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.

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.

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Leslee W. Brown ◽  
Lorenzo M. Smith
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Material Model ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Material Tests

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

On Formulas for the Velocity of Rayleigh Waves in Prestrained Incompressible Elastic Solids

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Pham Chi Vinh
Keyword(s):  
Rayleigh Wave ◽  
Energy Function ◽  
Rayleigh Waves ◽  
Strain Energy ◽  
Hydrostatic Stress ◽  
Strain Energy Function ◽  
Elastic Solids ◽  
Algebraic Form ◽  
Cubic Equation ◽  
Isotropic Solids

In the present paper, formulas for the velocity of Rayleigh waves in incompressible isotropic solids subject to a general pure homogeneous prestrain are derived using the theory of cubic equation. They have simple algebraic form and hold for a general strain-energy function. The formulas are concretized for some specific forms of strain-energy function. They then become totally explicit in terms of parameters characterizing the material and the prestrains. These formulas recover the (exact) value of the dimensionless speed of Rayleigh wave in incompressible isotropic elastic materials (without prestrain). Interestingly that, for the case of hydrostatic stress, the formula for the Rayleigh wave velocity does not depend on the type of strain-energy function.

On the Constitutive Equations of Biological Materials

1975 ◽  
Vol 42 (1) ◽  
pp. 242-243 ◽  
Author(s):  
H. Demiray
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Biological Materials ◽  
Biological Tissues

This paper deals with a simple possible form of the strain-energy function for biological tissues which are assumed to be transversely isotropic. Also the solution of a problem is studied and the result is compared with experiments.

scholarly journals Effects of Large Deformation and Velocity Impacts on the Mechanical Behavior of Filled Rubber: Microstructure-Based Constitutive Modeling and Mechanical Testing

Polymers ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2322
Author(s):  
Wei Wei ◽  
Yong Yuan ◽  
Xiaoyu Gao
Keyword(s):  
Mechanical Behavior ◽  
Large Deformation ◽  
Energy Function ◽  
Constitutive Modeling ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Shear Loading ◽  
Stress Strain ◽  
Cyclic Shear ◽  
Filled Rubber

Filled rubber has been extensively used in the repairing, retrofitting, and protecting of civil infrastructures due to its superior physical and mechanical properties. However, effects of large deformation and velocity impacts on the mechanical behavior of filled rubber are not well recognized, one of the major challenges in the past investigations is that the material exhibits significant nonlinearity and sensitivity to velocity. This paper presents a hyper-viscoelastic constitutive modeling and experimental study to capture both the hyperelastic and viscoelastic behaviors of filled rubber under large shear deformation and velocity impacts. Motivated by the micro-mechanism of filled rubber, the constitutive modeling consists of an equilibrium element in parallel with an improved Maxwell element to incorporate both nonlinear hyperelasticity and rate-dependent performance governed by the readjustment and rearrangement of molecular chains in the material. A new strain energy function is developed and the physical description of parameters in the strain energy function is highlighted. The Clausius-Duhem inequality is employed to consider the thermodynamic consistency of the model. Then, stress relaxation property and stress-strain response of filled rubber upon cyclic shear loading with different strain rates (ranging from 0.08 to 12.0 s−1) are experimentally studied, and some key observations are summarized. Subsequently, a “Gau-Poly” function is proposed based on the experimental data to describe the viscoelastic property of filled rubber versus strain and strain rate. Finally, stress-strain relationship and hysteretic area obtained from the experimental results were compared with the numerical results of the model, good agreement was achieved and the capacity of the model to accurately reproduce the mechanical behavior of filled rubber under a wide range of deformation and velocity impacts was verified.

New experiments on shear modulus of elasticity of arteries

1994 ◽  
Vol 266 (1) ◽  
pp. H1-H10 ◽  
Author(s):  
S. X. Deng ◽  
J. Tomioka ◽  
J. C. Debes ◽  
Y. C. Fung
Keyword(s):  
Blood Pressure ◽  
Shear Modulus ◽  
Modulus Of Elasticity ◽  
Vessel Wall ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
New Instrument ◽  
Rat Thoracic Aorta ◽  
The Difference

Although the mechanical properties of blood vessels have been studied extensively, the shear modulus of the blood vessel wall is still unknown. New data on the shear modulus of elasticity of rat arteries and its variation with axial stretch and blood pressure are presented. The data were obtained from a new instrument designed and constructed by us to perform simultaneous torsion, inflation, and longitudinal stretching tests. It was found under physiological conditions (pressure = 120 mmHg or 16 kPa; longitudinal stretch = 1.2 relative to zero-stress state), the shear modulus of normal rat thoracic aorta is G = 137 +/- 18 kPa. The difference of shear modulus at body temperature (37 degrees C) and room temperature (25 degrees C) is within 10%. The shear modulus varies significantly with changing longitudinal and circumferential strains in proportion to the strain energy due to these strains. A constitutive equation based on a pseudo strain energy function is proposed. The vessel wall is not transversely isotropic in the incremental sense. When the rat was subjected to high blood pressure due to constriction of its aorta, the shear modulus does not vary significantly with the length of time the animal was subjected to hypertension.

Orientation Effects in Short Fibre-Reinforced Elastomers

2014 ◽  
Author(s):  
Jacopo Ciambella ◽  
David C. Stanier
Keyword(s):  
Strain Energy ◽  
Large Strain ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Short Fibre ◽  
Rubber Matrix ◽  
Carbon Fibres ◽  
Reinforced Composite ◽  
Strain Behaviour ◽  
Short Carbon

The large strain behaviour of a short fibre-reinforced composite is studied through numerical simulations. The reinforcing fibres yield the macroscopic response transversely isotropic which is indeed the case of many reinforcements currently used in composites: short carbon fibres, cellulose whiskers, carbon nanotubes. As a result of the analysis, it is shown that the reorientation of the fibres that takes place at large strain has a significant effect on the overall material response by changing the axis of isotropy. This behaviour can be adequately described by using a transversely isotropic model whose strain energy function depends on three invariants: two isotropic and one representing the stretch along the direction of the fibres. To assess its capabilities, the model is compared to the results of experiments carried out by the authors on nickel-coated chopped carbon fibres in a vulcanised natural rubber matrix for which the fibre orientation is achieved by controlling an external magnetic field prior to curing. Possible applications include micro-sized propulsion devices and actuators.

Finite deformation of materials exhibiting curvilinear aeolotropy

1955 ◽  
Vol 229 (1176) ◽  
pp. 119-134 ◽  
Keyword(s):  
Spherical Shell ◽  
Strain Energy ◽  
Cylindrical Tube ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Special Cases ◽  
Incompressible Materials ◽  
General Strain ◽  
Limiting Case ◽  
Finite Elastic Deformations

Using tensor notation, a general theory is developed for finite elastic deformations of compressible and incompressible materials which exhibit curvilinear aeolotropy. The theory is formulated for materials which are completely unsymmetrical, orthotropic or transversely isotropic with respect to the curvilinear co-ordinate system which is employed to define the aeolotropy. In applications, attention is confined to cylindrically symmetrical and spherically symmetrical problems, from which emerge as special cases the inflation, extension and torsion of a cylindrical tube, and the inflation of a spherical shell. In addition, the flexure of a cuboid of rectilinearly aeolotropic material is considered as a limiting case of the cylindrically symmetrical problem. The conditions for the tube or spherical shell to be everted, and for the curved faces of the deformed cuboid to be free from applied stress, are obtained in terms of a general strain-energy function in forms which are independent of symmetries in the material.

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