Please cite this article as: Hamdaoui, M.E., Merodio, J., Ogden, R.W., Loss of ellipticity in the combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube, International Journal of Solids and Structures (2015), doi: http://dx.Abstract In this paper we consider theoretically the finite deformation of a circular cylindrical tube of a transversely isotropic elastic material, specifically the combined axial stretch, inflation and helical shear deformation, with particular reference to the failure of ellipticity. For a simple form of strain-energy function specific examples involving axial and radial directions of transverse isotropy are then considered, leading to different predictions of the onset of ellipticity failure.
We describe an analysis strategy to obtain ultrasonography-matched axial dimensions of small animal eyes using the LenStar biometer. The LenStar optical low-coherence reflectometer is an attractive device for animal research due to its high precision, non-invasiveness, and the ability to measure the axial dimensions of cornea, anterior chamber, lens, vitreous chamber, and axial length. However, this optical biometer was designed for clinical applications in human eyes and its internal analysis provides inaccurate values when used on small eyes due to species-dependent differences in refractive indices and relative axial dimensions. The LenStar uses a near infrared light source to measure optical path lengths (OPLs) that are converted by the LenStar's EyeSuite software into geometrical lengths (GLs) based on the refractive indices and axial dimensions of the human eye. We present a strategy that extracts the OPLs, determines refractive indices specific for the small animal eye of interest and then calculates corrected GLs. The refractive indices are obtained by matching the LenStar values to ultrasonography values to ultrasonography values in the same eyes. As compared to ultrasounography, we found that the internal calculations of the LenStar underestimate the axial dimensions of all ocular compartments of the tree shrew eye: anterior segment depth by 6.17 ± 4.50%, lens thickness by 1.37 ± 3.06%, vitreous chamber depth
The sclera uses unknown mechanisms to match the eye's axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the eye's refractive error. We define growth as a mechanism that changes the tissue volume and mass while remodeling involves internal micro-deformations that are volume-preserving at the macroscale. The model was fitted against longitudinal refractive measurements in tree shrews of different ages and exposed to three different visual conditions: (i) normal development; (ii) negative lens wear to induce myopia; and (iii) recovery from myopia by removing the negative lens. The model was able to replicate the age-and vision-dependent response of the tree shrew experiments. Scleral growth ceased at younger age than scleral remodeling. The remodeling rate decreased as the eye emmetropized but increased at any age when a negative lens was put on. The predictive power of the model was investigated by calculating the susceptibility to scleral remodeling and the response to form deprivation myopia in tree shrews. Both predictions were in good agreement with experimental data that were not used to fit the model. We propose the first model that distinguishes scleral growth from remodeling. The good agreement of our results with experimental data supports the notion that scleral growth and scleral remodeling are two independently controlled mechanisms during eye development.
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