A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Franz G. Sander ◽  
Christina Dorow ◽  
...  
Keyword(s):  
Strain Rate ◽  
Periodontal Ligament ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Experimental Testing ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Time Dependent ◽  
Large Strains ◽  
Free Energy Function

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

Constitutive Formulation for Numerical Analysis of Visco-Hyperelastic Damage Phenomena in Soft Biological Tissues

2006 ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Alessio Gasparetto ◽  
Franz G. Sander ◽  
...  
Keyword(s):  
Strain Rate ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Experimental Tests ◽  
Biological Tissues ◽  
Tissue Response ◽  
Time Dependent ◽  
Soft Biological Tissues ◽  
Constitutive Formulation

Soft biological tissues show a strongly non linear and time-dependent mechanical response and undergo large strains under physiological loads. The microstructural arrangement determines specific anisotropic macroscopic properties that must be considered within a constitutive formulation. The characterization of the mechanical behaviour of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non linearity. In the model presented here a hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for soft tissues and can be properly arranged for the investigation of viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. This phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. This makes it possible to perform numerical analyses of the mechanical response considering time-dependent effects and damage phenomena. The experimental tests develop investigated tissue response for different strain rate conditions, accounting for stretch situations capable of inducing damage phenomena. The reliability of the formulation is evaluated by a comparison with the results of experimental tests performed on pig periodontal ligament.

Phenomenological Hyperelastic Strain-Stiffening Constitutive Models for Rubber

2006 ◽  
Vol 79 (1) ◽  
pp. 152-169 ◽  
Author(s):  
Cornelius O. Horgan ◽  
Giuseppe Saccomandi
Keyword(s):  
Boundary Value Problems ◽  
Soft Tissues ◽  
Boundary Value ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Large Strains ◽  
Shear Mode ◽  
Crack Problems ◽  
Gent Model ◽  
Constitutive Parameters

Abstract Many rubber-like materials and soft biological tissues exhibit a significant stiffening or hardening in their stress-strain curves at large strains. The accurate modeling of this phenomenon is a key issue for a better understanding of the thermomechanics of rubber and the biomechanics of soft tissues. In this paper, we provide a review of some phenomenological hyperelastic constitutive models that have been proposed to model this strain stiffening effect and summarize recent advances in the solution of boundary-value problems that illustrate the utility of such models. The emphasis is on constitutive models that reflect limiting chain extensibility at the molecular level. A remarkably simple phenomenological model of this type has been proposed by Gent. The Gent model has a molecular basis related to the inverse Langevin function compact support non-Gaussian statistics for the end-to-end distance function. The mathematical simplicity of the Gent model, which contains just two constitutive parameters, has facilitated the analytic solution of a variety of specific boundary-value problems that are relevant to the rubber industry and we summarize the main results here. These problems include those of torsion, axial, azimuthal and helical shear, anti-plane shear, mode III crack problems, rotation induced deformation of circular cylinders and fracture problems. It is shown that the results are radically different from those obtained in the literature for classical models such as the neo-Hookean and Mooney-Rivlin models for incompressible rubber. Extensions to include thermoelasticity, material compressibility, anisotropy and stress softening are also briefly described.

Strain-Rate Sensitive Constitutive Modeling of Anisotropic Visco-Hyperelastic Materials

2012 ◽  
Author(s):  
Sahand Ahsanizadeh ◽  
LePing Li
Keyword(s):  
Strain Rate ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
Internal Variables ◽  
Current Configuration ◽  
Hyperelastic Materials ◽  
History Of ◽  
Viscoelastic Constitutive Model

Integral-based formulations of viscoelasticity have been widely used to describe the mechanical behavior of soft biological tissues and polymers. However, it is suggested that they are not suitable to be used under high strain rates. On the other hand, strain-rate sensitive models with an explicit dependence on the strain-rate have been developed for a certain class of materials. They predict the viscoelastic behavior during ramp loading more accurately while fail to account for the relaxation response. In order to overcome these drawbacks, a viscoelastic constitutive model has been proposed in this study based on the concept of internal variables. While the behavior of elastic materials is uniquely determined by the current state of deformation or external variables, the mechanical response of inelastic materials are regulated also by internal variables. The internal variables are associated with the dissipative mechanisms in the material and along with the evolution equations introduce the effect of history of the deformation to the current configuration. The current study employs short-term and long-term internal variables to account for the viscoelastic response during loading and relaxation respectively.

Finite Element Implementation of a Planar Soft Tissue Structural Constitutive Model for Heart Valve Simulations

2013 ◽  
Author(s):  
Rong Fan ◽  
Michael S. Sacks
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Tissues ◽  
Structural Model ◽  
Mechanical Response ◽  
Biological Tissues ◽  
Biaxial Test ◽  
Tissue Microstructure ◽  
Highly Nonlinear ◽  
Insight Into

Constitutive modeling is critical for numerical simulation and analysis of soft biological tissues. The highly nonlinear and anisotropic mechanical behaviors of soft tissues are typically due to the interaction of tissue microstructure. By incorporating information of fiber orientation and distribution at tissue microscopic scale, the structural model avoids ambiguities in material characterization. Moreover, structural models produce much more information than just simple stress-strain results, but can provide much insight into how soft tissues internally reorganize to external loads by adjusting their internal microstructure. It is only through simulation of an entire organ system can such information be derived and provide insight into physiological function. However, accurate implementation and rigorous validation of these models remains very limited. In the present study we implemented a structural constitutive model into a commercial finite element package for planar soft tissues. The structural model was applied to simulate strip biaxial test for native bovine pericardium, and a single pulmonary valve leaflet deformation. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber deformation fiber reorientation and fiber recruitment.

Implementation and Validation of Planar Soft Tissue Structural Constitutive Model

2013 ◽  
Author(s):  
Rong Fan ◽  
Michael S. Sacks
Keyword(s):  
Constitutive Model ◽  
Soft Tissues ◽  
Structural Model ◽  
Mechanical Response ◽  
Biological Tissues ◽  
Fetal Membrane ◽  
Tissue Microstructure ◽  
Highly Nonlinear ◽  
Finite Element Package ◽  
Insight Into

Constitutive modeling is of fundamental important for numerical simulation and analysis of soft biological tissues. The mechanical behaviors of soft tissues are usually highly nonlinear and anisotropic. The complex behavior is the results from the interaction of tissue microstructure. By incorporating information of fiber orientation and distribution at tissue microscopic scale, the structural model avoids ambiguities in material characterization. Moreover, structural models produce much more information than just simple stress-strain results, but can provide much insight into how soft tissues internally reorganize to external loads by adjusting their internal microstructure. Moreover, it is only through simulation of an entire organ system can such information be derived and provide insight into physiological function. However, accurate implementation and rigorous validation of these models remains very limited. In the present study we implemented a structural constitutive model into a commercial finite element package. The structural model was verified against experiential test data for native bovine pericardium and fetal membrane. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber reorientation and fiber recruitment.

Experimental Basis for Temperature-Dependent Viscoplastic Constitutive Equations

1990 ◽  
Vol 43 (5S) ◽  
pp. S338-S344 ◽  
Author(s):  
U. S. Lindholm
Keyword(s):  
Strain Rate ◽  
Constitutive Models ◽  
Inelastic Strain ◽  
Time Dependent ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Experimental Basis ◽  
Temperature Dependent ◽  
Evolutionary Equations ◽  
Nonproportional Loading

In this paper the author reviews experimental data which is felt to be illustrative of time-dependent, high temperature deformation of metals and, therefore, instructive for the development of constitutive models. Issues addressed are the interrelation between time (strain rate) and temperature, the development of evolutionary equations for both isotropic and directional hardening and recovery, and the orientation of the inelastic strain rate with respect to stress during nonproportional loading.

scholarly journals Variations in Hardness with Position In One Dimensionally Recovered Shock Loaded Metals

2018 ◽  
Vol 183 ◽  
pp. 02013 ◽  
Author(s):  
G. Whiteman ◽  
D.L. Higgins ◽  
B. Pang ◽  
J.C.F. Millett ◽  
Y-L. Chiu ◽  
...  
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Shock Loading ◽  
Mechanical Response ◽  
High Strain ◽  
Cold Work ◽  
Constitutive Models ◽  
Target Assembly ◽  
One Dimensional ◽  
The Impact

The microstructural and mechanical response of materials to shock loading is of the utmost importance in the development of constitutive models for high strain-rate applications. However, unlike a purely mechanical response, to ensure that the microstructure has been generated under conditions of pure one dimensional strain, the target assembly requires both a complex array of momentum traps to prevent lateral releases entering the specimen location from the edges and spall plates to prevent tensile interactions (spall) affecting the microstructure. In this paper, we examine these effects by performing microhardness profiles of shock loaded copper and tantalum samples. In general, variations in hardness both parallel and perpendicular to the shock direction were small indicating successful momentum trapping. Variations in hardness at different locations relative to the impact face are discussed in terms of the initial degree of cold work and the ability to generate and move dislocations in the samples.

scholarly journals Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

2005 ◽  
Vol 3 (6) ◽  
pp. 15-35 ◽  
Author(s):  
T. Christian Gasser ◽  
Ray W Ogden ◽  
Gerhard A Holzapfel
Keyword(s):  
Structural Model ◽  
Mechanical Response ◽  
Constitutive Relations ◽  
Polarized Light ◽  
Collagen Fibre ◽  
Middle Layer ◽  
Biological Tissues ◽  
Free Energy Function ◽  
Collagen Fibres ◽  
Small Pitch

Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress–strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng . 190 , 4379–4403) and Holzapfel et al . (Holzapfel et al . 2000 J. Elast . 61 , 1–48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.

Viscous–elastic–plastic modelling of one-dimensional time-dependent behaviour of clays

1989 ◽  
Vol 26 (2) ◽  
pp. 199-209 ◽  
Author(s):  
J.-H. Yin ◽  
J. Graham
Keyword(s):  
Strain Rate ◽  
Constitutive Models ◽  
Constitutive Modelling ◽  
Time Dependent ◽  
Creep Tests ◽  
Strain Rate Effects ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Constant Rate ◽  
Rate Effects

Increased attention has recently been directed towards the influence of time and strain-rate effects on the behaviour of clays in one-dimensional (1-D) laboratory consolidation. The improved understanding coming from these studies must now be incorporated into improved constitutive models that can be used for analysis of foundation settlements. This paper presents a 1-D model for stepped loading using a new concept for establishing "equivalent times" during time-dependent straining. This model is then developed into a general constitutive equation for continuous loading. The model uses three parameters, λ, κ, and ψ, that can be easily found using conventional oedometer tests.The general model has been used to develop analytical solutions for creep tests, relaxation tests, constant rate of strain (CRSN) tests, and tests with constant rate of stress (CRSS). Results from three different clays have been used to examine the validity of the model. Key words: consolidation, constitutive modelling, elastic-plastic, viscous, time, creep, strain rate, relaxation.

scholarly journals The mechanical properties of tibiofemoral and patellofemoral articular cartilage in compression depend on anatomical regions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Heng Li ◽  
Jinming Li ◽  
Shengbo Yu ◽  
Chengwei Wu ◽  
Wei Zhang
Keyword(s):  
Mechanical Properties ◽  
Articular Cartilage ◽  
Knee Joint ◽  
Strain Rate ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Rate Dependency ◽  
Unconfined Compression ◽  
Femoral Groove ◽  
Stiffening Effect

AbstractArticular cartilage in knee joint can be anatomically divided into different regions: medial and lateral condyles of femur; patellar groove of femur; medial and lateral plateaus of tibia covered or uncovered by meniscus. The stress–strain curves of cartilage in uniaxially unconfined compression demonstrate strain rate dependency and exhibit distinct topographical variation among these seven regions. The femoral cartilage is stiffer than the tibial cartilage, and the cartilage in femoral groove is stiffest in the knee joint. Compared with the uncovered area, the area covered with meniscus shows the stiffer properties. To investigate the origin of differences in macroscopic mechanical properties, histological analysis of cartilage in seven regions are conducted. The differences are discussed in terms of the cartilage structure, composition content and distribution. Furthermore, the commonly used constitutive models for biological tissues, namely Fung, Ogden and Gent models, are employed to fit the experimental data, and Fung and Ogden models are found to be qualified in representing the stiffening effect of strain rate.

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