Finite Element Formulation of Biphasic Poroviscoelastic Model for Articular Cartilage

1998 ◽  
Vol 120 (2) ◽  
pp. 195-201 ◽  
Author(s):  
Jun-Kyo Suh ◽  
Shi Bai
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Discrete Spectrum ◽  
Element Model ◽  
Solid Matrix ◽  
Element Formulation ◽  
Confined Compression ◽  
Computationally Efficient ◽  
Relaxation Responses ◽  
Creep And Stress Relaxation

The purpose of the present study was to develop a computationally efficient finite element model that could be useful for parametric analysis of the biphasic poroviscoelastic (BPVE) behavior of articular cartilage under various loading conditions. The articular cartilage was modeled as the BPVE mixture of a porous, linear viscoelastic, and incompressible solid and an inviscid and incompressible fluid. A finite element (FE) formulation of the BPVE model was developed using two different algorithms, the continuous and discrete spectrum relaxation functions for the viscoelasticity of the solid matrix. These algorithms were applied to the creep and stress relaxation responses to the confined compression of articular cartilage, and a comparison of their performances was made. It was found that the discrete spectrum algorithm significantly saved CPU time and memory, as compared to the continuous spectrum algorithm. The consistency analysis for the present FE formulation was performed in comparison with the IMSL, a commercially available numerical software package. It was found that the present FE formulation yielded consistent results in predicting model behavior, whereas the IMSL subroutine produced inconsistent results in the velocity field, and thereby in the strain calculation.

scholarly journals Simulating the Growth of Articular Cartilage Explants in a Permeation Bioreactor to Aid in Experimental Protocol Design

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Timothy P. Ficklin ◽  
Andrew Davol ◽  
Stephen M. Klisch
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Articular Cartilage ◽  
Element Model ◽  
Cartilage Explants ◽  
Solid Matrix ◽  
Cartilage Growth ◽  
Growth Laws ◽  
Competing Hypotheses

Recently a cartilage growth finite element model (CGFEM) was developed to solve nonhomogeneous and time-dependent growth boundary-value problems (Davol et al., 2008, “A Nonlinear Finite Element Model of Cartilage Growth,” Biomech. Model. Mechanobiol., 7, pp. 295–307). The CGFEM allows distinct stress constitutive equations and growth laws for the major components of the solid matrix, collagens and proteoglycans. The objective of the current work was to simulate in vitro growth of articular cartilage explants in a steady-state permeation bioreactor in order to obtain results that aid experimental design. The steady-state permeation protocol induces different types of mechanical stimuli. When the specimen is initially homogeneous, it directly induces homogeneous permeation velocities and indirectly induces nonhomogeneous solid matrix shear stresses; consequently, the steady-state permeation protocol is a good candidate for exploring two competing hypotheses for the growth laws. The analysis protocols were implemented through the alternating interaction of the two CGFEM components: poroelastic finite element analysis (FEA) using ABAQUS and a finite element growth routine using MATLAB. The CGFEM simulated 12 days of growth for immature bovine articular cartilage explants subjected to two competing hypotheses for the growth laws: one that is triggered by permeation velocity and the other by maximum shear stress. The results provide predictions for geometric, biomechanical, and biochemical parameters of grown tissue specimens that may be experimentally measured and, consequently, suggest key biomechanical measures to analyze as pilot experiments are performed. The combined approach of CGFEM analysis and pilot experiments may lead to the refinement of actual experimental protocols and a better understanding of in vitro growth of articular cartilage.

scholarly journals Methodology for Developing a Macro Finite Element Model of Lithium-Ion Pouch Cells for Predicting Mechanical Behaviour under Multiple Loading Conditions

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1921
Author(s):  
Richard Beaumont ◽  
Iain Masters ◽  
Abhishek Das ◽  
Steve Lucas ◽  
Arunn Thanikachalam ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cell Structure ◽  
Lithium Ion ◽  
Element Model ◽  
Confined Compression ◽  
Computationally Efficient ◽  
Internal Cell ◽  
Bending Load ◽  
Modelling Methodology

To assist in light weighting of electric vehicles by improving the volumetric and gravimetric energy density and the structural performance of the battery pack, a modelling methodology based on a macro finite element model of a pouch cell has been developed. This model treats the core cell structure as a homogeneous orthotropic honeycomb block with the pouch material being defined as an orthotropic fabric with compressive stress elimination. The model considers five compression and bending load cases simultaneously and allows a level of element discretisation that is computationally efficient and appropriate for inclusion in full vehicle and sub-system simulations. The methodology is scalable in that it can be applied to a range of chemistries, external geometries and internal cell constructions. When considering stacks of cells, the model is predictive for both lateral compression and three-point bend, but further work is required to improve the confined compression response.

Application of the u-p Finite Element Method to the Study of Articular Cartilage

1991 ◽  
Vol 113 (4) ◽  
pp. 397-403 ◽  
Author(s):  
Jennifer S. Wayne ◽  
Savio L.-Y. Woo ◽  
Michael K. Kwan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Articular Cartilage ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Fluid Pressure ◽  
Numerical Procedure ◽  
Solid Matrix ◽  
Confined Compression ◽  
Element Method

The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (u) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the tissue.

scholarly journals Biomechanical characteristics of tibio-femoral joint after partial medial meniscectomy in different flexion angles: a finite element analysis

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Xiaohui Zhang ◽  
Shuo Yuan ◽  
Jun Wang ◽  
Bagen Liao ◽  
De Liang
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Finite Element Model ◽  
Medial Meniscus ◽  
Lateral Meniscus ◽  
Element Model ◽  
Magnetic Resonance Images ◽  
Biomechanical Analysis ◽  
Joint Stress ◽  
Tibiofemoral Joint

Abstract Background Recent studies have pointed out that arthroscopy, the commonly-used surgical procedure for meniscal tears, may lead to an elevated risk of knee osteoarthritis (KOA). The biomechanical factors of KOA can be clarified by the biomechanical analysis after arthroscopic partial meniscectomy (APM). This study aimed to elucidate the cartilage stress and meniscus displacement of the tibiofemoral joint under flexion and rotation loads after APM. Methods A detailed finite element model of the knee bone, cartilage, meniscus, and major ligaments was established by combining computed tomography and magnetic resonance images. Vertical load and front load were applied to simulate different knee buckling angles. At the same time, by simulating flexion of different degrees and internal and external rotations, the stresses on tibiofemoral articular cartilage and meniscus displacement were evaluated. Results Generally, the contact stress on both the femoral tibial articular cartilage and the meniscus increased with the increased flexion degree. Moreover, the maximum stress on the tibial plateau gradually moved backward. The maximum position shift value of the lateral meniscus was larger than that of the medial meniscus. Conclusion Our finite element model provides a realistic three-dimensional model to evaluate the influence of different joint range of motion and rotating tibiofemoral joint stress distribution. The decreased displacement of the medial meniscus may explain the higher pressure on the knee components. These characteristics of the medial tibiofemoral joint indicate the potential biomechanical risk of knee degeneration.

A Finite Element Model of the Human Knee Joint for the Study of Tibio-Femoral Contact

2002 ◽  
Vol 124 (3) ◽  
pp. 273-280 ◽  
Author(s):  
Tammy L. Haut Donahue ◽  
M. L. Hull ◽  
Mark M. Rashid ◽  
Christopher R. Jacobs
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Three Dimensional ◽  
Element Model ◽  
Maximum Pressure ◽  
Contact Behavior ◽  
Element Size ◽  
Solid Models ◽  
Flexion Extension ◽  
Three Dimensional Coordinate

As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior, and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (i.e., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 mm by 5 mm to 1 mm by 1 mm. The solution was considered converged for an average element size of 2 mm by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.

Finite Element Formulation and Vibration Frequency Analysis of a Fluid Filled Pipe

2005 ◽  
Author(s):  
Yi Jia ◽  
Reinaldo E. Madeira ◽  
Frederick Just-Agosto
Keyword(s):  
Finite Element ◽  
Coriolis Force ◽  
Frequency Analysis ◽  
Cross Sections ◽  
Vibration Frequency ◽  
Dynamic Performance ◽  
Element Model ◽  
Piping System ◽  
Element Formulation ◽  
Variable Cross

This paper presents the formulation of a finite element model and vibration frequency analysis of a fluid filled pipe having variable cross sections. The finite element method with consideration of Coriolis force developed in [1] was adopted for frequency analysis of a pipe in this study. The stiffness matrix, the c-matrix (Coriolis force) and mass (for dynamic analysis) matrix that contain all parameters of the fluids properties and flow conditions have been developed. The numerical model was employed to simulate the dynamic performance of the piping system with the specific configurations for an application. A critical relationship between the natural frequencies and pipe geometry has been established. The results of frequencies analysis of the piping system gave us an insight whether a resonance frequency might occur.

scholarly journals Finite Element Implementation of Mechanochemical Phenomena in Neutral Deformable Porous Media Under Finite Deformation

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Michael B. Albro ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Finite Deformation ◽  
Biological Tissues ◽  
Solid Matrix ◽  
Element Formulation ◽  
Momentum Exchange ◽  
Deformable Porous Media ◽  
Chemical Effects ◽  
Highly Nonlinear

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software).

Nanocomposites Based on Multiwalled Carbon Nanotubes With Effective Young’s Modulus Dependent on Number of Layers

2014 ◽  
Author(s):  
Preeti Joshi ◽  
S. H. Upadhyay
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Multiwalled Carbon Nanotubes ◽  
Matrix Material ◽  
Tensile Modulus ◽  
Element Model ◽  
Solid Matrix ◽  
Multiwalled Carbon ◽  
Number Of Layers ◽  
Transverse Modulus

The excellent combination of high strength, stiffness, low density and aspect ratio makes carbon nanotubes ideal reinforcement for nanocomposites. The load transfer between the outer and inner layers of multiwalled carbon nanotubes (MWCNT) is one of the important factor in the reinforcement of nanocomposites. In this work, the effect of variation in number of layers of multiwalled carbon nanotubes on effective tensile, compressive and transverse modulus of composite is evaluated. A 3-D finite element model based on representative volume element, consisting of multiwalled carbon nanotube made of shell elements surrounded by solid matrix material is built. With the increase in number of layers in multiwalled carbon nanotubes, the compressive modulus of composite increases, while the tensile modulus decreases. The transverse modulus of composite is found to increase, with the increase in number of layers in MWCNT. The finite element results for composite are compared with the rule of mixtures results using formulae.

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