An automated approach for three-dimensional quantification of fibrillar structures in optically cleared soft biological tissues

We present a novel approach allowing for a simple, fast and automated morphological analysis of three-dimensional image stacks (z-stacks) featuring fibrillar structures from optically cleared soft biological tissues. Five non-atherosclerotic tissue samples from human abdominal aortas were used to outline the multi-purpose methodology, applicable to various tissue types. It yields a three-dimensional orientational distribution of relative amplitudes, representing the original collagen fibre morphology, identifies regions of isotropy where no preferred fibre orientations are observed and determines structural parameters throughout anisotropic regions for the analysis and numerical modelling of biomechanical quantities such as stress and strain. Our method combines optical tissue clearing with second-harmonic generation imaging, Fourier-based image analysis and maximum-likelihood estimation for distribution fitting. With a new sample preparation method for arteries, we present, for the first time to our knowledge, a continuous three-dimensional distribution of collagen fibres throughout the entire thickness of the aortic wall, revealing novel structural and organizational insights into the three arterial layers.     

Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue

Brain tissue modelling has been an active area of research for years. Brain matter does not follow the constitutive relations for common materials and loads applied to the brain turn into stresses and strains depending on tissue local morphology. In this work, a hyperviscoelastic fibre-reinforced anisotropic law is used for computational brain injury prediction. Thanks to a fibre-reinforcement dispersion parameter, this formulation accounts for anisotropic features and heterogeneities of the tissue owing to different axon alignment. The novelty of the work is the correlation of the material mechanical anisotropy with fractional anisotropy (FA) from diffusion tensor images. Finite-element (FE) models are used to investigate the influence of the fibre distribution for different loading conditions. In the case of tensile–compressive loads, the comparison between experiments and simulations highlights the validity of the proposed FA–k correlation. Axon alignment affects the deformation predicted by FE models and, when the strain in the axonal direction is large with respect to the maximum principal strain, decreased maximum deformations are detected. It is concluded that the introduction of fibre dispersion information into the constitutive law of brain tissue affects the biofidelity of the simulations.     

Automated extraction of symmetric microstructure features in serial sectioning images

Serial sectioning methods continue to produce a wealth of image data for quantifying the three-dimensional nature of material microstructures. In this work, we discuss a computational methodology for automated detection and 3D characterization of dendrite cores from images taken from slices of a production turbine blade made of a heat-treated single crystal Ni-based superalloy. The dendrite core locations are detected using an automated segmentation technique that incorporates information over multiple length scales and exploits the four-fold symmetry of the dendrites when viewed down the 〈100〉 growth direction. Additional rules that take advantage of the continuity of the dendrites from slice to slice help to exclude segmentation artifacts and improve dendrite core segmentation. The significance of this technique is that it may be extended to include any symmetric features.     

Quantification of uncertainty modelling in stochastic analysis of FRP composites

The extensive use of FRP composite materials in a wide range of industries, and their inherent variability, has prompted many researchers to assess their performance from a probabilistic perspective. This paper attempts to quantify the uncertainty in FRP composites and to summarise the different stochastic modelling approaches suggested in the literature. Researchers have considered uncertainties starting at a constituent (fibre/matrix) level, at the ply level or at a coupon or component level. The constituent based approach could be further classified as a random variable based stochastic computational mechanics approach (whose usage is comparatively limited due to complex test data requirements and possible uncertainty propagation errors) and the more widely used morphology based random composite modelling which has been recommended for exploring local damage and failure characteristics. The ply level analysis using either stiffness/strength or fracture mechanics based models is suggested when the ply characteristics influence the composite properties significantly, or as a way to check the propagation of uncertainties across length scales. On the other hand, a coupon or component level based uncertainty modelling is suggested when global response characteristics govern the design objectives. Though relatively unexplored, appropriate cross-fertilisation between these approaches in a multi-scale modelling framework seems to be a promising avenue for stochastic analysis of composite structures. It is hoped that this review paper could facilitate and strengthen this process.     

Flax/polypropylene composites for lightened structures: Multiscale analysis of process and fibre parameters

The optimization of the processing method for poly-(propylene) (PP)/plant fibre composites compounding is a key point in the development of semi-structural parts, especially for automotive applications. The aim of this original and innovating work is to study, at different scales, the impact of extrusion equipment and fibre length on the composite's mechanical performances. Firstly, we studied the flax fibre morphology after compounding and injection as well as their individualization in injected specimens. Secondly, we focused on the effects they had on tensile properties. The impact of the processing tool was observed on fibre morphology and division; as well as the use of a BUSS system instead of a twin-screw extruder, which enhances the fibre individualization, however, the number of kneading areas should be reduced in order to preserve the reinforcement aspect ratio. We highlight the fact that the composite's mechanical performances are highly impacted by the fibre division and cell wall stiffness, as demonstrated by in-situ nanoindentation tests. Finally, the use of longer fibres is not a priority for the improvement of mechanical performances; it induces a more difficult fibre division and an increase in the compound viscosity, which could endanger the moulding process of the final part.     

The multi-load method of determining discrete system parameters in a loaded three dimensional photoelastic model

The determination of the secondary principal stress difference and their orientations for a discrete slice of thickness dz along a particular light path in a loaded three dimensional photoelastic model is discussed in this paper. It is well known that once the geometry of the loaded member and the geometry of loading on the member are fixed, the secondary principal stress directions at any particular point along any line of consideration remain constant. The secondary principal stress values will get multiplied by the factor through which the loading on the component is increased. This has been made use of in the present method and from the characteristic parameters obtained at the end of any light path for different loadings on the three dimensional model, the secondary principal stress difference and their orientations are obtained. The method proposed is a fully non-destructive method of testing and involves measurements only on a transmission polariscope.     

Automatic image analysis and morphology of fibre reinforced concrete

Automatic image analysis is an efficient tool to quantify the morphology of materials. Moreover, it can aid to understand their mechanical behaviour. Several applications of automatic methods are presented to investigate concrete reinforced by ribbon shaped amorphous cast iron fibres. Introducing ribbons into the plain matrix entrapped air voids. This affected the workability and, later on, the compressive strength of the fibre reinforced concrete (FRC). Both were improved by additions of superplasticizer in order to keep the water to cement ratio constant. The influence of the superplasticizer and fibre contents on the compactness of the FRC was characterized by the dimensional and the spatial distributions of the air voids. The orientations of fibres and microcracks were quantified by Fourier image transforms. Due to the casting procedure of the FRC, the fibres were located in “horizontal layers”, perpendicular to the casting axis. Whatever the direction of compression with respect to the layers of fibres, the microcrack network was getting more and more oriented in the direction of compression as stresses increased. The analysis of fibre and microcrack orientations suggests that, under uniaxial compression, the inelastic strain domain should be characterized by an anisotropic biaxial damage model, whose principal axes are the orthogonal and parallel directions to the layers of fibres.     

Constitutive modelling of arteries considering fibre recruitment and three-dimensional fibre distribution

Structurally motivated material models may provide increased insights into the underlying mechanics and physics of arteries under physiological loading conditions. We propose a multiscale model for arterial tissue capturing three different scales (i) a single collagen fibre; (ii) bundle of collagen fibres; and (iii) collagen network within the tissue. The waviness of collagen fibres is introduced by a probability density function for the recruitment stretch at which the fibre starts to bear load. The three-dimensional distribution of the collagen fibres is described by an orientation distribution function using the bivariate von Mises distribution, and fitted to experimental data. The strain energy for the tissue is decomposed additively into a part related to the matrix material and a part for the collagen fibres. Volume fractions account for the matrix/fibre constituents. The proposed model only uses two parameters namely a shear modulus of the matrix material and a (stiffness) parameter related to a single collagen fibre. A fit of the multiscale model to representative experimental data obtained from the individual layers of a human thoracic aorta shows that the proposed model is able to adequately capture the nonlinear and anisotropic behaviour of the aortic layers.     

改进的数字全息光弹方法理论研究

该文通过改变参考光偏振方向,对数字全息光弹法进行改进,从而可以高效、高精度的检测二维应力场.从理论上导出了该方法的实验原理：加载前后在对应的4 个不同参考光偏振位置拍摄数字全息图,对这4 对数字全息图进行傅里叶变换、滤波及反变换,可以获得4 个光强方程,数值求解这4 个光强方程,再结合应力-光学定律就可以精确获得二维应力场的2 个主应力值和主应力方向.与传统的数字全息光弹法相比,新方法具有以下优点：不需要分离等差线与等倾线条纹;不需要确定条纹级数;方法简单,不需要已有技术以外的实验装置或实验模型.     

An optical channel modeling of a single mode fiber

The evaluation of the optical channel model that accurately describes the single mode fibre as a coherent transmission medium is reviewed through analytical, numerical and experimental analysis. We used the numerical modelling of the optical transmission medium and experimental measurements to determine the polarization drift as a function of time for a fixed length of fibre. The probability distribution of the birefringence vector was derived, which is associated to the ‘Poole’ equation. The theory and experimental evidence that has been disclosed in the literature in the context of polarization mode dispersion – Stokes & Jones formulations and solutions for key statistics by integration of stochastic differential equations has been investigated. Besides in-depth definition of the single-mode fibre-optic channel, the modelling which concerns an ensemble of fibres each with a different instance of environmental perturbation has been analysed.     

Microstructural characterisation of 3D printed and injection-moulded glass fibre-reinforced polypropylene by image analysis,simulation and experimental methods

The mechanical properties of fibre-reinforced thermoplastics and their dependencies on the manufacturing process, fibre properties, fibre concentration and strain rate have been researched intensively for years in order to predict their macroscopic behaviour by numerical simulations as precisely as possible. Including the microstructure in both real and virtual experiments has improved prediction precision for injection-moulded glass fibre-reinforced thermoplastics significantly. In this work, we apply three established methods for characterisation and modelling to an injection-moulded and to a 3D printed material. The geometric properties of the fibre component as fibre orientation, fibre length and fibre diameter distributions are identified by analysing reconstructed tomographic images. For comparing the fibre lengths, a recently suggested new method is applied. Based on segmentations of the tomographic images, we calculate the elastic stiffness of both composites numerically on the microscale. Finally, the mechanical behaviour of both materials is experimentally characterised by micro tensile tests. The simulation results agree well with the measured stiffness in case of the injection-moulded material. However, for the 3D printed material, measurement and simulation differ strongly. The prediction from the simulation agrees with the values expected from the image analytic findings on the microstructure. Therefore, the differences in the measured behaviour have to be contributed to the matrix material. This proves demand for further research for 3D printed materials for predictable prototypes, preproduction series and possible serial application.     

Deformation micromechanisms of collagen fibrils under uniaxial tension

Collagen, an essential building block of connective tissues, possesses useful mechanical properties due to its hierarchical structure. However, little is known about the mechanical properties of collagen fibril, an intermediate structure between the collagen molecule and connective tissue. Here, we report the results of systematic molecular dynamics simulations to probe the mechanical response of initially unflawed finite size collagen fibrils subjected to uniaxial tension. The observed deformation mechanisms, associated with rupture and sliding of tropocollagen molecules, are strongly influenced by fibril length, width and cross-linking density. Fibrils containing more than approximately 10 molecules along their length and across their width behave as representative volume elements and exhibit brittle fracture. Shorter fibrils experience a more graceful ductile-like failure. An analytical model is constructed and the results of the molecular modelling are used to find curve-fitted expressions for yield stress, yield strain and fracture strain as functions of fibril structural parameters. Our results for the first time elucidate the size dependence of mechanical failure properties of collagen fibrils. The associated molecular deformation mechanisms allow the full power of traditional material and structural engineering theory to be applied to our understanding of the normal and pathological mechanical behaviours of collagenous tissues under load.     

The thermal conductivity of Kevlar fibre-reinforced composites

The thermal conductivities of a series of blocks consisting of Shell DX210/BF₃400 resin reinforced with Kevlar 49 fibre are reported in the approximate temperature range 180–270 K. The results are used to calculate the thermal conductivities of the fibres in directions parallel and perpendicular to their length. Varying the angle between the principal fibre directions of bidirectional laminates produced in-plane results that varied in a manner which was quantitatively consistent with expectation. The out-of-plane results proved to be independent of fibre orientation, as expected. In-plane and out-of-plane results for a Kevlar 49 fabric reinforced laminate proved to be essentially similar to results for a laminate reinforced with unwoven fibres of the same type, arranged in a 90° cross-plied disposition at the same fibre volume density.     

Investigation of cladding effects on optical guidance of microstructured holey fibres based on FDM and FDTD methods

Effects of the hexagonal air-hole cladding layer of a microstructured holey fibre on propagation characteristics are investigated based on the two-dimensional (2D) finite difference method and the 2D finite-difference time-domain technique. A holey fibre with parameters of r = 0.6 µm and Λ = 2.0 µm is designed and analyzed numerically by changing the number of hexagonal cladding layers. It is found that the layers beyond which fields become sufficiently small in the transverse plane (air-hole layers out of the fifth hexagonal cladding layer in the designed holey fibre) have little influence on propagation characteristics around the wavelength range of 1.3 and 1.55 µm for general optical communications, which means the air-hole layers close to the core region play an important role on its performance. Chromatic dispersion of the holey fibre with five cladding layers of air holes is approaching zero around 0.9 µm wavelength.     

Psuedo-affine behaviour of collagen fibres during the uniaxial deformation of leather

Chromium tanned bovine leather has been dried under uniaxial strain and its collagen fibre distribution examined using high-angle X-ray diffraction. Microstructural modelling of the fibre kinematics showed that under large-strain deformation (30%) the fibres behave in a psuedo-affine manner. At decreasingly lower strains the fibre re-orientation is seen to progressively deviate from the pseudo-affine prediction; an observation which can be understood in terms of a combination of fibre-fibre adhesion and changes in fibre substructure. The material was also subjected to mechanical testing and tensile data is presented here which indicates how fibre orientation affects tensile modulus. This work represents the first quantitative microstructural model for collagen fibre distribution in strained leather.