Polymer Dynamics as a Mechanistic Model for the Flow-Independent Viscoelasticity of Cartilage

2003 ◽  
Vol 125 (5) ◽  
pp. 578-584 ◽  
Author(s):  
D. P. Fyhrie ◽  
J. R. Barone
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Molecular Interaction ◽  
Relaxation Function ◽  
Mechanistic Model ◽  
Polymer Dynamics ◽  
Mechanistic Models ◽  
Apparent Stress ◽  
Rapid Flow

The initial, rapid, flow independent, apparent stress relaxation of articular cartilage disks deformed by unconfined compressive displacement is shown to be consistent with the theory of polymer dynamics. A relaxation function for polymers based upon a mechanistic model of molecular interaction (reptation) appropriately approximated early, flow independent relaxation of stress. It is argued that the theory of polymer dynamics, with its reliance on mechanistic models of molecular interaction, is an appropriate technique for application to and the understanding of rapid, flow independent, stress relaxation in 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.

scholarly journals Simulating the Effects of Intensifying Silviculture on Desired Species Yields across a Broad Environmental Gradient

Forests ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 755
Author(s):  
Eric B. Searle ◽  
F. Wayne Bell ◽  
Guy R. Larocque ◽  
Mathieu Fortin ◽  
Jennifer Dacosta ◽  
...  
Keyword(s):  
Climate Change ◽  
Forest Management ◽  
Planning Process ◽  
Mechanistic Model ◽  
Natural Disturbance ◽  
Fine Tuning ◽  
Mechanistic Models ◽  
Paradigm Shifts ◽  
Ecological Processes ◽  
Forest Modelling

In the past two decades, forest management has undergone major paradigm shifts that are challenging the current forest modelling architecture. New silvicultural systems, guidelines for natural disturbance emulation, a desire to enhance structural complexity, major advances in successional theory, and climate change have all highlighted the limitations of current empirical models in covering this range of conditions. Mechanistic models, which focus on modelling underlying ecological processes rather than specific forest conditions, have the potential to meet these new paradigm shifts in a consistent framework, thereby streamlining the planning process. Here we use the NEBIE (a silvicultural intervention scale that classifies management intensities as natural, extensive, basic, intensive, and elite) plot network, from across Ontario, Canada, to examine the applicability of a mechanistic model, ZELIG-CFS (a version of the ZELIG tree growth model developed by the Canadian Forest Service), to simulate yields and species compositions. As silvicultural intensity increased, overall yield generally increased. Species compositions met the desired outcomes when specific silvicultural treatments were implemented and otherwise generally moved from more shade-intolerant to more shade-tolerant species through time. Our results indicated that a mechanistic model can simulate complex stands across a range of forest types and silvicultural systems while accounting for climate change. Finally, we highlight the need to improve the modelling of regeneration processes in ZELIG-CFS to better represent regeneration dynamics in plantations. While fine-tuning is needed, mechanistic models present an option to incorporate adaptive complexity into modelling forest management outcomes.

QUASI-LINEAR VISCOELASTIC MODELLING OF UNCURED PREPREGS UNDER COMPACTION

2021 ◽  
Author(s):  
SIDDHESH S. KULKARNI ◽  
KAMRAN A. KHAN ◽  
REHAN UMER
Keyword(s):  
Stress Relaxation ◽  
Relaxation Function ◽  
Soft Tissues ◽  
Volume Fraction ◽  
Time Dependent ◽  
Strain History ◽  
Manufacturing Processes ◽  
Fiber Volume ◽  
Consolidation Process ◽  
Thermoset Resin

Reinforcement compaction sometimes referred as consolidation process and is one of the key steps in various composite manufacturing processes such as autoclave and out-of-autoclave processing. The prepregs consist of semi-cured thermoset resin system impregnating the fibers. hence, the prepreg shows strong viscoelastic compaction response, which strongly depends on compaction speed and stress relaxation. modeling of time-dependent response is of utmost importance to understand the behavior of prepregs during different stages of composites manufacturing processes. The quasilinear viscoelastic (QLV) theory has been extensively used for the modeling of viscoelastic response of soft tissues in biomedical applications. In QLV approach, the stress relaxation can be expressed in terms of the nonlinear elastic function and the reduced relaxation function. The constitutive equation can be represented by a convolution integral of the nonlinear strain history, and reduced relaxation function. This study adopted a quasilinear viscoelastic modeling approach to describe the time dependent behavior of uncured-prepregs under compression. The model was modified to account for the compaction behavior of the prepreg under a compressive load. The deformation behavior of the prepreg is usually characterized by the fiber volume fraction, V . In this study, the material used was a 2/2 Twill weave glass prepreg (M26T) supplied by Hexcel® Industries USA. We performed a compaction experiment of the uncured prepreg at room temperature at different displacement rate and subsequent relaxation to describe the viscoelastic behavior of the prepreg. The model parameter calibration was performed using the trust-region-reflective algorithm in matlab to a selected number of test data. The calibrated model was then used to predict the rate dependent compaction and relaxation response of prepregs for different fiber volume fractions and strain rates.

scholarly journals Inferring node dates from tip dates in fossil Canidae: the importance of tree priors

2016 ◽  
Author(s):  
Nicholas J. Matzke ◽  
April Wright
Keyword(s):  
Phylogenetic Trees ◽  
Mechanistic Model ◽  
Mechanistic Models ◽  
Dating Methods ◽  
Uniform Tree ◽  
Key Nodes ◽  
Birth Death

AbstractTip-dating methods are becoming popular alternatives to traditional node calibration approaches for building time-scaled phylogenetic trees, but questions remain about their application to empirical datasets. We compared the performance of the most popular methods against a dated tree of fossil Canidae derived from previously published monographs. Using a canid morphology dataset, we performed tip-dating using Beast 2.1.3 and MrBayes 3.2.5. We find that for key nodes (Canis, ~3.2 Ma, Caninae ~11.7 Ma) a non-mechanistic model using a uniform tree prior produces estimates that are unrealistically old (27.5, 38.9 Ma). Mechanistic models (incorporating lineage birth, death, and sampling rates) estimate ages that are closely in line with prior research. We provide a discussion of these two families of models (mechanistic vs. non-mechanistic) and their applicability to fossil datasets.

Stress relaxation function of bone and bone collagen

1993 ◽  
Vol 26 (12) ◽  
pp. 1369-1376 ◽  
Author(s):  
Naoki Sasaki ◽  
Yoshinori Nakayama ◽  
Makoto Yoshikawa ◽  
Atsushi Enyo
Keyword(s):  
Stress Relaxation ◽  
Relaxation Function ◽  
Bone Collagen

Comparison of biphasic material properties of equine articular cartilage estimated from stress relaxation and creep indentation tests

2021 ◽  
Vol 7 (2) ◽  
pp. 363-366
Author(s):  
Thomas Reuter ◽  
Christof Hurschler
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Material Properties ◽  
Soft Tissues ◽  
Sensitivity Analyses ◽  
Creep Model ◽  
Fe Model ◽  
Relaxation Model ◽  
Marquardt Algorithm ◽  
Indentation Tests

Abstract Mechanical parameters of hard and soft tissues are explicit markers for quantitative tissue characterization. In this study, we present a comparison of biphasic material properties of equine articular cartilage estimated from stress relaxation (ε = 6 %, t = 1000 s) and creep indentation tests (F = 0.1 N, t = 1000 s). A biphasic 3D-FE-based method is used to determine the biomechanical properties of equine articular cartilage. The FE-model computation was optimized by exploiting the axial symmetry and mesh resolution. Parameter identification was executed with the Levenberg- Marquardt-algorithm. Additionally, sensitivity analyses of the calculated biomechanical parameters were performed. Results show that the Young’s modulus E has the largest influence and the Poisson’s ratio of ν ≤ 0.1 is rather insensitive. The R² of the fit results varies between 0.882 and 0.974 (creep model) and between 0.695 and 0.930 (relaxation model). The averaged parameters E and k determined from the creep model yield higher values in comparison to the relaxation model. The differences can be traced back to the experimental settings and to the biphasic material model.

scholarly journals Modified Mechanistic Model Based on Gaussian Process Adjusting Technique for Cutting Force Prediction in Micro-End Milling

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Xiaoping Liao ◽  
Zhenkun Zhang ◽  
Kai Chen ◽  
Kang Li ◽  
Junyan Ma ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Mechanistic Model ◽  
Machining Process ◽  
Mechanistic Models ◽  
Machining Processes ◽  
Model Based ◽  
Micro End Milling

Micro-end milling is in common use of machining micro- and mesoscale products and is superior to other micro-machining processes in the manufacture of complex structures. Cutting force is the most direct factor reflecting the processing state, the change of which is related to the workpiece surface quality, tool wear and machine vibration, and so on, which indicates that it is important to analyze and predict cutting forces during machining process. In such problems, mechanistic models are frequently used for predicting machining forces and studying the effects of various process variables. However, these mechanistic models are derived based on various engineering assumptions and approximations (such as the slip-line field theory). As a result, the mechanistic models are generally less accurate. To accurately predict cutting forces, the paper proposes two modified mechanistic models, modified mechanistic models I and II. The modified mechanistic models are the integration of mathematical model based on Gaussian process (GP) adjustment model and mechanical model. Two different models have been validated on micro-end-milling experimental measurement. The mean absolute percentage errors of models I and II are 7.76% and 6.73%, respectively, while the original mechanistic model’s is 15.14%. It is obvious that the modified models are in better agreement with experiment. And model II performs better between the two modified mechanistic models.

Direct Osmotic Pressure Measurements in Articular Cartilage Demonstrate Nonideal and Concentration-Dependent Phenomena

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Brandon K. Zimmerman ◽  
Robert J. Nims ◽  
Alex Chen ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Osmotic Pressure ◽  
Electrostatic Interactions ◽  
Swelling Pressure ◽  
Confined Compression ◽  
Human Cartilage ◽  
Poisson Boltzmann ◽  
Triphasic Theory

Abstract The osmotic pressure in articular cartilage serves an important mechanical function in healthy tissue. Its magnitude is thought to play a role in advancing osteoarthritis. The aims of this study were to: (1) isolate and quantify the magnitude of cartilage swelling pressure in situ; and (2) identify the effect of salt concentration on material parameters. Confined compression stress-relaxation testing was performed on 18 immature bovine and six mature human cartilage samples in solutions of varying osmolarities. Direct measurements of osmotic pressure revealed nonideal and concentration-dependent osmotic behavior, with magnitudes approximately 1/3 those predicted by ideal Donnan law. A modified Donnan constitutive behavior was able to capture the aggregate behavior of all samples with a single adjustable parameter. Results of curve-fitting transient stress-relaxation data with triphasic theory in febio demonstrated concentration-dependent material properties. The aggregate modulus HA increased threefold as the external concentration decreased from hypertonic 2 M to hypotonic 0.001 M NaCl (bovine: HA=0.420±0.109 MPa to 1.266±0.438 MPa; human: HA=0.499±0.208 MPa to 1.597±0.455 MPa), within a triphasic theory inclusive of osmotic effects. This study provides a novel and simple analytical model for cartilage osmotic pressure which may be used in computational simulations, validated with direct in situ measurements. A key finding is the simultaneous existence of Donnan osmotic and Poisson–Boltzmann electrostatic interactions within cartilage.

A Continuum Theory and an Experiment for the Ion-Induced Swelling Behavior of Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 151-158 ◽  
Author(s):  
E. R. Myers ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Tensile Force ◽  
Continuum Theory ◽  
Swelling Behavior ◽  
Bovine Articular Cartilage ◽  
Free Swelling ◽  
Transient Force

Swelling of normal bovine articular cartilage equilibrated in NaCl solutions was dimensionally measured in thin strips of tissue. The ion-induced strains show that free swelling of articular cartilage is anisotropic and inhomogeneous. For the molar concentrations used, contraction increased linearly with concentration, defining a “coefficient of chemical contraction” (αc). Isometrically constrained specimens registered a rise in tensile force followed by stress relaxation. An extension of the biphasic theory incorporating this ion-induced strain is proposed. This theory can describe the equilibrium anisotropic swelling behavior of cartilage and explain the transient force history observed in the isometric experiment.

scholarly journals Effects of enzymatic degradation on the frictional response of articular cartilage in stress relaxation

2005 ◽  
Vol 38 (6) ◽  
pp. 1343-1349 ◽  
Author(s):  
Ines M. Basalo ◽  
David Raj ◽  
Ramaswamy Krishnan ◽  
Faye H. Chen ◽  
Clark T. Hung ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Enzymatic Degradation
Sign in / Sign up

Export Citation Format

Share Document