Orientation Distribution Function

We discuss methods to map crystallographic textures in crystal plasticity finite element simulations. Fourier-type series expansion methods which use spherical harmonic library functions as well as the direct pole figure inversion methods are not well suited to reproduce texture information in a sufficiently localized spherical form onto finite element grids. Mathematically compact Gauss-shaped spherical texture components represent a better approach for including textures in finite element models since they represent an excellent compromise between discreteness (spherical localization), compactness (simple functions), mathematical precision (very good approximation also of complex orientation distribution functions already with small sets of texture components), scalability (the number of used texture components can be systematically varied according to the desired exactness of the texture fit), conceptual simplicity (simple mathematical handling), and physical significance (texture components can be directly linked to characteristic metallurgical mechanisms). The use of texture component functions has also advantages over the use of large sets of discrete single orientations with equal scatter and height since they are more compact, practical, and provide better physical insight into microstructural mechanisms and composition sensitive effects. The article presents a new approach for the mathematical reproduction of such crystallographic texture components in crystal plasticity finite element simulations. It explains in some detail why they are particularly suited for this purpose and how they can be used to map and recover textures in/from plasticity simulations.

Short glass fiber Type E was coated with electrically conducting polyaniline (PAn) by in situ chemical polymerization. The resulting PAn coated glass fiber, with surface conductivity of 3.3 × 10−1 S/cm, was melt-compounded with isotactic polypropylene (iPP). Polypropylene grafted with maleic anhydride was investigated as an adhesion promoter for these composites. Differential scanning calorimeter and polarized light microscopy indicates that the PAn coated glass fiber has a strong nucleating activity towards iPP. Scanning electron microscopy showed the improvement in the wetting and dispersion of the fibers when the adhesion promoter was added, although this also led to fiber encapsulation and lowering the electrical conductivity of the composites. The adhesion promoter greatly improved the Young's modulus of the composites, and a reaction between the maleic anhydride groups of the adhesion promoter and the PAn was proposed. Composites with an electrical conductivity greater than 10−9 S/cm were achieved using a 30 wt % of PAn coated glass fiber. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007

An anisotropic damage model for vascular tissue is presented here. The widely used strain energy function in the quasi incompressible framework is exploited on its decoupled form to, additively, take into account the volumetric and the deviatoric contributions. Since a well-established neo-Hooke law is used to model the deviatoric part of the isotropic ground substance, this work focus on the contribution of the fibers (collagen from now on) over the overall behavior of the material, which is assumed as the anisotropic contribution to the deviatoric part of the splitting. For this purpose, a micro-structurally or more precisely a micro-sphere-based approach was employed to model the contribution of the fibers. In order to deal with the distribution of the fibers, a von Mises orientation distribution function is incorporated. The mechanical (phenomenological) behavior of the micro-fibers is formulated with an exponential model. Moreover, a directional damage model is incorporated over the fiber contribution through a yet developed thermodynamic formulation, which is directly applied in the hyperelastic formulation of the micro-fibers to gather the softening of the tissue. The way or bridge from micro-structural contribution to the macroscopic response is carried out through a computational homogenization scheme involving a numerical integration over the surface of each micro-sphere. A fitting of material parameters (including damage parameters) are performed from uniaxial tension tests with a least-square-based iterative scheme which is able to reproduce the experimental curves. Moreover, the model is formulated in a finite element code where a homogeneous deformation in just an element was simulated to test the micro-response.

This paper reports on equal channel angular extrusion experiments (ECAE). The material is a laboratory-cast Al-4%Cu alloy, in the T4 condition. The die has two channels with 15 x 15 mm2 square section, intersecting at 120 o , and deformation was accomplished at room temperature and consisted of up to 5 passes with no rotation between passes. After deformation, all samples were subjected to hardness measurements and tensile tests. The several passes extrusion process has been simulated using Fine Element Methods (FEM). A finite element code specially developed to model large deformation processes, like the ones involved in forging, was used with tetrahedral elements and an elastic-viscoplastic material model. That kind of elements requires re-meshing in order to keep the coherence of the elements under high sustained deformation. The material model parameters were obtained from previous simple tensile mechanical tests. The simulation was used to assist in the selection of sample-cutt...

The time evolution of director orientation in the cell subject to the external magnetic field in the case of time-dependent boundary conditions is investigated. The case when one substrate has strong anchoring and at other substrate director anchoring is ...

We propose a deterministic and a probabilistic extension of classical diffusion tensor imaging (DTI) tractography algorithms based on a sharp fi ber orientation distribution function (ODF) reconstruction from Q-Ball Imaging (QBI). An importa nt contribution of the paper is the integration of some of the latest state-of-the-art high ang ular resolution diffusion imaging (HARDI) data processing methods to obtain accurate and convincing r esults of complex fiber bundles with crossing, fanning and branching configurations. First, we d evelop a new deconvolution sharpening transformation from diffusion ODF (dODF) to fiber ODF (fODF) . We show that this sharpening transformation improves angular resolution and fiber detec tion of QBI and thus greatly improves tractography results. The angular resolution of QBI is in fa ct improved by approximately 20 ◦ and the fODF is shown to behave very similarly of the fiber orienta tion density (FOD) estimated from the spherical deconvolution method o...

A number of non-parametrically represented High Angular Resolution Diffusion Imaging (HARDI) spherical diffusion functions have been proposed to infer more and more accurately the heterogeneous and complex tissue microarchitecture of the cerebral white-matter. These spherical functions overcome the limitation of Diffusion Tensor Imaging (DTI) at discerning crossing, merging and fanning axonal fiber bundle configurations inside a voxel. Tractography graphically reconstructs the axonal connectivity of the cerebral white-matter in vivo and non-invasively, by integrating along the direction indicated by the local geometry of the spherical diffusion functions. Tractography is acutely sensitive to the local geometry and its correct estimation. In this paper we first propose a polynomial approach for analytically bracketing and numerically refining with high precision all the maxima, or fiber directions, of any spherical diffusion function represented non-parametrically. This permits an ac...