Elliptic crack in transversely isotropic magneto-electro-elasticity under shear loading

2019 ◽  
Vol 134 ◽  
pp. 47-65 ◽  
Author(s):  
R.-F. Zheng ◽  
T.-H. Wu ◽  
X.-Y. Li
Keyword(s):  
Transversely Isotropic ◽  
Shear Loading ◽  
Elliptic Crack

The Elastic Field Resulting From Elliptical Hertzian Contact of Transversely Isotropic Bodies: Closed-Form Solutions for Normal and Shear Loading

1997 ◽  
Vol 64 (3) ◽  
pp. 457-465 ◽  
Author(s):  
M. T. Hanson ◽  
I. W. Puja
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Field ◽  
Transversely Isotropic ◽  
Normal Pressure ◽  
Shear Loading ◽  
Potential Functions ◽  
Hertzian Contact ◽  
Elementary Functions ◽  
Shear Traction

This analysis presents the elastic field in a half-space caused by an ellipsoidal variation of normal traction on the surface. Coulomb friction is assumed and thus the shear traction on the surface is taken as a friction coefficient multiplied by the normal pressure. Hence the shear traction is also of an ellipsoidal variation. The half-space is transversely isotropic, where the planes of isotropy are parallel to the surface. A potential function method is used where the elastic field is written in three harmonic functions. The known point force potential functions are utilized to find the solution for ellipsoidal loading by quadrature. The integrals for the derivatives of the potential functions resulting from ellipsoidal loading are evaluated in terms of elementary functions and incomplete elliptic integrals of the first and second kinds. The elastic field is given in closed-form expressions for both normal and shear loading.

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.

THREE-DIMENSIONAL ANALYSIS OF ARBITRARY-SHAPED CRACKS IN PIEZOELECTRIC SOLIDS UNDER SHEAR LOADING

2006 ◽  
Vol 03 (03) ◽  
pp. 321-336
Author(s):  
HE-GEN YU ◽  
MENG-CHENG CHEN
Keyword(s):  
Electric Displacement ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Shear Loading ◽  
Elastic Fields ◽  
Uniform Shear ◽  
Closed Type ◽  
Ellipsoidal Coordinates ◽  
Crack Problems ◽  
Planar Crack

This paper is a sequel of the author's previous work [Chen (2004)]. It deals with some basic linear electro-elastic fracture problems for an arbitrary-shaped planar crack in a three-dimensional infinite transversely isotropic piezoelectric material subjected to shear loading that is antisymmetric with respect to the crack. The finite-part integral concept is used to derive hypersingular integral equations for the crack from available solutions of the point force and charge for an infinite transversely isotropic piezoelectric solid. Closed-type solutions for the full electro-elastic fields, for the stress and electric displacement K-fields and the energy release rate G are obtained. In particular, under uniform shear loading, exact expressions for an elliptical crack are derived with introducing the ellipsoidal coordinates. Finally, numerical examples for some typical crack problems are also demonstrated in table and graphic forms.

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