Three-Dimensional Stress Distribution in Arteries

1983 ◽  
Vol 105 (3) ◽  
pp. 268-274 ◽  
Author(s):  
C. J. Chuong ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Strain Energy ◽  
Arterial Wall ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Exponential Form ◽  
Strain Relationship ◽  
Longitudinal Stretch

A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

Patient-Specific Aneurysms Rupture Prediction Using CFD Modelling With Strain Energy Function

2013 ◽  
Author(s):  
A. H. Embong ◽  
A. M. Al-Jumaily ◽  
Giri Mahadevan ◽  
Shukei Sugita ◽  
Andrew Lowe
Keyword(s):  
Vessel Wall ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Wall Stress ◽  
Aneurysm Rupture ◽  
Patient Specific ◽  
Cfd Model ◽  
Cfd Modelling ◽  
Strain Relationship ◽  
Strain Function

This paper proposes a new Patient-Specific Aneurysm CFD Model (PSAM) which is based on the energy strain function combined with dilated vessel wall stress-strain relationship to predict aneurysm rupture. The PSAM relies on the available mechanical properties and parameters obtained from a personalized model. A personalized model is developed based on instantaneous arterial deformations obtained from Doppler Ultrasound (US) images at 6–9 MHz. It is shown that PSAM has the ability to correlate the deformation wall energy based on continuous patient-specifics in predicting rupture.

MATHEMATICAL MODEL FOR THE RUPTURE OF CEREBRAL SACCULAR ANEURYSMS THROUGH THREE-DIMENSIONAL STRESS DISTRIBUTION IN THE ANEURYSM WALL

2006 ◽  
Vol 06 (03) ◽  
pp. 325-335 ◽  
Author(s):  
HANS R. CHAUDHRY ◽  
DAWN A. LOTT ◽  
CHARLES J. PRESTIGIACOMO ◽  
THOMAS W. FINDLEY
Keyword(s):  
Mathematical Model ◽  
Stress Distribution ◽  
Strain Energy ◽  
Finite Strain ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Unruptured Aneurysms ◽  
Aneurysm Wall ◽  
Thin Spherical Shell ◽  
Saccular Aneurysms

A mathematical model for the rupture of cerebral saccular aneurysms is developed through the analysis of three-dimensional stress distribution in the aneurysm wall. We assume in this paper that a saccular aneurysm resembles a thin spherical shell (a spherical membrane), and then develop a strain-energy function valid for finite strain to analyze three-dimensional stress distribution in the aneurysm wall. We find that rupture occurs when the ratio of the wall thickness to the radius of the aneurysm is 6.1 × 10-3. We also conclude from our analysis that rupture can occur when the ratio of thickness to radius of the parent aneurysm equals the ratio of thickness to radius of the daughter aneurysm. These findings may be helpful to the neurosurgeon for predicting the rupture potential in patients presenting with unruptured aneurysms.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

Fatigue Strength of Three Dimensional Welded Joints: A Synthesis Based on the Strain Energy Density over a Control Volume

2007 ◽  
Vol 348-349 ◽  
pp. 413-416
Author(s):  
M. Zappalorto ◽  
Filippo Berto ◽  
Paolo Lazzarin
Keyword(s):  
Experimental Data ◽  
Energy Density ◽  
Welded Joints ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Complex Geometry ◽  
Control Volume ◽  
Three Dimensional ◽  
Weld Toe ◽  
Weld Root

A recent approach based on the local strain energy density (SED) averaged over a given control volume is applied to well documented experimental data taken from the literature, all related to steel welded joints of complex geometry. This small size volume embraces the weld root or the weld toe, both regions modelled as sharp (zero notch radius) V-notches with different opening angles. The SED is evaluated from three-dimensional finite element models by using a circular sector with a radius equal to 0.28 mm. The data expressed in terms of the local energy fall in a scatter band recently reported in the literature, based on about 650 experimental data related to fillet welded joints made of structural steel with failures occurring at the weld toe or at the weld root.

Analytical and Experimental Study of Beam Torsional Stiffness With Large Axial Elongation

1988 ◽  
Vol 55 (1) ◽  
pp. 171-178 ◽  
Author(s):  
M. Degener ◽  
D. H. Hodges ◽  
D. Petersen
Keyword(s):  
Experimental Data ◽  
Axial Force ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Torsional Stiffness ◽  
Deformation Tensor ◽  
Axial Elongation ◽  
Green Strain ◽  
Strain Components

The axial force and effective torsional stiffness versus axial elongation are investigated analytically and experimentally for a beam of circular cross section and made of an incompressible material that can sustain large elastic deformation. An approach based on a strain energy function identical to that used in linear elasticity, except with its strain components replaced by those of some finite-deformation tensor, would be expected to provide only limited predictive capability for this large-strain problem. Indeed, such an approach based on Green strain components (commonly referred to as the geometrically nonlinear theory of elasticity) incorrectly predicts a change in volume and predicts the wrong trend regarding the experimentally determined axial force and effective torsional stiffness. On the other hand, use of the same strain energy function, only with the Hencky logarithmic strain components, correctly predicts constant volume and provides excellent agreement with experimental data for lateral contraction, tensile force, and torsional stiffness—even when the axial elongation is large. For strain measures other than Hencky, the strain energy function must be modified to consistently account for large strains. For comparison, theoretical curves derived from a modified Green strain energy function are added. This approach provides results identical to those of the Neo-Hookean formulation for incompressible materials yielding fair agreement with the experimental results for coupled tension and torsion. An alternative approach, proposed in the present paper and based on a modified Almansi strain energy function, provides very good agreement with experimental data and is somewhat easier to manage than the Hencky strain energy approach.

Finding the Constitutive Relation for a Specific Elastomer

1993 ◽  
Vol 115 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Yun Ling ◽  
Peter A. Engel ◽  
Wm. L. Brodskey ◽  
Yifan Guo
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Strain Energy ◽  
Pure Shear ◽  
Strain Energy Function ◽  
Invariant Polynomial ◽  
Energy Functions ◽  
Finite Element Program ◽  
Biaxial Extension ◽  
Strain Energy Functions

The main purpose of this study was to determine a suitable strain energy function for a specific elastomer. A survey of various strain energy functions proposed in the past was made. For natural rubber, there were some specific strain energy functions which could accurately fit the experimental data for various types of deformations. The process of determining a strain energy function for the specific elastomer was then described. The second-order invariant polynomial strain energy function (James et al., 1975) was found to give a good fit to the experimental data of uniaxial tension, uniaxial compression, equi-biaxial extension, and pure shear. A new form of strain energy function was proposed; it yielded improved results. The equi-biaxial extension experiment was done in a novel way in which the moire techniques (Pendleton, 1989) were used. The obtained strain energy functions were then utilized in a finite element program to calculate the load-deflection relation of an electrometric spring used in an electrical connector.

ON THE DEVELOPMENT OF COMPRESSIBLE PSEUDO-STRAIN ENERGY DENSITY FUNCTION FOR HYPERELASTIC MATERIAL: EXPERIMENT, THEORY AND FEM

2005 ◽  
Vol 29 (3) ◽  
pp. 459-475
Author(s):  
Hamid Ghaemi ◽  
A. Spence ◽  
K. Behdinan
Keyword(s):  
Mechanical Behavior ◽  
Density Function ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Material Parameter Identification ◽  
Constitutive Function ◽  
Strain Energy Density Function ◽  
Biaxial Tests

This study was carried out to develop a compressible pseudo-strain energy function that describes the mechanical behavior of rubber-like materials. The motivation for this work was two fold; first was to define a single-term strain energy function derived from constitutive equations that can describe the mechanical behavior of rubber-like materials and taking into account the coupling between principal stretches and the nearly incompressibility characteristic of elastomers. Second was to implement this strain energy function into the Finite Element Method (FEM) to study the suitability of the model in FEM. A one-term three-dimensional strain energy function based on the principal stretch ratios was proposed. The three dimensional constitutive function was then reduced to describe the behavior of rubber-like materials under biaxial and uniaxial loading condition based on the membrane theory. The work presented here was based on the decoupling of the strain density function into a deviatoric and a volumetric part. Using pure gum, GMS-SS-A40, uniaxial and equi-biaxial experiments were conducted employing different strain rate protocols. The material was assumed to be isotropic and homogenous. The experimental data from uniaxial and biaxial tests were used simultaneously to determine the material parameters of the proposed strain energy function. A GA curve fitting technique was utilized in the material parameter identification. The proposed strain energy function was compared to a few well-known strain energy functions as well as the experimental results. It was determined that the proposed strain energy function predicted the mechanical behavior of rubber-like material with greater accuracy as compared to other models both analytical and numerical results.

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

2019 ◽  
Vol 17 (01) ◽  
pp. 1844006
Author(s):  
Mahmood Jabareen ◽  
Yehonatan Pestes
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Nonlinear Dynamic Analysis ◽  
Strain Energy Function ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Dynamic Simulations ◽  
Cosserat Point

The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

scholarly journals A generalized strain approach to anisotropic elasticity

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
M. H. B. M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

AbstractThis work proposes a generalized Lagrangian strain function $$f_\alpha$$ f α (that depends on modified stretches) and a volumetric strain function $$g_\alpha$$ g α (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions $$f_\alpha$$ f α and $$g_\alpha$$ g α to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

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