On the elastic moduli and compliances of transversely isotropic and orthotropic materials

Lubarda, Vlado A.; Chen, Michelle C.

doi:10.2140/jomms.2008.3.153

Cited by 59 publications

(30 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where E L is the longitudinal Young modulus. For details on how to derive the last equality in (29) we refer to [43] and the references therein. The incompressible limit of equation (27) then becomes…”

Section: The Incompressible Limitmentioning

confidence: 99%

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

2018

View full text Add to dashboard Cite

The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

show abstract

Section: The Incompressible Limitmentioning

confidence: 99%

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

2018

View full text Add to dashboard Cite

show abstract

“…Assuming circumferential symmetry ε θ = ε φφ = ε θθ and ε r = ε rr , Hook's law for a transversely isotropic material (Lubarda and Chen, 2008) can be written as:…”

Section: Estimation Of the Stress-strain Relationshipmentioning

confidence: 99%

Optical Coherence Elastography-Based Corneal Strain Imaging During Low-Amplitude Intraocular Pressure Modulation

Kling

Khodadadi

Göksel

2020

Front. Bioeng. Biotechnol.

View full text Add to dashboard Cite

Purpose: Optical coherence elastography (OCE) is a promising technique for high-resolution strain imaging in ocular tissues. A major strain-inducing factor in the eye is intraocular pressure (IOP), with diurnal physiological fluctuations reaching up to 5 mmHg. We study herein low-amplitude IOP modulation to assess local corneal strain patterns.Methods: Ex vivo porcine eye globes were adjusted to an initial IOP of 15 mmHg and subsequently 25 mmHg. Corneal strain was induced by two subsequent pressure cycles, in which IOP was first increased and then decreased, each by a total of 5 mmHg. Two-dimensional optical coherence tomography (2D-OCT) B-scans were recorded after each loading step. Axial strain maps were obtained from magnitude and phase changes and supra-pixel displacements from cross-correlation. The strain detection sensitivity was evaluated in an isotropic material.Results: Deformations arising from a single 1-mmHg step could be resolved. The largest strain amplitudes (5.11·10 −3 ) were observed in the posterior stroma at a low initial IOP. Strain amplitude was 1.34 times higher at 15 mmHg than at 25 mmHg (p = 0.003). Upon IOP increase, the anterior cornea was compressed, whereas the posterior cornea showed axial expansion. Both morphological images and strain maps were sensitive to postmortem time. Strains that are larger than 2.44·10 −5 could be reliably measured.Conclusions: Low-amplitude IOP modulation, similar to diurnal physiological changes, induced measurable deformations in corneal tissue. Axial strain maps permit a localized comparison of the corneal biomechanical response. Small-strain OCE can likely be extended to other domains.

show abstract

“…Because the shear block of each matrix is diagonal, the shear moduli and shear compliances are reciprocals of one another: The equations for compressional moduli in terms of compressional compliances are more complicated but can be simply derived from the expression for the matrix inverse from the compressional block of , combined with simplifications resulting from the VTI symmetries . They are (Jaeger et al 2007; Lubarda 2008, section 5.10): where The above equations are for calculating moduli from given compliances. To calculate compliances from moduli, one simply interchanges the letters ‘C’ and ‘S’ in all expressions.…”

Section: Compliances and Modulimentioning

confidence: 99%

Compressive strength and elastic properties of a transversely isotropic calcareous mudstone

Miller¹,

Plumb

Boitnott

2013

Geophysical Prospecting

View full text Add to dashboard Cite

A B S T R A C TThis paper reports measurements of static and dynamic elastic properties plus compressive strength performed on a block of calcareous mudstone retrieved from an exploration well. Measurements of mechanical properties indicate that the mudstone is anisotropic with respect to all three properties. A detailed analysis of the elastic moduli computed using small unload reload cycles and simultaneous ultrasonic wave velocities shows both strong anisotropy and strong anelasticity. Surprisingly, the measurements are consistent with a mathematical description of a special type of anisotropic linear viscoelastic medium that is obtained by adding a set of compliant elements (e.g., contacts between clay particles, kerogen lenses, or micro-fractures) to an isotropic viscoelastic solid. This medium is fully characterized by density plus four parameters defining the viscoelastic solid and the excess normal compliance associated with the compliant elements. The mathematical model predicts a full set of parameters characterizing a transversely isotropic medium with a vertical axis of symmetry (a 'tiv' medium) for both low-and high-strain rate behaviour.

show abstract

On the elastic moduli and compliances of transversely isotropic and orthotropic materials

Cited by 59 publications

References 26 publications

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

Optical Coherence Elastography-Based Corneal Strain Imaging During Low-Amplitude Intraocular Pressure Modulation

Compressive strength and elastic properties of a transversely isotropic calcareous mudstone

Contact Info

Product

Resources

About