scholarly journals Inhomogeneous Cartilage Properties Enhance Superficial Interstitial Fluid Support and Frictional Properties, But Do Not Provide a Homogeneous State of Stress

2003 ◽  
Vol 125 (5) ◽  
pp. 569-577 ◽  
Author(s):  
Ramaswamy Krishnan ◽  
Seonghun Park ◽  
Felix Eckstein ◽  
Gerard A. Ateshian
Keyword(s):  
Finite Element ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Interstitial Fluid ◽  
Elastic Stress ◽  
Articular Surface ◽  
Homogeneous State ◽  
Wear Properties ◽  
State Of Stress ◽  
Fluid Load

It has been well established that articular cartilage is compositionally and mechanically inhomogeneous through its depth. To what extent this structural inhomogeneity is a prerequisite for appropriate cartilage function and integrity is not well understood. The first hypothesis to be tested in this study was that the depth-dependent inhomogeneity of the cartilage acts to maximize the interstitial fluid load support at the articular surface, to provide efficient frictional and wear properties. The second hypothesis was that the inhomogeneity produces a more homogeneous state of elastic stress in the matrix than would be achieved with uniform properties. We have, for the first time, simultaneously determined depth-dependent tensile and compressive properties of human patellofemoral cartilage from unconfined compression stress relaxation tests. The results show that the tensile modulus increases significantly from 4.1±1.9MPa in the deep zone to 8.3±3.7MPa at the superficial zone, while the compressive modulus decreases from 0.73±0.26MPa to 0.28±0.16MPa. The experimental measurements were then implemented with the finite-element method to compute the response of an inhomogeneous and homogeneous cartilage layer to loading. The finite-element models demonstrate that structural inhomogeneity acts to increase the interstitial fluid load support at the articular surface. However, the state of stress, strain, or strain energy density in the solid matrix remained inhomogeneous through the depth of the articular layer, whether or not inhomogeneous material properties were employed. We suggest that increased fluid load support at the articular surface enhances the frictional and wear properties of articular cartilage, but that the tissue is not functionally adapted to produce homogeneous stress, strain, or strain energy density distributions. Interstitial fluid pressurization, but not a homogeneous elastic stress distribution, appears thus to be a prerequisite for the functional and morphological integrity of the cartilage.

Finite Element Modeling of Grain Aspect Ratio and Strain Energy Density in a Textured Copper Thin Film

1996 ◽  
Vol 436 ◽  
Author(s):  
R. P. Vinci ◽  
J. C. Bravman
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Aspect Ratio ◽  
Finite Element Modeling ◽  
Strain Energy Density ◽  
Driving Force ◽  
Strain Energy ◽  
Interface Energy ◽  
Element Modeling ◽  
Grain Aspect Ratio

AbstractWe have modeled the effects of grain aspect ratio on strain energy density in (100)-oriented grains in a (111)-textured Cu film on a Si substrate. Minimization of surface energy, interface energy, and strain energy density (SED) drives preferential growth of grains of certain crystallographic orientations in thin films. Under conditions in which the SED driving force exceeds the surface- and interface-energy driving forces, Cu films develop abnormally large (100) oriented grains during annealing. In the elastic regime the SED differences between the (100) grains and the film average arise from elastic anisotropy. Previous analyses indicate that several factors (e.g. elimination of grain boundaries during grain growth) may alter the magnitude of the SED driving force. We demonstrate, using finite element modeling of a single columnar (100) grain in a (111) film, that changes in grain aspect ratio can significantly affect the SED driving force. A minimum SED driving force is found for (100) Cu grains with diameters on the order of the film thickness. In the absence of other stagnation mechanisms, such behavior could cause small grains to grow abnormally and then stagnate while large grains continue to grow. This would lead to a bimodal grain size distribution in the (100) grains preferred by the SED minimization.

Reliability Analysis of Radial Tire

2011 ◽  
Vol 120 ◽  
pp. 436-439
Author(s):  
Chang Shun Zhu ◽  
Guo Lin Wang ◽  
Ping Ping Li ◽  
Ru Yu Ma
Keyword(s):  
Finite Element ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Failure Modes ◽  
Structural Parameters ◽  
Random Variable ◽  
Analysis Method ◽  
Rubber Material ◽  
Material Parameters ◽  
Sensitivity Analysis Method

Aimed at the radial tire's randomness in the structural parameters and material properties, etc., took the strain energy density of the tire carcass ply turn-up end as the objective function on the basis of analysis of the tire’s main failure modes, chose the tire carcass ply turn-up height and the rubber material parameters as random variable by using the Finite Element sensitivity analysis method(DSA), On this basis, adopted Monte-Carlo stochastic finite element method to calculate the reliability of the fatigue life of tire.

Large Deformation Analysis of the Arterial Cross Section

1971 ◽  
Vol 93 (2) ◽  
pp. 138-145 ◽  
Author(s):  
B. R. Simon ◽  
A. S. Kobayashi ◽  
D. E. Strandness ◽  
C. A. Wiederhielm
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Numerical Integration ◽  
Density Function ◽  
Cross Section ◽  
Finite Deformation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Exponential Form ◽  
Strain Energy Density Function

Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1/δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

Creep Analysis and Thermal-Fatigue Life Prediction of the Lead-Free Solder Sealing Ring of a Photonic Switch

2002 ◽  
Vol 124 (4) ◽  
pp. 403-410 ◽  
Author(s):  
J. Lau ◽  
Z. Mei ◽  
S. Pang ◽  
C. Amsden ◽  
J. Rayner ◽  
...  
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Energy Density ◽  
Thermal Fatigue ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Constitutive Law ◽  
Isothermal Fatigue ◽  
Thermal Fatigue Life ◽  
Sealing Ring

Thermal reliability of the solder sealing ring of Agilent Technologies’ bubble-actuated photonic cross-connect switches has been investigated in this paper. Emphasis is placed on the determination of the thermal-fatigue life of the solder sealing ring under shipping/storing/handling conditions. The solder ring is assumed to obey the Garofalo-Arrhenius creep constitutive law. The nonlinear responses such as the deflections, stresses, creep strains, and creep strain energy density of the 3-D photonic package have been determined with a commercial finite element code. In addition, isothermal fatigue tests have been performed to obtain the relationship between the number of cycle-to-failure and the strain energy density. Thus, by combining the finite element results and the isothermal fatigue test results, the average thermal-fatigue life of the solder sealing ring is readily determined and is found to be more than adequate for shipping/storing/handling the photonic switches.

Potential Failure Sites in a Flip-Chip Package With and Without Underfill

1998 ◽  
Vol 120 (4) ◽  
pp. 336-341 ◽  
Author(s):  
E. Madenci ◽  
S. Shkarayev ◽  
R. Mahajan
Keyword(s):  
Finite Element ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Flip Chip ◽  
Singular Behavior ◽  
Stress Concentrations ◽  
Finite Element Approach ◽  
Element Approach ◽  
Potential Failure ◽  
Material Discontinuities

In this study, the effect of underfill on the level of stress concentrations is investigated and possible failure sites are identified by using a global/local finite element approach. The global elements capture the exact singular behavior of the stresses near the geometric and material discontinuities. Application of the strain energy density criterion indicates the possible failure sites and how they shift due to the presence of underfill.

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