Finite element implementation of a new model of slight compressibility for transversely isotropic materials

<div><p>Modelling transversely isotropic materials in finite strain problems is a complex task in biomechanics, and is usually addressed by using finite element (FE) simulations. The standard method developed to account for the quasi-incompressible nature of soft tissues is to decompose the strain energy function (SEF) into volumetric and deviatoric parts. However, this decomposition is only valid for fully incompressible materials, and its use for slightly compressible materials yields an unphysical response during the simulation of hydrostatic tension/compression of a transversely isotropic material. This paper presents the FE implementation as subroutines of a new volumetric model solving this deficiency in two FE codes: Abaqus and FEBio. This model also has the specificity of restoring the compatibility with small strain theory. The stress and elasticity tensors are first derived for a general SEF. This is followed by a successful convergence check using a particular SEF and a suite of single-element tests showing that this new model does not only correct the hydrostatic deficiency but may also affect stresses during shear tests (Poynting effect) and lateral stretches during uniaxial tests (Poisson's effect). These FE subroutines have numerous applications including the modelling of tendons, ligaments, heart tissue, etc. The biomechanics community should be aware of specificities of the standard model, and the new model should be used when accurate FE results are desired in the case of compressible materials.</p></div

HO[subscript x] observations over West Africa during AMMA: impact of isoprene and NO[subscript x]

Aircraft OH and HO[subscript 2] measurements made over West Africa during the AMMA field campaign in summer 2006 have been investigated using a box model constrained to observations of long-lived species and physical parameters. "Good" agreement was found for HO[subscript 2] (modelled to observed gradient of 1.23 ± 0.11). However, the model significantly overpredicts OH concentrations. The reasons for this are not clear, but may reflect instrumental instabilities affecting the OH measurements. Within the model, HO[subscript x] concentrations in West Africa are controlled by relatively simple photochemistry, with production dominated by ozone photolysis and reaction of O([superscript 1]D) with water vapour, and loss processes dominated by HO[subscript 2] + HO[subscript 2] and HO[subscript 2] + RO[subscript 2]. Isoprene chemistry was found to influence forested regions. In contrast to several recent field studies in very low NO[subscript x] and high isoprene environments, we do not observe any dependence of model success for HO[subscript 2] on isoprene and attribute this to efficient recycling of HO[subscript x] through RO[subscript 2] + NO reactions under the moderate NO[subscript x] concentrations (5–300 ppt NO in the boundary layer, median 76 ppt) encountered during AMMA. This suggests that some of the problems with understanding the impact of isoprene on atmospheric composition may be limited to the extreme low range of NO[subscript x] concentrations