The Role of Flow-Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage

2001 ◽  
Vol 123 (5) ◽  
pp. 410-417 ◽  
Author(s):  
Chun-Yuh Huang ◽  
Van C. Mow ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Viscoelastic Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Molecular Organization ◽  
Solid Matrix ◽  
Uniaxial Tensile ◽  
Elastic Model ◽  
Compressive Properties ◽  
Stress Strain

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension–compression stress–strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102, pp. 73–84] to incorporate tension–compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122, pp. 576–586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37, pp. 1–38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123–130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension–compression nonlinearity.

scholarly journals Ability of Constitutive Models to Characterize the Temperature Dependence of Rubber Hyperelasticity and to Predict the Stress-Strain Behavior of Filled Rubber under Different Defor Mation States

Polymers ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 369
Author(s):  
Xintao Fu ◽  
Zepeng Wang ◽  
Lianxiang Ma
Keyword(s):  
Experimental Data ◽  
Temperature Dependence ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Chain Model ◽  
Stress Strain ◽  
Filled Rubber ◽  
Yeoh Model

In this paper, some representative hyperelastic constitutive models of rubber materials were reviewed from the perspectives of molecular chain network statistical mechanics and continuum mechanics. Based on the advantages of existing models, an improved constitutive model was developed, and the stress–strain relationship was derived. Uniaxial tensile tests were performed on two types of filled tire compounds at different temperatures. The physical phenomena related to rubber deformation were analyzed, and the temperature dependence of the mechanical behavior of filled rubber in a larger deformation range (150% strain) was revealed from multiple angles. Based on the experimental data, the ability of several models to describe the stress–strain mechanical response of carbon black filled compound was studied, and the application limitations of some constitutive models were revealed. Combined with the experimental data, the ability of Yeoh model, Ogden model (n = 3), and improved eight-chain model to characterize the temperature dependence was studied, and the laws of temperature dependence of their parameters were revealed. By fitting the uniaxial tensile test data and comparing it with the Yeoh model, the improved eight-chain model was proved to have a better ability to predict the hyperelastic behavior of rubber materials under different deformation states. Finally, the improved eight-chain model was successfully applied to finite element analysis (FEA) and compared with the experimental data. It was found that the improved eight-chain model can accurately describe the stress–strain characteristics of filled rubber.

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.

Relaxation and Creep Quasilinear Viscoelastic Models for Normal Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 159-164 ◽  
Author(s):  
B. R. Simon ◽  
R. S. Coats ◽  
S. L.-Y. Woo
Keyword(s):  
Articular Cartilage ◽  
Soft Tissues ◽  
Least Squares Method ◽  
Viscoelastic Model ◽  
Generalized Least Squares ◽  
Constitutive Law ◽  
Analytical Models ◽  
Creep Data ◽  
Bovine Articular Cartilage ◽  
Generalized Least Squares Method

A quasilinear viscoelastic model was used to develop relaxation and creep forms for a constitutive law for soft tissues. Combined relaxation and cyclic test data as well as preconditioned and nonpreconditioned creep data were used to demonstrate the approach for normal bovine articular cartilage. Values for mechanical parameters in the analytical models were determined using a generalized least squares method.

scholarly journals Dynamic characterization and modeling of rubber shock absorbers: A comprehensive case study

2017 ◽  
Vol 37 (3) ◽  
pp. 509-518 ◽  
Author(s):  
H Ucar ◽  
I Basdogan
Keyword(s):  
Dynamic Properties ◽  
Viscoelastic Model ◽  
Constitutive Models ◽  
Material Model ◽  
Uniaxial Tensile ◽  
Primary Concern ◽  
Dynamic Characterization ◽  
Time Frequency ◽  
Shock Absorbers

Rubber or elastomeric materials are widely used for shock absorbers having elastic and viscous properties such as high inherent damping, deflection capacity, and energy storage. The dynamic properties of these components are of primary concern in designing rubber absorbers to reduce the shock loading given as well as the structure-borne noise transmissibility. Besides, the dynamic response of the mechanical systems, at where the rubber shock absorbers are used, is directly associated with the properties of the shock absorbers. In order to determine these properties of the rubber, mathematical models are created in terms of hyperelasticity and viscoelasticity. The hyperelastic and viscoelastic material models represent the nonlinear elastic and strain rate dependencies of the overall rubber behavior, respectively. Hyperelastic material model captures the material’s nonlinear elasticity with no-time dependence whereas viscoelastic model describes the material response which contains an elastic and viscous part depending on time, frequency, and temperature. This paper presents the dynamic characterization of rubber shock absorbers, having different shore hardness values, in terms of hyperelastic and viscoelastic constitutive models. The parameters of the constitutive models are determined from the uniaxial tensile and relaxation tests. These parameters are used for the numerical model of the rubber components and the accuracy of the characterization is presented by means of a numerical case study.

Applicability of Duncan-Chang Model and its Modified Versions to Methane Hydrate-Bearing Sands

2011 ◽  
Vol 347-353 ◽  
pp. 3384-3387 ◽  
Author(s):  
Ju Hua Xiong ◽  
Xiao Yong Kou ◽  
Fang Liu ◽  
Ming Jing Jiang
Keyword(s):  
Methane Hydrate ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Triaxial Tests ◽  
Elastic Model ◽  
Clathrate Compound ◽  
Constitutive Response ◽  
Nonlinear Elastic ◽  
Hydrate Bearing Sediments ◽  
Chang Model

Methane hydrate is ice-like clathrate compound that attracts global attention due to its huge potential as a future energy source. The constitutive law of methane hydrate-bearing sediments remains unknown and becomes a barrier in sustainable exploitation of methane hydrate from marine sediments. The Duncan-Change model is a nonlinear elastic model which was widely accepted by the geotechnical community in approximating the constitutive response of geo-materials. This model and its evolved versions were employed in this study to model the stress-strain response observed in triaxial tests on methane hydrate-bearing sands. Duncan-Chang type models capture well the strain hardening behaviors. However, they fall short of incorporating the dependency of temperature and saturation degree of methane hydrate, which have to be taken into account in future constitutive models of methane hydrate-bearing deposits.

A Biphasic Transversely Isotropic Poroviscoelastic Model for the Unconfined Compression of Hydrated Soft Tissue

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
H. Hatami-Marbini ◽  
R. Maulik
Keyword(s):  
Articular Cartilage ◽  
Soft Tissue ◽  
Stress Relaxation ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Viscoelastic Model ◽  
Transversely Isotropic ◽  
Solid Matrix ◽  
Unconfined Compression ◽  
Material Parameters

The unconfined compression experiments are commonly used for characterizing the mechanical behavior of hydrated soft tissues such as articular cartilage. Several analytical constitutive models have been proposed over the years to analyze the unconfined compression experimental data and subsequently estimate the material parameters. Nevertheless, new mathematical models are still required to obtain more accurate numerical estimates. The present study aims at developing a linear transversely isotropic poroviscoelastic theory by combining a viscoelastic material law with the transversely isotropic biphasic model. In particular, an integral type viscoelastic model is used to describe the intrinsic viscoelastic properties of a transversely isotropic solid matrix. The proposed constitutive theory incorporates viscoelastic contributions from both the fluid flow and the intrinsic viscoelasticity to the overall stress-relaxation behavior. Moreover, this new material model allows investigating the biomechanical properties of tissues whose extracellular matrix exhibits transverse isotropy. In the present work, a comprehensive parametric study was conducted to determine the influence of various material parameters on the stress–relaxation history. Furthermore, the efficacy of the proposed theory in representing the unconfined compression experiments was assessed by comparing its theoretical predictions with those obtained from other versions of the biphasic theory such as the isotropic, transversely isotropic, and viscoelastic models. The unconfined compression behavior of articular cartilage as well as corneal stroma was used for this purpose. It is concluded that while the proposed model is capable of accurately representing the viscoelastic behavior of any hydrated soft tissue in unconfined compression, it is particularly useful in modeling the behavior of those with a transversely isotropic skeleton.

A new pseudo-energy function to simulate the Mullins effect

2017 ◽  
Vol 50 (6) ◽  
pp. 554-575
Author(s):  
Eduardo Guilherme Mötke Wrubleski ◽  
Rogério Marczak
Keyword(s):  
Experimental Data ◽  
Pure Shear ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Hyperelastic Material ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Mullins Effect ◽  
Softening Effect ◽  
Material Models

Several authors have proposed different parameters to include the softening effect in hyperelastic models; however, for a number of materials, softening parameters could be further improved. This article proposes a new softening parameter to include Mullins effect in hyperelastic material models. The methodology employed can be also used in cases with hysteresis or damage in a hyperelastic material, however this methodology modifies the behavior of the material differently from damage theories. Common hyperelastic constitutive models do not include dissipation effects and so the present work intends to fill this gap. Experimental data for silicone in uniaxial tensile test, equibiaxial, and pure shear tests were modeled in order to calibrate the models. The softening parameters essentially changes the constitutive law from the loading to the unloading path. Therefore, it is still necessary to use a hyperelastic model, and here Ogden and Hoss-Marczak material models were used. The obtained results show good agreement with experimental data even when simulating with a compressible finite element code and it can model isotropic Mullins effect.

The Influence of Depth-Dependent Inhomogeneity on the Contact Response of Human Patellar Cartilage

2001 ◽  
Author(s):  
Ramaswamy Krishnan ◽  
Seonghun Park ◽  
Michael A. Soltz ◽  
Robert J. Pawluk ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Functional Response ◽  
Material Properties ◽  
Articular Surface ◽  
Solid Matrix ◽  
Homogeneous Distribution ◽  
Primary Role ◽  
Homogeneous State ◽  
Compressive Properties ◽  
State Of Stress

Abstract One of the aims of modeling articular cartilage is to determine its ability to sustain its physiological loading environment and the mechanisms by which this functional response might be compromised. It has long been hypothesized that excessive stresses in cartilage might initiate osteoarthritis, thus a determination of the state of stress within the tissue has been an important objective. It has also been hypothesized that the interstitial water of articular cartilage plays a primary role in producing low friction and wear as well as shielding the collagen-proteoglycan solid matrix from a significant portion of the loads applied across joints [1]. Furthermore, cartilage exhibits inhomogeneity through its depth, both in its tensile and compressive properties, though the significance of this inhomogeneity on the functional response of cartilage remains to be elucidated. The specific aims of the current study are to (a) experimentally determine the depth-dependent tensile and compressive properties of human patellar articular cartilage; (b) determine the response of cartilage to loading under a contact configuration using finite element models which employ these experimentally determined material properties; and (c) compare the response of the tissue to a hypothetical homogeneous distribution of material properties through the depth. The first hypothesis is that the inhomogeneity of articular cartilage acts to maximize the interstitial fluid load support at the articular surface. The second hypothesis is that the depth-dependent inhomogeneous distribution of cartilage properties acts to produce a more homogeneous state of stress than would be achieved had the properties been constant through the depth. This study extends our previous contact analyses of homogeneous cartilage layers [2,3].

Nonlinear Stress–Strain Characterization of Cast Iron Used to Manufacture Pipes for Water Supply

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Balvant Rajani
Keyword(s):  
New York ◽  
Cast Iron ◽  
Water Supply ◽  
Mechanical Design ◽  
Constitutive Law ◽  
Uniaxial Tensile ◽  
Normal Strain ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Compressive Tests

The stress–strain response of cast iron under tension or compression is nonlinear. This paper examines how the hyperbolic constitutive law can be applied to characterize nonlinear stress–strain behavior of cast iron used in water supply networks. Procedures are described to obtain parameters of the hyperbolic constitutive law from either the response (data) obtained from simple uniaxial tensile and compressive tests or from bending tests. To demonstrate its applicability, this hyperbolic constitutive law is first applied to data obtained from uniaxial tensile and compressive tests conducted by Schlick and Moore (1936, “Strength and Elastic Properties of Cast Iron in Tension, Compression, Flexure, and Combined Tension and Flexure,” Bulletin 127, Iowa Engineering Experiment Station, Ames, IA). In addition, an approach to extract parameters for the hyperbolic constitutive law from bending (beam and pipe rings) tests is proposed and subsequently applied to tests conducted by Talbot (1908, “Tests of Cast-Iron and Reinforced Concrete Culvert Pipe,” Bulletin No. 22, University of Illinois, Urbana, IL). This latter approach is attractive for practical purposes because the test set up is simple and the test coupons are very easy to prepare. The hyperbolic constitutive law in conjunction with maximum normal strain theory as proposed by St. Venant (Collins, J. A., 1993, Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, John Wiley, New York, NY) was also used to predict failure loads.

scholarly journals Stochastic homogenization of a scalar viscoelastic model exhibiting stress–strain hysteresis

2020 ◽  
Vol 54 (3) ◽  
pp. 879-928
Author(s):  
Thomas Hudson ◽  
Frédéric Legoll ◽  
Tony Lelièvre
Keyword(s):  
Numerical Simulations ◽  
Viscoelastic Model ◽  
Constitutive Law ◽  
Stochastic Homogenization ◽  
Stress Strain ◽  
Hysteretic Behaviour ◽  
One Dimensional ◽  
Filled Rubber ◽  
Homogenized Model

Motivated by rate-independent stress–strain hysteresis observed in filled rubber, this article considers a scalar viscoelastic model in which the constitutive law is random and varies on a lengthscale which is small relative to the overall size of the solid. Using a variant of stochastic two-scale convergence as introduced by Bourgeat et al., we obtain the homogenized limit of the evolution, and demonstrate that under certain hypotheses, the homogenized model exhibits hysteretic behaviour which persists under asymptotically slow loading. These results are illustrated by means of numerical simulations in a particular one-dimensional instance of the model.

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