Hartig's law and linear elasticity with initial stress

Man, Chi‐Sing

doi:10.1088/0266-5611/14/2/007

Cited by 55 publications

(50 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Man [Man98] proposes for elastodynamics with residual stress R a more general constituitive law S = R + ∇u · R + CE where the elasticity tensor C also depends linearly on R. In the isotropic case CE consists of the right-hand side in (3) plus the R dependent terms β 1 tr(E) tr(R)I + β 2 tr(R)E + β 3 tr(E)R + tr(ER)I + β 4 ER + RE .…”

Section: Isotropic Elastodynamic Equationsmentioning

confidence: 99%

Propagation of polarization in elastodynamics with residual stress and travel times

Hansen

Uhlmann

2003

Math. Ann.

View full text Add to dashboard Cite

Section: Isotropic Elastodynamic Equationsmentioning

confidence: 99%

Propagation of polarization in elastodynamics with residual stress and travel times

Hansen

Uhlmann

2003

Math. Ann.

View full text Add to dashboard Cite

“…The characterization of the stress-dependence in N was first given by Turner and Ghoshal 17 and later demonstrated experimentally by Kube et al 18,19 The present theory utilizes a more commonly used elastic constitutive relation, [31][32][33][34][35][36][37] which is valid for both residual and mechanical stresses. This constitutive relation leads to different stress-dependent elastic properties than those given by Turner and Ghoshal.…”

Section: Theorymentioning

confidence: 96%

Stress-dependent second-order grain statistics of polycrystals

Kube

Turner

2015

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

In this article, the second-order statistics of the elastic moduli of randomly oriented grains in a polycrystal are derived for the case when an initial stress is present. The initial stress can be either residual stress or stresses generated from external loading. The initial stress is shown to increase or decrease the variability of the grain's elastic moduli from the average elastic moduli of the polycrystal. This variation in the elastic properties of the individual grains causes acoustic scattering phenomenon in polycrystalline materials to become stress-dependent. The influence of the initial stress on scattering is shown to be greater than the influence on acoustic phase velocities, which defines the acoustoelastic effect. This work helps the development of scattering based tools for the nondestructive analysis of material stresses in polycrystals.

show abstract

“…A set of invariants equivalent to the above has been used by [Hoger 1993a;1996]. For related work concerned with the constitutive equations and material symmetry for a residually stressed elastic material we refer to [Coleman and Noll 1964;Hoger 1986;1993b;Man and Lu 1987;Johnson and Hoger 1993;Man 1998;Saravanan 2008;Tanuma and Man 2008]. We have not for the moment defined particular notation for the invariants (25)-(27).…”

Section: Equations Of Motionmentioning

confidence: 99%

Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited

Ogden

Singh²

2011

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

In this paper, the general constitutive equation for a transversely isotropic hyperelastic solid in the presence of initial stress is derived, based on the theory of invariants. In the general finite deformation case for a compressible material this requires 18 invariants (17 for an incompressible material). The equations governing infinitesimal motions superimposed on a finite deformation are then used in conjunction with the constitutive law to examine the propagation of both homogeneous plane waves and, with the restriction to two dimensions, Rayleigh surface waves. For this purpose we consider incompressible materials and a restricted set of invariants that is sufficient to capture both the effects of initial stress and transverse isotropy. Moreover, the equations are specialized to the undeformed configuration in order to compare with the classical formulation of Biot. One feature of the general theory is that the speeds of homogeneous plane waves and surface waves depend nonlinearly on the initial stress, in contrast to the situation of the more specialized isotropic and orthotropic theories of Biot. The speeds of (homogeneous plane) shear waves and Rayleigh waves in an incompressible material are obtained and the significant differences from Biot's results for both isotropic and transversely isotropic materials are highlighted with calculations based on a specific form of strain-energy function.

show abstract

Hartig's law and linear elasticity with initial stress

Cited by 55 publications

References 15 publications

Propagation of polarization in elastodynamics with residual stress and travel times

Propagation of polarization in elastodynamics with residual stress and travel times

Stress-dependent second-order grain statistics of polycrystals

Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited

Contact Info

Product

Resources

About