO3 and BaCO3 prepared by precipitation is a linear function of the initial concentration of precipitated solutions since it is affected by the size and polydispersity of originating particles in dependence on concentration of precipitated solutions. The cakes formed at filtration of precipitated suspensions of CaCO3, SrCO3 and BaCO3 aged for up to 2 hours from the instant of their preparation have a constant porosity which is independent of the time of suspension aging.

Kinematic and Dynamic Parameters of a Liquid-Solid Pipe Flow Using DPIV∕Accelerometry

2007 ◽  
Vol 129 (11) ◽  
pp. 1415-1421 ◽  
Author(s):  
Joseph Borowsky ◽  
Timothy Wei
Keyword(s):  
Pipe Flow ◽  
Solid Phase ◽  
Fluid Phase ◽  
Central Moment ◽  
Steady Flows ◽  
Dynamic Parameters ◽  
Two Phase ◽  
Turbulence Structures ◽  
Two Phases ◽  
Flat Profile

An experimental investigation of a two-phase pipe flow was undertaken to study kinematic and dynamic parameters of the fluid and solid phases. To accomplish this, a two-color digital particle image velocimetry and accelerometry (DPIV∕DPIA) methodology was used to measure velocity and acceleration fields of the fluid phase and solid phase simultaneously. The simultaneous, two-color DPIV∕DPIA measurements provided information on the changing characteristics of two-phase flow kinematic and dynamic quantities. Analysis of kinematic terms indicated that turbulence was suppressed due to the presence of the solid phase. Dynamic considerations focused on the second and third central moments of temporal acceleration for both phases. For the condition studied, the distribution across the tube of the second central moment of acceleration indicated a higher value for the solid phase than the fluid phase; both phases had increased values near the wall. The third central moment statistic of acceleration showed a variation between the two phases with the fluid phase having an oscillatory-type profile across the tube and the solid phase having a fairly flat profile. The differences in second and third central moment profiles between the two phases are attributed to the inertia of each particle type and its response to turbulence structures. Analysis of acceleration statistics provides another approach to characterize flow fields and gives some insight into the flow structures, even for steady flows.

On the Natural Lubrication of Synovial Joints: Normal and Degenerate

1977 ◽  
Vol 99 (2) ◽  
pp. 163-172 ◽  
Author(s):  
Joseph M. Mansour ◽  
Van C. Mow
Keyword(s):  
Articular Cartilage ◽  
Solid Phase ◽  
Articular Surface ◽  
Moving Load ◽  
Frictional Resistance ◽  
Elastic Solid ◽  
Surface Load ◽  
Two Phase ◽  
Tissue Properties ◽  
Synovial Joints

Fluid flow and mass transport mechanisms associated with articular cartilage function are important biomechanical processes of normal and pathological synovial joints. A three-layer permeable, two-phase medium of an incompressible fluid and a linear elastic solid are used to model the flow and deformational behavior of articular cartilage. The frictional resistance of the relative motion of the fluid phase with respect to the solid phase is given by a linear diffusive dissipation term. The subchondral bony substrate is represented by an elastic solid. The three-layer model of articular cartilage is chosen because of the known histological, ultrastructural, and biomechanical variations of the tissue properties. The calculated flow field shows that for material properties of normal healthy articular cartilage the tissue creates a naturally lubricated surface. The movement of the interstitial fluid at the surface is circulatory in manner, being exuded in front and near the leading half of the moving surface load and imbibed behind and near the trailing half of the moving load. The flow fields of healthy tissues are capable of sustaining a film of fluid at the articular surface whereas pathological tissues cannot.

A Fundamental Study of the Interaction of Residual Stress and Applied Loading on Fracture

2010 ◽  
Author(s):  
C. J. Aird ◽  
M. J. Pavier ◽  
D. J. Smith
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stress Field ◽  
Crack Closure ◽  
Applied Load ◽  
Element Model ◽  
Residual Stress Field ◽  
Fundamental Study ◽  
Analytical Expression ◽  
Applied Loading

This paper presents the results of a fundamental finite-element based study of the crack-closure effects associated with combined residual and applied loading. First, an analytical expression for a representative two-dimensional residual stress field is derived. This residual stress field contains a central compressive region surrounded by an equilibrating tensile region. The analytical expression allows the size and shape of the field to be varied along with the magnitude of the residual stress. The residual stress field is then used as a prescribed initial stress field in a finite element model, in addition to a far field applied load. By introducing cracks of increasing length into these models, charts of stress-intensity-factor versus crack length are produced for different relative magnitudes of residual stress and applied load and for different sizes and shape of the residual stress field. These charts provide insight into the way in which crack-tip conditions evolve with crack growth under conditions of combined residual and applied loading and also enable conditions of crack closure and partial closure to be identified.

scholarly journals Determination of Phase-Eigenvalues by Rational Factorization and Enhanced Simulation of Two-Phase Mass Flow

2019 ◽  
Vol 2 (2) ◽  
pp. 61-77
Author(s):  
Puskar R. Pokhrel ◽  
Bhadra Man Tuladhar
Keyword(s):  
Fluid Dynamics ◽  
Debris Flows ◽  
Lateral Pressure ◽  
Solid Phase ◽  
Fluid Phase ◽  
Factorization Method ◽  
Phase Interaction ◽  
Two Phase ◽  
Simulation Results

In this paper, we present simple and exact eigenvalues for both the solid- and fluid-phases of the real two-phase general model developed by Pudasaini (2012); we call these phase-eigenvalues, the solid- phase-eigenvalues and the fluid-phase-eigenvalues. Results are compared by applying the derived phase- eigenvalues that incorporate the phase-interactions in the two-phase debris movements against the simple and classical solid and fluid eigenvalues without any phase interaction. We have constructed several different set of eigenvalues including the coupled phase eigenvalues by using rational factorization method. At first, we consider for general debris height; factorizing the solid and fluid lateral pressure contributions by considering the negligible pressure gradient; negligible solid lateral pressure; negligible fluid lateral pressure; negligible solid and fluid lateral pressure. Secondly, for a thin debris ow height, we also construct the fourth set of eigenvalues in three different cases. These phase-eigenvalues incorporate strong interaction between the solid and fluid dynamics. The simulation results are produced by taking all these different sets of coupled phase-eigenvalues and are compared with the classical uncoupled set of solid and fluid eigenvalues. The results indicate the importance of phase-eigenvalues and supports for a complete description of the phase- eigenvalues for the enhanced description of real two-phase debris flows and landslide motions.

Trabecular Surface Remodeling Simulation for Cancellous Bone Using Microstructural Voxel Finite Element Models

2001 ◽  
Vol 123 (5) ◽  
pp. 403-409 ◽  
Author(s):  
Taiji Adachi ◽  
Ken-ichi Tsubota ◽  
Yoshihiro Tomita ◽  
Scott J. Hollister
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Cancellous Bone ◽  
Applied Load ◽  
Morphological Changes ◽  
Finite Element Models ◽  
Structural Level ◽  
Loading Direction ◽  
Surface Remodeling ◽  
Trabecular Surface

A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional adaptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcomputed tomography (μCT), and was uniaxially compressed. As a result, the apparent stiffness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investigation of the adaptive bone remodeling phenomenon.

Selecting the Optimum Bolt Assembly Stress: Influence of Flange Type on Flange Load Limit

2008 ◽  
Author(s):  
Warren Brown
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Carbon Steel ◽  
Applied Load ◽  
Hoop Stress ◽  
Elastic Analysis ◽  
Steel Weld ◽  
Element Analysis ◽  
Load Limit ◽  
Stress Influence

In previous papers, practical limits on the maximum applied load for standard ASME B16.5 and B16.47 carbon steel, weld neck pipe flanges were examined. A new code equation for the tangential (hoop) stress at the small end of the hub for a weld neck flange was developed to facilitate calculation of the limits using elastic analysis. The results were verified against elastic-plastic Finite Element Analysis (FEA). In this paper, the work is extended to include other flange configurations, including loose ring flanges, slip-on flanges and flat plate flanges. This paper is a continuation of the papers presented during PVP 2006 and PVP 2007 (Brown [1, 2]) and it extends the scope of the proposed methodology for determining flange stress limits in determining the maximum allowable bolt load for any given flange size and configuration.

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