On the Ability of Structural and Phenomenological Hyperelastic Models to Predict the Mechanical Behavior of Biological Tissues Submitted to Multiaxial Loadings

2012 ◽  
Author(s):  
Mathieu Nierenberger ◽  
Yves Rémond ◽  
Saïd Ahzi
Keyword(s):  
Experimental Data ◽  
Mechanical Behavior ◽  
Strain Energy ◽  
Soft Tissues ◽  
Least Squares Method ◽  
Biological Tissues ◽  
Physical Parameters ◽  
Cauchy Stress ◽  
Specific Loading ◽  
Hyperelastic Models

Medical surgery is currently rapidly improving and requires modeling faithfully the mechanical behavior of soft tissues. Various models exist in literature; some of them created for the study of biological materials, and others coming from the field of rubber mechanics. Indeed biological tissues show a mechanical behavior close to the one of rubbers. But while building a model, one has to keep in mind that its parameters should be loading independent and that the model should be able to predict the behavior under complex loading conditions. In addition, keeping physical parameters seems interesting since it allows a bottom up approach taking into account the microstructure of the material. In this study, the authors consider different existing hyperelastic models based on strain energy functions and identify their coefficients successively on single loading stress-stretch curves. The experimental data used, come from a paper by Zemanek dated 2009 and concerning uniaxial, equibiaxial and plane tension tests on porcine arterial walls taken in identical experimental conditions. To achieve identification, the strain energy function of each model is derived differently to provide an expression of the Cauchy stress associated to each loading case. Firstly the parameters of each model are identified on the uniaxial tension curve using a least squares method. Then, keeping the obtained parameters, predictions are made for the two other loading cases (equibiaxial and plane tension) using the associated expressions of stresses. A comparison of these predictions with experimental data is done and allows evaluating the predictive capabilities of each model for the different loading cases. A similar approach is used after swapping the loading types. Since the predictive capabilities of the models are really dependent on the loading chosen to determine their parameters, another type of identification procedure is set up. It consists in adding the residues over the three loading cases during identification. This alternative identification method allows a better agreement between each model and the various types of experiments. This study evaluated the ability of some classical hyperelastic models to be used for a predictive scope after being identified on a specific loading type. Besides it brought to light some existing models which can describe at best the mechanical behavior of biological tissues submitted to various loadings.

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

2015 ◽  
Vol 60 (6) ◽  
Author(s):  
Cora Wex ◽  
Susann Arndt ◽  
Anke Stoll ◽  
Christiane Bruns ◽  
Yuliya Kupriyanova
Keyword(s):  
Mechanical Behaviour ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Tissue Response ◽  
Large Strains ◽  
Energy Functions ◽  
Strain Energy Functions ◽  
Hyperelastic Models

AbstractModelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function – a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

Finite Elastic Deformation for a Class of Soft Biological Tissues

1977 ◽  
Vol 99 (2) ◽  
pp. 98-103
Author(s):  
Han-Chin Wu ◽  
R. Reiss
Keyword(s):  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Soft Tissues ◽  
Broad Class ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Tension Test ◽  
Soft Biological Tissues ◽  
Precise Form

The stress response of soft biological tissues is investigated theoretically. The treatment follows the approach of Wu and Yao [1] and is now extended for a broad class of soft tissues. The theory accounts for the anisotropy due to the presence of fibers and also allows for the stretching of fibers under load. As an application of the theory, a precise form for the strain energy function is proposed. This form is then shown to describe the mechanical behavior of annulus fibrosus satisfactorily. The constants in the strain energy function have also been approximately determined from only a uniaxial tension test.

A Novel Compression Tester for Detecting Anisotropy in Very Soft Biological Tissues

2012 ◽  
Author(s):  
Roy Wang ◽  
Rudolph L. Gleason
Keyword(s):  
Adipose Tissue ◽  
Mechanical Behavior ◽  
Uniaxial Compression ◽  
Material Properties ◽  
Soft Tissues ◽  
Tensile Tests ◽  
Biological Tissues ◽  
Compression Tests ◽  
Anisotropic Behavior ◽  
Soft Biological Tissues

Quantifying the mechanical behavior of very soft tissues (VST) is important when studying responses to injury or designing therapeutic devices; fat, brain, or liver being examples of such tissues. VST can have poor suture retention or clamp holding strength, making tensile tests difficult. As a result, uniaxial compression tests are typically the preferred choice to quantify the mechanical behavior. In these tests, isotropy is generally assumed and measuring the deformation in only one direction is needed if the material is considered incompressible [13]. In this study we present a novel testing apparatus for use on VST under uniaxial compression that can detect anisotropic behavior of the tissue if present. We validate the tester using cardiac adipose tissue and isotropic rubber as the control. Understanding the directional behavior of the tissue is important since anisotropy would require testing in multiple directions to fully characterize the material properties.

Proposal and validation of polyconvex strain-energy function for biological soft tissues

2021 ◽  
pp. 1-14
Author(s):  
Takashi Funai ◽  
Hiroyuki Kataoka ◽  
Hideo Yokota ◽  
Taka-aki Suzuki
Keyword(s):  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Stress Strain ◽  
Increasing Trend ◽  
Strain Energy Functions ◽  
Derived Function

BACKGROUND: Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE: Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD: Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS: A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS: The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

scholarly journals On Ellipticity of Hyperelastic Models Based on Experimental Data

2017 ◽  
Vol 63 (3) ◽  
pp. 504-515
Author(s):  
V Yu Salamatova ◽  
Yu V Vasilevskii
Keyword(s):  
Experimental Data ◽  
Mechanical Behavior ◽  
Equilibrium Equation ◽  
Deformation Gradient ◽  
Necessary Condition ◽  
Strong Ellipticity ◽  
Correct Description ◽  
Ellipticity Condition ◽  
Strong Ellipticity Condition ◽  
Hyperelastic Models

The condition of ellipticity of the equilibrium equation plays an important role for correct description of mechanical behavior of materials and is a necessary condition for new defining relationships. Earlier, new deformation measures were proposed to vanish correlations between the terms, that dramatically simplifies restoration of defining relationships from experimental data. One of these new deformation measures is based on the QR-expansion of deformation gradient. In this paper, we study the strong ellipticity condition for hyperelastic material using the QR-expansion of deformation gradient.

A REVIEW OF THE MECHANICAL STRESSES PREDISPOSING ABDOMINAL AORTIC ANEURYSMAL RUPTURE: UNIAXIAL EXPERIMENTAL APPROACH

2020 ◽  
Vol 20 (08) ◽  
pp. 2030001
Author(s):  
MARIYA ANTONOVA ◽  
SOFIA ANTONOVA ◽  
LYUDMILA SHIKOVA ◽  
MARIA KANEVA ◽  
VALENTIN GOVEDARSKI ◽  
...  
Keyword(s):  
Strain Energy ◽  
Experimental Approach ◽  
Strain Energy Function ◽  
Ultimate Stress ◽  
Physical Parameters ◽  
Stress And Strain ◽  
Cauchy Stress ◽  
Biomechanical Behavior ◽  
Abdominal Aortic ◽  
Experimental Protocols

In this paper, problems concerning the uniaxial experimental investigation of the human abdominal aortic aneurysm (AAA) biomechanical characteristics, concomitant values of the associated Cauchy stress, failure (ultimate) stress in AAA, and the constitutive modeling of AAA are considered. The aim of this paper is to review and compare the disposable experimental data, to reveal the reasons for the high dissipation of the results between studies, and to propound some unification criteria. We examined 22 literature sources published between 1994 and 2017 and compared their results, including our own results. The experiments in the reviewed literature have been designed to obtain the stress–strain characteristics and the failure (ultimate) stress and strain of the aneurysmal tissue. A variety of forms of the strain–energy function (SEF) have been applied in the considered studies to model the biomechanical behavior of the aneurysmal wall. The specimen condition and physical parameters, the experimental protocols, the failure stress and strain, and SEFs differ between studies, contributing to the differences between the final results. We propound some criteria and suggestions for the unification of the experiments leading to the comparable results.

A visco-hyperelastic constitutive model of short- and long-term viscous effects on isotropic soft tissues

2019 ◽  
Vol 234 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Zahra Matin ◽  
Mahdi Moghimi Zand ◽  
Mehdi Salmani Tehrani ◽  
Brianna Regina Wendland ◽  
Roozbeh Dargazany
Keyword(s):  
Experimental Data ◽  
Strain Energy ◽  
Soft Tissues ◽  
Bovine Liver ◽  
Constitutive Behavior ◽  
Homogeneous Material ◽  
Viscous Effects ◽  
Important Challenge

Understanding and modeling the constitutive behavior of soft tissues represents an important challenge with significant relevance in medicine and biology. In this paper, we propose a new visco-hyperelastic model to describe the constitutive behavior of soft tissues as an isotropic and homogeneous material. The model is based on the nonlinear framework of continuum mechanics. A generalized Rivlin strain energy and a short-term viscous strain energy are used to describe the elastic part and time-dependence viscous part, respectively, while a long-term viscous function is derived through an integral framework of the applied stretch. To calibrate the material parameters, a set of self-designed uniaxial compression and relaxation tests are carried out on cylindrical samples of bovine liver. Moreover, the model is also validated against the experimental data of synthetic tissues reported by Khan et al. The good agreement between the predicted results and experimental data establishes the relevance of the proposed model. To investigate the model reliability, we have developed a “user-defined materials” subroutine to implement the constitutive behavior of the liver tissue in ABAQUS. By using the model, we simulate in vitro bovine liver behavior under compression and in relaxation and study the relative effects of the hyperelastic and viscous components on liver biomechanics.

Development of Generalized Parameters for Canine Multibody Meniscus Models From Experimental Data

2011 ◽  
Author(s):  
Gavin Paiva ◽  
Trent Guess
Keyword(s):  
Experimental Data ◽  
Soft Tissues ◽  
Biological Tissues ◽  
Finite Element Models ◽  
Santa Ana ◽  
Modeling Techniques ◽  
Flexible Behavior ◽  
Rigid Body Mechanics ◽  
Generalized Parameters ◽  
The Impact

It has been established that in order to accurately model a knee joint a reasonable approximation of the soft tissues present is necessary1. Models which include these soft tissue structures are able to better reproduce joint kinematics, loading, and analyze the impact of damage and pathological joint behavior1. Simulating the behavior of these tissues requires either a detailed understanding of materials properties that can be implemented via finite element models or the production of an empirical model that can be implemented inside other model frameworks2,3. This study explores the application of multibody (MB) modeling techniques in an attempt to capture the flexible behavior of biological tissues inside of a rigid body mechanics software, MD ADAMS (MSC software, Santa Ana, California), by tuning the performance to experimental data using design of experiments (DOE).

scholarly journals COMPRESSION INSTABILITIES OF TISSUES WITH LOCALIZED STRAIN SOFTENING

2011 ◽  
Vol 03 (01) ◽  
pp. 69-83 ◽  
Author(s):  
MICHEL DESTRADE ◽  
JOSE MERODIO
Keyword(s):  
Energy Density ◽  
Mechanical Behavior ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Softening ◽  
Softening Effect ◽  
Bulk Surface ◽  
Strain Relationship ◽  
Relationship Of

The stress–strain relationship of biological soft tissues affected by Marfan's syndrome is believed to be nonconvex. More specifically, Haughton and Merodio recently proposed a strain energy density leading to localized strain-softening, in order to model the unusual mechanical behavior of these isotropic, incompressible tissues. Here we investigate how this choice of strain energy affects the results of some instabilities studies, such as those concerned with the compression of infinite and semi-infinite solids, slabs, and cylinders, or with the bending of blocks, and draw comparisons with known results established previously for the case of a classical neo-Hookean solid. We find that the localized strain-softening effect leads to early instability only when instability occurs at severe compression ratios for neo-Hookean solids, as is the case for bulk, surface, and bending instabilities.

scholarly journals Numerical analysis of wood-high-density polyethylene composites: A hyperelastic approach

2018 ◽  
Vol 53 (1) ◽  
pp. 73-82
Author(s):  
Alejandro E Rodríguez-Sánchez ◽  
Alejandro Vega-Rios ◽  
Sergio G Flores-Gallardo ◽  
E Armando Zaragoza-Contreras ◽  
Mónica E Mendoza-Duarte
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Energy Density ◽  
Mechanical Behavior ◽  
High Density Polyethylene ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Wood Fiber ◽  
Element Model ◽  
High Density

The application of a hyperelastic approach to simulate the tensile mechanical behavior of wood fiber/polymer composites is proposed. This research was conducted with the purpose of selecting the theoretical model that best fits the experimental data for use in the finite element model. The analyses by the four strain energy density functions (Polynomial, Ogden, Yeoh, and Marlow models) and the Cauchy-Green tensor invariants were used as the theoretical models. The experimental mechanical behavior of three wood fiber/polymer composites formulated with high-density polyethylene as the polymer matrix, and pine, cherry, and walnut sawdust as the fillers, at a concentration of 40 wt%, was evaluated. Experimental data showed that with filler addition, the tensile modulus of the high-density polyethylene matrix increased almost 131% regarding the neat high-density polyethylene; however, no significant differences were found respecting the kind of sawdust. Nevertheless, it was found that the elongation (%) at break was higher when walnut sawdust was employed. As for the strain energy density function analyses, the best approximation to the experimental data was achieved by the Marlow model, because this model only demands the sum of the principal extension ratios for a polymer-based material, I1. The numerical results showed that the proposed finite element model predicts the response with less than 1% error, regarding the experimental data, and consequently the use of the finite element models was simplified for the prediction of the tensile mechanical behavior of this kind of composites.

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