Nonlinear Dynamic Viscoelastic Model for Osteoarthritic Cartilage Indentation Force

2011 ◽  
Author(s):  
A. Vidal-Lesso ◽  
E. Ledesma-Orozco ◽  
R. Lesso-Arroyo ◽  
L. Daza-Benitez
Keyword(s):  
Mechanical Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Indentation Test ◽  
Maxwell Model ◽  
Relaxation Curve ◽  
Geometrical Parameters ◽  
Osteoarthritic Cartilage

Biomechanical properties and dynamic response of soft tissues as articular cartilage remains issues for attention. Currently, linear isotropic models are still used for cartilage analysis in spite of its viscoelastic nature. Therefore, the aim of this study was to propose a nonlinear viscoelastic model for cartilage indentation that combines the geometrical parameters and velocity of the indentation test with the thickness of the sample as well as the mechanical properties of the tissue changing over time due to its viscoelastic behavior. Parameters of the indentation test and mechanical properties as a function of time were performed in Laplace space where the constitutive equation for viscoelasticity and the convolution theorem was applied in addition with the Maxwell model and Hayes et al. model for instantaneous elastic modulus. Results of the models were compared with experimental data of indentation tests on osteoarthritic cartilage of a unicompartmental osteoarthritis cases. The models showed a strong fit for the axial indentation nonlinear force in the loading curve (R2 = 0.992) and a good fit for unloading (R2 = 0.987), while an acceptable fit was observed in the relaxation curve (R2 = 0.967). These models may be used to study the mechanical response of osteoarthritic cartilage to several dynamical and geometrical test conditions.

scholarly journals Soft-Tissue-Mimicking Using Hydrogels for the Development of Phantoms

Gels ◽  
2022 ◽  
Vol 8 (1) ◽  
pp. 40
Author(s):  
Aitor Tejo-Otero ◽  
Felip Fenollosa-Artés ◽  
Isabel Achaerandio ◽  
Sergi Rey-Vinolas ◽  
Irene Buj-Corral ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Linear Elastic ◽  
Lack Of Information ◽  
Wide Range ◽  
Significant Difference ◽  
Promising Solution ◽  
Living Tissues

With the currently available materials and technologies it is difficult to mimic the mechanical properties of soft living tissues. Additionally, another significant problem is the lack of information about the mechanical properties of these tissues. Alternatively, the use of phantoms offers a promising solution to simulate biological bodies. For this reason, to advance in the state-of-the-art a wide range of organs (e.g., liver, heart, kidney as well as brain) and hydrogels (e.g., agarose, polyvinyl alcohol –PVA–, Phytagel –PHY– and methacrylate gelatine –GelMA–) were tested regarding their mechanical properties. For that, viscoelastic behavior, hardness, as well as a non-linear elastic mechanical response were measured. It was seen that there was a significant difference among the results for the different mentioned soft tissues. Some of them appear to be more elastic than viscous as well as being softer or harder. With all this information in mind, a correlation between the mechanical properties of the organs and the different materials was performed. The next conclusions were drawn: (1) to mimic the liver, the best material is 1% wt agarose; (2) to mimic the heart, the best material is 2% wt agarose; (3) to mimic the kidney, the best material is 4% wt GelMA; and (4) to mimic the brain, the best materials are 4% wt GelMA and 1% wt agarose. Neither PVA nor PHY was selected to mimic any of the studied tissues.

scholarly journals Fabrication and Testing of Breast Tissue-Mimicking Phantom for Needle Biopsy Cutting: A Pilot Study

2017 ◽  
Author(s):  
Yu-Chen Jheng ◽  
Chi-Lun Lin
Keyword(s):  
Mechanical Properties ◽  
Pilot Study ◽  
Needle Biopsy ◽  
Large Scale ◽  
Soft Tissues ◽  
Indentation Test ◽  
Cutting Conditions ◽  
Insertion Force ◽  
Tissue Cutting ◽  
Tissue Phantoms

Breast lesion tissue can be extremely stiff, e.g. calcification or soft, e.g. adipose. When performing needle biopsy, too small or scanty samples can be retrieved due to the tissue is mainly compressed instead of being cut. In order to studying the tissue cutting performance in various cutting conditions, tissue-mimicking phantoms are frequently used as a surrogate of human tissue. The advantage of using tissue phantoms is that their mechanical properties can be controlled. The stiffness of a tissue phantom can be measured by an indentation test. Previous studies have demonstrated mathematic models to estimate Young’s moduli of tissue phantoms from force-displacement data with an adjustable coefficient according to the geometry of the indenter. Tissue force reactions occurred needle insertion has been largely researched [1], but few studies investigated the tissue cutting with a rotational needle, which is a cutting method largely used in the breast needle biopsy. Research has demonstrated that the influence of rotation can significantly reduce the insertion force [2], but the experiment was conducted on a specific formula of silicone-based tissue phantoms. This paper served as a pilot study of a large-scale experiment to study the effect of rotational cutting on various cutting conditions and target materials, including artificial and biological soft tissues. Two most common types of soft tissue phantoms, biopolymers (gelatin gels and agar) and chemically synthesized polymers (polydimethylsiloxane, PDMS) were investigated. Indentation tests were performed to estimate the mechanical properties of tissue phantoms which were then verified by finite element simulations. Tissue cutting tests with and without rotation were conducted to evaluate the effect of needle rotation on the tissue force reactions.

A Nonlinear Anisotropic Viscoelastic Model for the Tensile Behavior of the Corneal Stroma

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
T. D. Nguyen ◽  
R. E. Jones ◽  
B. L. Boyce
Keyword(s):  
Soft Tissues ◽  
Viscoelastic Model ◽  
Corneal Stroma ◽  
Viscoelastic Behavior ◽  
Cyclic Stress ◽  
Uniaxial Tensile ◽  
Nonlinear Creep ◽  
Stress Strain ◽  
Highly Nonlinear ◽  
Tensile Strip

Tensile strip experiments of bovine corneas have shown that the tissue exhibits a nonlinear rate-dependent stress-strain response and a highly nonlinear creep response that depends on the applied hold stress. In this paper, we present a constitutive model for the finite deformation, anisotropic, nonlinear viscoelastic behavior of the corneal stroma. The model formulates the elastic and viscous response of the stroma as the average of the elastic and viscous response of the individual lamellae weighted by a probability density function of the preferred in-plane lamellar orientations. The result is a microstructure-based model that incorporates the viscoelastic properties of the matrix and lamellae and the lamellar architecture in the response of the stroma. In addition, the model includes a fully nonlinear description of the viscoelastic response of the lamellar(fiber) level. This is in contrast to previous microstructure-based models of fibrous soft tissues, which relied on quasilinear viscoelastic formulations of the fiber viscoelasticity. Simulations of recent tensile strip experiments show that the model is able to predict, well within the bounds of experimental error and natural variations, the cyclic stress-strain behavior and nonlinear creep behavior observed in uniaxial tensile experiments of excised strips of bovine cornea.

Experimental Determination of Layer-Specific Hyperelastic Parameters of Human Descending Thoracic Aortas

2019 ◽  
Author(s):  
Isabella Bozzo ◽  
Marco Amabili ◽  
Prabakaran Balasubramanian ◽  
Ivan Breslavsky ◽  
Giovanni Ferrari
Keyword(s):  
Storage Modulus ◽  
Thoracic Aorta ◽  
Loss Tangent ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Axial Direction ◽  
Maxwell Model ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Descending Thoracic Aorta

Abstract Heart disease is the second leading cause of death in Canada resulting in $20.9 billion annual healthcare expenditures [1,2]. Understanding the mechanics of the human descending thoracic aorta is fundamental for comprehending the development of pathologies and improving surgical prostheses. This study presents hyperelastic and viscoelastic material characterizations of the human descending thoracic aorta from twelve different donors, with a mean age of 49.4 years. The specimens were dissected into the three constituent layers: intima, media and adventitia. Evaluating the layer-specific opening angles led to the computation of the circumferential residual stresses. Uniaxial tensile tests of each layer, in both the circumferential and axial direction, were used to model the hyperelastic behavior according to the Gasser-Ogden-Holzapfel model (GOH). The storage modulus and loss tangent for the layers were obtained from uniaxial harmonic excitations at varied frequencies, to model the viscoelastic behavior with the generalized Maxwell model. The results showed a positive correlation between age and stiffness for all layers, both axially and circumferentially. Similar loss tangent values were found across the three layers. A large increase in the storage modulus from static to dynamic experiments further corroborates the importance of a viscoelastic model of the aorta, rather than solely hyperelastic.

Viscoelastic Damping Effect on Brake Squeal Noise

2009 ◽  
Author(s):  
Gael Chevallier ◽  
Franck Renaud ◽  
Jean-Luc Dion
Keyword(s):  
Degrees Of Freedom ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Element Model ◽  
Brake Squeal ◽  
Generalized Maxwell Model ◽  
Space Formulation ◽  
Damping Materials ◽  
Squeal Noise

Brake squeal remains a widespread cause for discomfort in automobiles. Manufacturers overcome this problem by adding damping materials in their systems. The purpose of this work is to take into account the damping in the modeling. As the materials exhibit a viscoelastic behavior, the authors chose to model the damping with the Generalized Maxwell model. Moreover, the authors have tested their method on a detailed Finite Element-model of a brake system. To compute the complex poles of the model, the authors have established a state-space formulation of the viscoelastic model with a new assumption that allows one to reduce the number of states. Making the computation on the whole model is rather difficult due to the number of Degrees Of Freedom, the model is thus reduced on a basis constituted with the eigenvectors of the undamped model. Several results are also presented and discussed as the observed phenomena are rather different from the results obtained with undamped systems.

Corrigendum to: Elastic properties of the forisome

2007 ◽  
Vol 34 (11) ◽  
pp. 1053
Author(s):  
Stephen A. Warmann ◽  
William F. Pickard ◽  
Amy Q. Shen
Keyword(s):  
Mechanical Properties ◽  
Radial Direction ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Strain Curve ◽  
Longitudinal Direction ◽  
Tensile Tests ◽  
Before And After

Forisomes are elongate Ca2+-responsive contractile protein bodies and act as flow blocking gates within the phloem of legumes. Because an understanding of their mechanical properties in vitro underpins understanding of their physiology in vivo, we undertook, using a microcantilever method, microscopic tensile tests (incremental stress-relaxation measurements) on forisomes from Canavalia gladiata (Jacq.) DC Akanata Mame and Vicia faba L. Witkiem Major. Viscoelastic properties of forisomes in their longitudinal direction were investigated before and after Ca2+-induced contraction, but in the radial direction only before contraction. Forisomes showed mechanical properties typical of a biological material with a unidirectional fibrous structure, i.e. the modulus of elasticity in the direction of their fibers is much greater than in the radial direction. Creep data were collected in all tensile tests and fit with a three parameter viscoelastic model. The pre-contraction longitudinal elastic moduli of the forisomes were not differentiable between the two species (V. faba, 660���360�kPa; C. gladiata, 600���360�kPa). Both species showed a direction-dependent mechanical response: the elastic modulus was dramatically smaller in the radial direction than in the longitudinal direction, suggesting a weak protein cross-linking amongst longitudinal protein fibers. Activation of forisomes decreased forisome stiffness longitudinally, as evidenced by the loss of toe-region in the stress strain curve, suggesting that the forisome may have dispersed or disordered its protein structure in a controlled fashion. Contractile forces generated by single forisomes undergoing activation were also measured for V. faba (510���390�nN) and C. gladiata (570���310�nN).

Stress Relaxation of Articular Cartilage in Unconfined Compression

2012 ◽  
Author(s):  
Patrick Smyth ◽  
Itzhak Green ◽  
Robert Jackson ◽  
R. Reid Hanson
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Osteoarthritic Cartilage ◽  
Healthy Cartilage ◽  
Storage And Loss Moduli ◽  
Relaxation Experiments ◽  
Insight Into

The articular cartilage function is to allow the bones in a joint to move without causing excess friction and damage. When this cartilage becomes damaged, the supportive and lubricating mechanisms break down, leading to injuries which can be permanent or take extended periods of time for recovery. Because of its importance in general health and body mobility, the unique lubricating properties of cartilage have been studied for many decades. Many current theories exist to characterize the biphasic and triphasic nature of cartilage; however, an important reason that cartilage is so effective is its viscoelastic nature, which allows elastic and dissipative mechanisms to exist simultaneously. It is desired to derive the material properties of cartilage in order to better understand its mechanical effectiveness. Utilizing a CETR-UMT-3 Tribometer, stress relaxation experiments will be performed on freshly harvested equine cartilage plugs that remain hydrated in a fluid bath. Viscoelastic models, such as the Prony series and fractional derivative, are applied to the experimental data to determine the storage and loss moduli of the sample explants. The storage and loss information characterizes the mechanical response of cartilage, and provides insight into the effectiveness and longevity of biological joints. A comparison will be made between joints that experience similar loads, but undergo different relative motions, to determine if the mechanical properties of cartilage are tailored to joint function. Osteoarthritic cartilage will also be explored for deviations in viscoelastic behavior compared to healthy cartilage. Ultimately, it is hoped that a viscoelastic characterization of articular cartilage will lead to insight into the precursors of osteoarthritis, more advanced prosthetics, and biomimetric applications such as the integration of flexible surfaces in mechanical systems.

Factors Affecting Spherical Nano-Indentation of Thin Film/Substrate Systems

2014 ◽  
Author(s):  
A. Hossain ◽  
A. Mian
Keyword(s):  
Thin Film ◽  
Mechanical Properties ◽  
Mechanical Response ◽  
Indentation Test ◽  
Element Analysis ◽  
Factors Affecting ◽  
Nano Indentation ◽  
Fea Modeling ◽  
Soft Biological Materials ◽  
Film Substrate

Great interests have been made over the last few years in the development of techniques to measure the mechanical properties of many engineering materials at the nano scale. In nano-indentation, a hard tip with known mechanical properties is pressed into a sample whose properties are unknown. The load, indentation depth and deformed area resulting from this test are then used to determine the desired mechanical properties, such as hardness and modulus. In this study, the computer-based finite element analysis (FEA) method is used to investigate factors effecting nano-indentation to ensure reliable measurement of thin film properties. First, the FEA method is used to predict the mechanical response of bulk aluminum (Al) using a spherical indenter. The numerical prediction is then compared with existing published results to validate the FEA modeling scheme. Once the model is validated, additional numerical analyses are conducted to investigate the response of Al-film deposited on different substrate materials. New mathematical formulations are proposed to determine the film modulus from nano-indentation test. The film modulus obtained from the new and existing mathematical formulations are also compared. Results obtained from this research can be used to characterize the mechanical properties of soft biological materials such as biofilm or tissue scaffolds.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Ghislain Maquer ◽  
Marc Laurent ◽  
Vaclav Brandejsky ◽  
Michael L. Pretterklieber ◽  
Philippe K. Zysset
Keyword(s):  
Mechanical Properties ◽  
Intervertebral Disc ◽  
Material Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Parameter Study ◽  
Nonlinear Normalization ◽  
Highly Nonlinear ◽  
Flexion Extension ◽  
Linear And Nonlinear

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Analysis of steady-state frictional rolling contact problems in Schapery–nonlinear viscoelasticity

2018 ◽  
Vol 233 (6) ◽  
pp. 911-926 ◽  
Author(s):  
Alaa A Abdelrahman ◽  
Ahmed G El-Shafei ◽  
Fatin F Mahmoud
Keyword(s):  
Steady State ◽  
Mechanical Response ◽  
Past History ◽  
Rotational Velocity ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Contact Problems ◽  
Rolling Contact ◽  
Nonlinear Viscoelastic ◽  
Steady State Rolling

In the context of an updated Lagrangian formulation, a computational model is developed for analyzing the steady-state frictional rolling contact problems in nonlinear viscoelastic solids. Schapery's nonlinear viscoelastic model is adopted to simulate the viscoelastic behavior. In addition to the material nonlinearity, the model accounts for geometrical nonlinearities, large displacements, and rotations with small strains. To satisfy the steady-state rolling contact condition, a spatially dependent incremental form of the viscoelastic constitutive equations is derived. Consequently, the dependence on the past history of the strain rate in the stress–strain law is expressed in terms of the spatial variation of the strain. The contact conditions are exactly satisfied by employing the Lagrange multiplier approach to enforce the contact constraints. The classical Coulomb's friction law is used to simulate friction. The developed model is verified and compared and good agreement is obtained. The applicability of the developed model is demonstrated by analyzing the steady-state rolling contact response of viscoelastically walled-wheel over rigid foundation. Moreover, the obtained results show remarkable effects of the rotational velocity and the viscoelastic material parameters on the mechanical response of steady-state frictional rolling contact.

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