On the Transversely Isotropic, Hyperelastic Response of CNS white Matter Using a Hybrid Approach

2020 ◽  
Author(s):  
Yi Pan ◽  
David Shreiber ◽  
Assimina Pelegri
Keyword(s):  
Experimental Data ◽  
White Matter ◽  
Hybrid Approach ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Element Model ◽  
Shear Loading ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Hyperelastic Model

Abstract A numerical and experimental hybrid approach is developed to study the constitutive behavior of the central nervous system white matter. A published transversely isotropic hyperelastic strain energy function is reviewed and used to determine stress-strain relationships for three idealized, simple loading scenarios. The proposed constitutive model is simplified to a three-parameter hyperelastic model by assuming the white matter's incompressibility. Due to a lack of experimental data in all three loading scenarios, a finite element model that accounts for micro-structural axons and their kinematics is developed to simulate behaviors in simple shear loading scenarios to supplement existing uniaxial tensile test data. The parameters of the transversely isotropic hyperelastic material model are determined regressively using the hybrid data. The results highlight that a hybrid numerical virtual test coupled with experimental data, can determine the transversely isotropic hyperelastic model. Besides, it is noted that the model is not limited to small strains, but it is also applied to large deformations.

MECHANICAL BEHAVIOUR OF TRANSVERSELY ISOTROPIC POROUS NEO-HOOKEAN SOLIDS

2010 ◽  
Vol 02 (01) ◽  
pp. 11-39 ◽  
Author(s):  
ZAOYANG GUO ◽  
FERHUN C. CANER
Keyword(s):  
Strain Energy ◽  
Hydrostatic Stress ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Axial Direction ◽  
Shear Loading ◽  
Porous Solid ◽  
Mechanical Responses ◽  
Cylindrical Pores ◽  
Hyperelastic Model

In this paper, the mechanical responses of a recently developed hyperelastic model for the neo-Hookean solids with aligned continuous cylindrical pores under finite homogeneous deformation that can capture the anisotropic compressibility as well as the coupling between the volumetric and deviatoric behaviours are examined. To this end, the strain energy function of this hyperelastic compressible transversely isotropic model contains terms for the coupling of volumetric and deviatoric behaviours. It is shown that, the asymptotic response of this anisotropic compressible model under extreme loading situations is considerably different from that of incompressible models. The unstable behaviour of the porous solid under hydrostatic stress/strain loadings is discussed in detail. When a general simple 2D shear deformation is applied to this porous solid in i1 – i2 plane, the normal stress in the third axial direction (i3) is nonzero. The loss of monotonicity of the stress tensor under off-axis simple 2D shear loading is demonstrated as well.

Pseudo 3D RVE Based Finite Element Simulation on White Matter

2012 ◽  
Author(s):  
Yi Pan ◽  
Vivak Patel ◽  
Assimina A. Pelegri ◽  
David I. Shreiber
Keyword(s):  
Finite Element ◽  
White Matter ◽  
Spinal Cord Injuries ◽  
Axonal Injury ◽  
Mechanical Strain ◽  
Element Model ◽  
Tissue Level ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Brain White Matter

Axonal injury represents a critical target for traumatic brain and spinal cord injuries prevention and treatment. Finite element head models are often used to predict brain injury caused by mechanical loading exerted on the head. Many studies have been attempted to understand injury mechanisms and to define mechanical parameters of axonal injury. Mechanical strain has been identified as the proximal cause of axonal injury. Since the microstructure of the brain white matter is locally oriented, the stress and strain fields are highly axon orientation dependent. The accuracy of the finite element simulations depends not only on correct determination of the material properties but also on precise depiction of the tissues’ microstructure (microscopic level). We applied a finite element method and a mircomechanics approach to simulate the kinematics of axon, which was developed according to experimental data, and found that the degree of coupling between the axons and surrounding cells within the tissue will affect the behavior of the tissue. In this study, the finite element model and the kinematic axonal model are applied to the Representative Volume Element (RVE) of central nervous system (CNS) white matter to investigate the tissue level mechanical behavior. The uniaxial tensile test on the white matter tissue will be presented as an example using the RVE.

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.

MULTISCALE COMPUTATIONAL EVALUATION OF ELASTO-VISCOPLASTIC DEFORMATION BEHAVIOR OF AMORPHOUS POLYMER CONTAINING MICROSCOPIC HETEROGENEITY DURING UNIAXIAL TENSILE TEST

2010 ◽  
Vol 02 (03n04) ◽  
pp. 235-255 ◽  
Author(s):  
MAKOTO UCHIDA ◽  
NAOYA TADA
Keyword(s):  
Finite Element ◽  
Deformation Behavior ◽  
Volume Fraction ◽  
Amorphous Polymer ◽  
Element Model ◽  
Strength Distribution ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Viscoplastic Deformation ◽  
Heterogeneous Microstructures

The two-scale elasto-viscoplastic deformation behavior of amorphous polymer was investigated using the large deformation finite element homogenization method. In order to enable a large time increment for the simulation step in the plastic deformation stage, the tangent modulus method is introduced into the nonaffine molecular chain network theory, which is used to represent the deformation behavior of pure amorphous polymer. Two kinds of heterogeneous microstructures were prepared in this investigation. One was the void model, which contains uniformly or randomly distributed voids, and the other was the heterogeneous strength (HS) model, which contains a distribution of initial shear strength. In the macroscopic scale, initiation and propagation processes of necking during uniaxial tension were considered. The macroscopic nominal stress–strain relation was strongly characterized by the volume fraction and distribution of voids for the void model and by the width of the strength distribution for the HS model. Non-uniform deformation behaviors in microscopic and macroscopic scales are closely related to each other for amorphous polymers because continuous stretching and hardening in the localized zone of the microstructure brings about an increase in macroscopic deformation resistance. Furthermore, computational results obtained from the homogenization model are compared to those obtained from the full-scale finite element model, and the effect of the scale difference between microscopic and macroscopic fields is discussed.

Research on Thermal Mechanical Properties of Rubber Like Materials Based on Numerical Simulation

2011 ◽  
Vol 704-705 ◽  
pp. 811-816
Author(s):  
Jian Bin Sang ◽  
Wen Ying Yu ◽  
Bo Liu ◽  
Xiao Lei Li ◽  
Tie Feng Liu
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Analysis ◽  
Nonlinear Finite Element ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Rubber Seal ◽  
Thermal Mechanical Analysis

This paper start with a discussion on various types of strain energy functions of rubber like materials. Theoretical analysis based on the strain energy function given in by Y.C.Gao in 1997 is proposed. The material parameters of strain energy function were curve-fitted from the uniaxial tensile test. The selected constitutive relation of rubber like materials was implemented into a finite element code MSC.Marc as a user material subroutine to analyze the thermal and mechanical behavior of rubber seal under the plane strain conditions. Contact force and distribution of the contact stress between lip seal and shaft are analyzed and coupled thermal mechanical analysis of rubber seal was proposed. The contact pressure distribution is readily obtainable from the nonlinear finite element analysis and the coupled thermal mechanical analyses results indicate that the thermal stress only have minor influence on the deformed shape of rubber seal, which will be a useful technique for predicting the properties of rubber seal and providing reference for engineering design. Keywords:rubber like materials, nonlinear finite element, contact analysis, thermal mechanical analysis

scholarly journals Stochastic micromechanical modeling of transverse punch shear damage behavior of unidirectional composites

2018 ◽  
Vol 53 (9) ◽  
pp. 1197-1213 ◽  
Author(s):  
Bazle Z (Gama) Haque ◽  
Molla A Ali ◽  
Raja H Ganesh ◽  
Sandeep Tamrakar ◽  
Chian F Yen ◽  
...  
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Shear Strength ◽  
Finite Element Model ◽  
Shear Failure ◽  
Element Model ◽  
Shear Loading ◽  
Unidirectional Composites ◽  
Micromechanical Damage ◽  
The Continuum

Punch shear in unidirectional composites is induced by transverse shear loading that progressively perforates the laminate within a narrow shear annulus. At lower micromechanical length scales, punch shear loading creates unique micromechanical damage mechanisms dominated by transverse fiber shear failure, fiber–matrix interphase debonding and large inelastic deformation and cracking of the matrix. A new punch shear experimental method has been developed to test unidirectional S glass/DER353 epoxy composite ribbons at sub-millimeter length scale. The experimental data consist of a statistical measurement of the continuum response (load-deformation and punch shear strength) and the characterization of micromechanical damage modes. A simplified 2D micromechanical finite element model incorporating Weibull fiber strength distribution has been developed and correlated with the experimental data. The 2D micromechanical finite element model can simulate the punch shear failure of the ribbon incorporating mixed mode fiber fracture, and fiber–matrix debonding mechanisms using zero thickness cohesive elements. Results from stochastic simulations of punch shear experiments show that an equivalent 2D micromechanical finite element model can predict the micromechanical damage mechanisms and the statistical distribution of punch shear strength of the continuum with favorable correlation with the experiments. This paper presents a combined experimental and computational approach in simulating the stochastic non-linear progressive punch shear behavior of unidirectional composites for the first time in the literature.

scholarly journals The Role of Pre-Conditioning Frequency in the Experimental Characterization of Hyper-Elastic Materials as Models for Soft Tissue Applications

2016 ◽  
Vol 08 (05) ◽  
pp. 1650066 ◽  
Author(s):  
Serena de Gelidi ◽  
Gianluca Tozzi ◽  
Andrea Bucchi
Keyword(s):  
Experimental Data ◽  
Biological Tissues ◽  
Experimental Simulation ◽  
Elastic Behavior ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Elastic Materials ◽  
Hyper Elastic ◽  
The Impact

Rubber-like materials as many soft tissues can be described as incompressible and hyper-elastic materials. Their comparable elastic behavior, up to a certain extent, has been exploited to develop and test experimental methodologies to be then applied to soft biological tissues such as aortic wall. Hence, theoretical and experimental simulation of aortic tissue, and more generally blood vessel tissue, has been often conducted using rubbers. Despite all the efforts in characterizing such materials, a clear and comprehensive testing procedure is still missing. In particular, the influence of pre-conditioning in the mechanical response of hyper-elastic materials has been often neglected. In this paper, the importance of pre-conditioning is demonstrated by: (i) exploring the effect of stretching frequency applied before the uniaxial tensile test; (ii) recognizing the role of specimen geometry and strain amplitude; (iii) verifying the impact of experimental data acquisition on finite element predictions. It was found that stress–strain relationship shows a statistical difference between some frequencies of pre-conditioning and its absence. Only certain pre-conditioning frequencies were able to generate repeatable experimental data for strip or dumb-bell shapes. This feature corresponds to a consistent reduction in the scatter of critical pressures obtained by numerical simulations.

A Compressible, Transversely Isotropic, Hyperelastic Constitutive Model of the Guinea Pig Spinal Cord White Matter

2007 ◽  
Author(s):  
Beth Galle ◽  
Hui Ouyang ◽  
Riyi Shi ◽  
Eric A. Nauman
Keyword(s):  
Spinal Cord ◽  
White Matter ◽  
Guinea Pig ◽  
Constitutive Model ◽  
Spinal Cord Injuries ◽  
Transversely Isotropic ◽  
Element Model ◽  
Plane Shear ◽  
Tissue Compression

Slow compression spinal cord injuries occur when the spinal canal narrows, the consequence of degenerative, infective, or oncologic legion growth, and exerts pressure throughout the spinal cord. Transverse tissue compression results in an amalgamation of mechanical insults at the cellular level [1]. However, the mechanism of cellular injury has yet to be elucidated. We have recently developed a hyperelastic, isotropic plane strain finite element model (FEM) of the guinea pig spinal cord white matter response to transverse compression based on force-deformation curves measured in vitro. The strongest correlation with in vitro axonal injury density was the combination of the in-plane shear stress with the in- and out-of-plane normal stresses quantified using the FEM [2]. However, we hypothesize that the guinea pig spinal cord white matter is a transversely isotropic material. Material anisotropy must be incorporated into the FEM to achieve enhanced model accuracy, specifically, the prediction of axial stresses within the spinal cord parenchyma during transverse tissue compression. Therefore, the objective of the present study was to propose a compressible, transversely isotropic, hyperelastic constitutive model of the guinea pig spinal cord white matter.

Effect of Various Side Grooves on 3D Crack-Front J-Integral for CT Specimens

2016 ◽  
Vol 853 ◽  
pp. 46-50 ◽  
Author(s):  
Xiang Qing Li ◽  
Chuan Xiao Wu ◽  
Jian Feng Mao ◽  
Shi Yi Bao ◽  
Zeng Liang Gao
Keyword(s):  
Fracture Toughness ◽  
Crack Front ◽  
Numerical Study ◽  
Three Dimensional ◽  
Element Model ◽  
Compact Tension ◽  
Test Method ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Strain Relationship

Three-dimensional (3D) elastic-plastic finite element model (FEM) is adopted to research the effect of side groove on the crack-front J-integral for different size of Compact Tension (CT) specimens. Although the side-grooved CT specimen is widely used in the existing test method, such as ASTM E1820-13, the test data of fracture toughness is varying with the various geometric parameters. Before FE calculation, the material properties of Q345 steel were obtained by uniaxial tensile test, especially for the true stress-strain relationship. In this paper, it focuses on the numerical study of geometric parameter effects on the fracture toughness. Toward this end, the commercial FE software of ABAQUS is adopted to calculate the J-integral. Since the side groove of CT specimen is so important to make the fracture test success, the various parameters of side groove is intensively analyzed for obtaining the accurate J-integral along the crack front, including the effects of the angle, depth and root radius. In fact, the side groove effect is so significant around the crack front that cannot be ignored in the J-integral calculation. Through rigorous FE investigation, the influence of the side groove on the fracture toughness testing is fully disclosed, and the appropriate side groove configuration is recommended accordingly.

3D Mechanical Properties of the Layered Esophagus: Experiment and Constitutive Model

2006 ◽  
Vol 128 (6) ◽  
pp. 899-908 ◽  
Author(s):  
W. Yang ◽  
T. C. Fung ◽  
K. S. Chian ◽  
C. K. Chong
Keyword(s):  
Constitutive Model ◽  
Fiber Orientation ◽  
Strain Energy ◽  
Physiological State ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Esophageal Wall ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Esophageal Diseases

The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases.

Sign in / Sign up

Export Citation Format

Share Document