scholarly journals A comparison of hyperelastic constitutive models applicable to brain and fat tissues

2015 ◽  
Vol 12 (110) ◽  
pp. 20150486 ◽  
Author(s):  
L. Angela Mihai ◽  
LiKang Chin ◽  
Paul A. Janmey ◽  
Alain Goriely
Keyword(s):  
Experimental Data ◽  
Tensile Strain ◽  
Large Scale ◽  
Soft Tissues ◽  
Compressive Strain ◽  
Finite Elasticity ◽  
Constitutive Models ◽  
Mechanical Behaviours ◽  
Incompressible Hyperelastic Material ◽  
Hyperelastic Models

In some soft biological structures such as brain and fat tissues, strong experimental evidence suggests that the shear modulus increases significantly under increasing compressive strain, but not under tensile strain, whereas the apparent Young's elastic modulus increases or remains almost constant when compressive strain increases. These tissues also exhibit a predominantly isotropic, incompressible behaviour. Our aim is to capture these seemingly contradictory mechanical behaviours, both qualitatively and quantitatively, within the framework of finite elasticity, by modelling a soft tissue as a homogeneous, isotropic, incompressible, hyperelastic material and comparing our results with available experimental data. Our analysis reveals that the Fung and Gent models, which are typically used to model soft tissues, are inadequate for the modelling of brain or fat under combined stretch and shear, and so are the classical neo-Hookean and Mooney–Rivlin models used for elastomers. However, a subclass of Ogden hyperelastic models are found to be in excellent agreement with the experiments. Our findings provide explicit models suitable for integration in large-scale finite-element computations.

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.

Interpretation of Experimental Data is Substantial for Constitutive Characterization of Arterial Tissue

2021 ◽  
Author(s):  
Ondrej Lisický ◽  
Anna Hrubanová ◽  
Jiri Bursa
Keyword(s):  
Experimental Data ◽  
Soft Tissues ◽  
Constitutive Models ◽  
Uniaxial Stress ◽  
Mechanical Tests ◽  
Data Sets ◽  
Stress Strain ◽  
Rigorous Approach ◽  
Carotid Wall

Abstract The paper aims at evaluation of mechanical tests of soft tissues and creation of their representative stress-strain responses and respective constitutive models. Interpretation of sets of experimental results depends highly on the approach to the data analysis. Their common representation through mean and standard deviation may be misleading and give non-realistic results. In the paper, raw data of 7 studies consisting of 11 experimental data sets (concerning carotid wall and atheroma tissues) are re-analysed to show the importance of their rigorous analysis. The sets of individual uniaxial stress-strain curves are evaluated using three different protocols: stress-based, stretch-based and constant-based, and the population-representative response is created by their mean or median values. Except for nearly linear responses, there are substantial differences between the resulting curves, being mostly the highest for constant-based evaluation. But also the stretch-based evaluation may change the character of the response significantly. Finally, medians of the stress-based responses are recommended as the most rigorous approach for arterial and other soft tissues with significant strain stiffening.

Strain Capacity of X100 High-Strain Linepipe for Strain-Based Design Application

2008 ◽  
Author(s):  
Satoshi Igi ◽  
Joe Kondo ◽  
Nobuhisa Suzuki ◽  
Joe Zhou ◽  
Da-Ming Duan
Keyword(s):  
Tensile Strain ◽  
Large Scale ◽  
High Strain ◽  
Compressive Strain ◽  
Local Buckling ◽  
Ground Movement ◽  
Frozen Ground ◽  
Long Distance ◽  
Element Analysis ◽  
Strain Capacity

In recent years, several natural gas pipeline projects have been planned for permafrost regions. Pipelines laid in such areas are subjected to large plastic deformation as a result of ground movement due to repeated thawing and freezing of the frozen ground. Likewise, in pipeline design methods, research on application of strain-based design as an alternative to the conventional stress-based design method has begun. Much effort has been devoted to the application of strain-based design to high strength linepipe materials. In order to verify the applicability of high-strain X100 linepipe to long distance transmission, a large-scale X100 pipeline was constructed using linepipe with an OD of 42″ and wall thickness of 14.3mm. This paper presents the results of experiments and Finite Element Analysis (FEA) focusing on the strain capacity of high-strain X100 linepipes. The critical compressive strain of X100 high-strain linepipes is discussed based on the results of FEA taking into account geometric imperfections. The critical tensile strain for high-strain X100 pipelines is obtained based on a curved wide plate (CWP) tensile test using specimens taken from girth welded joints. Specifically, the effect of external coating treatment on the strain capacity of X100 high-strain linepipe is investigated. The strain capacity of the 42″ X100 pipeline is considered by comparing the tensile strain limit obtained from girth weld fracture and critical compressive strain which occurs in local buckling under pure bending deformation.

scholarly journals An Investigation of Uniaxial Mechanical Properties of Excised Sheep Heart Muscle Fibre – Fitting of Different Hyperelastic Constitutive Models

2021 ◽  
Author(s):  
Fulufhelo Nemavhola ◽  
Harry M Ngwangwa ◽  
Thanyani Pandelani
Keyword(s):  
Experimental Data ◽  
Soft Tissues ◽  
Constitutive Models ◽  
Finite Element Models ◽  
Predictive Capability ◽  
Material Parameters ◽  
Linear Finite Element ◽  
Fitting Algorithm ◽  
Testing Data

Abstract : This paper presents the investigation of biomechanical behaviour of sheep heart fibre using uniaxial tests in various samples. Non-linear Finite Element models (FEA) that are utilised in understanding mechanisms of different diseases may not be developed without the accurate material properties. This paper presents uniaxial mechanical testing data of the sheep heart fibre. The mechanical uniaxial data of the heart fibre was then used in fitting four constitutive models including the Fung model, Polynomial (Anisotropic), Holzapfel (2005) model, Holzapfel (2000) model and the Four-fibre Family model. Even though the constitutive models for soft tissues including heart myocardium have been presented over several decades, there is still a need for accurate material parameters from reliable hyperelastic constitutive models. Therefore, the aim of this research paper is to select five hyperelastic constitutive models and fit experimental data in the uniaxial experimental data of the sheep heart fibre. A fitting algorithm was made used to optimally fitting and determination of the material parameters based on selected hyperelastic constitutive model. In this study, the evaluation index (EI) was used to measure the performance and capability of each selected anisotropic hyperelatic model. It was observed that the best predictive capability of the mechanical behaviour of sheep heart fibre the Polynomial (anisotropic) model has the EI of 100 and this means that it is the best performance when compared to all the other models.

A Fracture Characterization Framework for Large-Scale Marine Metal Structures

2020 ◽  
Author(s):  
Juan G. Londono ◽  
Mostafa E. Mobasher ◽  
Pawel Woelke
Keyword(s):  
Experimental Data ◽  
Large Scale ◽  
Experimental Testing ◽  
Constitutive Models ◽  
Stress Triaxiality ◽  
Shell Element ◽  
Material Model ◽  
Surrogate Data ◽  
Marine Structures ◽  
Fracture Characterization

Abstract Prediction of large-scale marine structures under extreme loading conditions (e.g. impact, fire) requires the use of computational tools that are both accurate and efficient. To resolve models at this scale, engineers normally use shell elements in which two of the (in-plane) dimensions are much larger than the third (thickness) one. Herein, we propose a consistent characterization framework for shell-element models commonly used in metal marine structures. The underlying model is based on a three stress-invariant plasticity model that accounts for the effects of stress triaxiality and shear-dominated stress states and accounts for the micromechanical void growth and coalescence that leads to fracture. This framework serves as both a constitutive model as well as a back-end calibration engine which outputs material cards that can be readily used with commercial finite element solvers like LS-DYNA and Abaqus. The calibration framework supports data-driven constitutive models that require engineers to prescribe the Fracture Locus (FL) and Instability Curves (IC) from experimental data, such as the Johnson-Cook model. Moreover, the calibration framework uses the underlying physics based model to computationally generate additional surrogate data that compliments the experimental testing. Thus, it allows the analyst to calibrate a material model based on limited experimental data, hence, reducing the costs associated with data acquisition and processing. A standalone calibration tool (VistaCal) that highlights the benefits of this characterization framework is also presented.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

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.

scholarly journals A study of computational methods for wake structure and base pressure prediction of a generic SUV model with fixed and rotating wheels

2017 ◽  
Vol 231 (9) ◽  
pp. 1222-1238 ◽  
Author(s):  
David Forbes ◽  
Gary Page ◽  
Martin Passmore ◽  
Adrian Gaylard
Keyword(s):  
Experimental Data ◽  
Computational Methods ◽  
Large Scale ◽  
Ground Plane ◽  
Computational Cost ◽  
Rear Wheel ◽  
Base Pressure ◽  
Detached Eddy Simulation ◽  
Wake Structure ◽  
Wake Interactions

This study is an evaluation of the computational methods in reproducing experimental data for a generic sports utility vehicle (SUV) geometry and an assessment on the influence of fixed and rotating wheels for this geometry. Initially, comparisons are made in the wake structure and base pressures between several CFD codes and experimental data. It was shown that steady-state RANS methods are unsuitable for this geometry due to a large scale unsteadiness in the wake caused by separation at the sharp trailing edge and rear wheel wake interactions. unsteady RANS (URANS) offered no improvements in wake prediction despite a significant increase in computational cost. The detached-eddy simulation (DES) and Lattice–Boltzmann methods showed the best agreement with the experimental results in both the wake structure and base pressure, with LBM running in approximately a fifth of the time for DES. The study then continues by analysing the influence of rotating wheels and a moving ground plane over a fixed wheel and ground plane arrangement. The introduction of wheel rotation and a moving ground was shown to increase the base pressure and reduce the drag acting on the vehicle when compared to the fixed case. However, when compared to the experimental standoff case, variations in drag and lift coefficients were minimal but misleading, as significant variations to the surface pressures were present.

Investigation on hydrodynamic forces leading to coarse particle entrainment using Large-Eddy Simulations

2021 ◽  
Author(s):  
Gaston Latessa ◽  
Angela Busse ◽  
Manousos Valyrakis
Keyword(s):  
Experimental Data ◽  
Flow Field ◽  
Large Scale ◽  
Large Eddy Simulations ◽  
Flow Conditions ◽  
Mean Flow ◽  
Protection Measures ◽  
Practical Applications ◽  
Particle Entrainment ◽  
Large Eddy

<p>The prediction of particle motion in a fluid flow environment presents several challenges from the quantification of the forces exerted by the fluid onto the solids -normally with fluctuating behaviour due to turbulence- and the definition of the potential particle entrainment from these actions. An accurate description of these phenomena has many practical applications in local scour definition and to the design of protection measures.</p><p>In the present work, the actions of different flow conditions on sediment particles is investigated with the aim to translate these effects into particle entrainment identification through analytical solid dynamic equations.</p><p>Large Eddy Simulations (LES) are an increasingly practical tool that provide an accurate representation of both the mean flow field and the large-scale turbulent fluctuations. For the present case, the forces exerted by the flow are integrated over the surface of a stationary particle in the streamwise (drag) and vertical (lift) directions, together with the torques around the particle’s centre of mass. These forces are validated against experimental data under the same bed and flow conditions.</p><p>The forces are then compared against threshold values, obtained through theoretical equations of simple motions such as rolling without sliding. Thus, the frequency of entrainment is related to the different flow conditions in good agreement with results from experimental sediment entrainment research.</p><p>A thorough monitoring of the velocity flow field on several locations is carried out to determine the relationships between velocity time series at several locations around the particle and the forces acting on its surface. These results a relevant to determine ideal locations for flow investigation both in numerical and physical experiments.</p><p>Through numerical experiments, a large number of flow conditions were simulated obtaining a full set of actions over a fixed particle sitting on a smooth bed. These actions were translated into potential particle entrainment events and validated against experimental data. Future work will present the coupling of these LES models with Discrete Element Method (DEM) models to verify the entrainment phenomena entirely from a numerical perspective.</p>

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