Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model

In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic–plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described. In order to significantly reduce the computing time, a new method drawn from viscoplastic formulations is introduced so that the slip system activity can be efficiently determined. The different aspects of the single crystal hardening (self and latent hardening, dislocation storage and annihilation, mean free path, etc.) are taken into account both by the introduction of dislocation densities per slip system as internal variables and the corresponding evolution equations. Comparisons are made with experimental results for single and dual-phase steels involving linear and complex loading paths. Rice’s criterion is then coupled and applied to this constitutive model in order to determine the ellipticity loss of the polycrystalline tangent modulus. This criterion, which does not need any additional “fitting” parameter, is used to build Ellipticity Limit Diagrams (ELDs).ArcelorMittal Researc

Morphological segmentation analysis and texture-based support vector machines classification on mice liver fibrosis microscopic images

Background To reduce the intensity of the work of doctors, pre-classification work needs to be issued. In this paper, a novel and related liver microscopic image classification analysis method is proposed. Objective For quantitative analysis, segmentation is carried out to extract the quantitative information of special organisms in the image for further diagnosis, lesion localization, learning and treating anatomical abnormalities and computer-guided surgery. Methods in the current work, entropy based features of microscopic fibrosis mice’ liver images were analyzed using fuzzy c-cluster, k-means and watershed algorithms based on distance transformations and gradient. A morphological segmentation based on a local threshold was deployed to determine the fibrosis areas of images. Results the segmented target region using the proposed method achieved high effective microscopy fibrosis images segmenting of mice liver in terms of the running time, dice ratio and precision. The image classification experiments were conducted using Gray Level Co-occurrence Matrix (GLCM). The best classification model derived from the established characteristics was GLCM which performed the highest accuracy of classification using a developed Support Vector Machine (SVM). The training model using 11 features was found to be as accurate when only trained by 8 GLCMs. Conclusion The research illustrated the proposed method is a new feasible research approach for microscopy mice liver image segmentation and classification using intelligent image analysis techniques. It is also reported that the average computational time of the proposed approach was only 2.335 seconds, which outperformed other segmentation algorithms with 0.8125 dice ratio and 0.5253 precision

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Curvature-driven PDE methods for matrix-valued images

Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edgelike structures in tensor fields, we first generalise Di Zenzo\u27s concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts

Microstructure modeling and crystal plasticity parameter identification for predicting the cyclic mechanical behavior of polycrystalline metals

Computational homogenization permits to capture the influence of the microstructure on the cyclic mechanical behavior of polycrystalline metals. In this work we investigate methods to compute Laguerre tessellations as computational cells of polycrystalline microstructures, propose a new method to assign crystallographic orientations to the Laguerre cells and use Bayesian optimization to find suitable parameters for the underlying micromechanical model from macroscopic experiments

Phase-field modeling of equilibrium precipitate shapes under the influence of coherency stresses

Coherency misfit stresses and their related anisotropies are known to influence the equilibrium shapes of precipitates. Additionally, mechanical properties of the alloys are also dependent on the shapes of the precipitates. Therefore, in order to investigate the mechanical response of a material which undergoes precipitation during heat treatment, it is important to derive the range of precipitate shapes that evolve. In this regard, several studies have been conducted in the past using sharp interface approaches where the influence of elastic energy anisotropy on the precipitate shapes has been investigated. In this paper, we propose a diffuse interface approach which allows us to minimize grid-anisotropy related issues applicable in sharp-interface methods. In this context, we introduce a novel phase-field method where we minimize the functional consisting of the elastic and surface energy contributions while preserving the precipitate volume. Using this method we reproduce the shape-bifurcation diagrams for the cases of pure dilatational misfit that have been studied previously using sharp interface methods and then extend them to include interfacial energy anisotropy with different anisotropy strengths which has not been a part of previous sharp-interface models. While we restrict ourselves to cubic anisotropies in both elastic and interfacial energies in this study, the model is generic enough to handle any combination of anisotropies in both the bulk and interfacial terms. Further, we have examined the influence of asymmetry in dilatational misfit strains along with interfacial energy anisotropy on precipitate morphologies

Macro-permeability distribution and anisotropy in a 3D fissured and fractured clay rock: ‘Excavation Damaged Zone’ around a cylindrical drift in Callovo-Oxfordian Argilite (Bure)

The Underground Research Laboratory at Bure (CMHM), operated by ANDRA, the French National Radioactive Waste Management Agency, was developed for studying the disposal of radioactive waste in a deep clayey geologic repository. It comprises a network of underground galleries in a 130 m thick layer of Callovo Oxfordian clay rock (depths 400–600 m). This work focuses on hydraulic homogenization (permeability upscaling) of the Excavation Damaged Zone (EDZ) around a cylindrical drift, taking into account: (1) the permeability of the intact porous rock matrix; (2) the geometric structure of micro-fissures and small fractures synthesized as a statistical set of planar discs; (3) the curved shapes of large ‘chevron’ fractures induced by excavation (periodically distributed). The method used for hydraulic homogenization (upscaling) of the 3D porous and fractured rock is based on a ‘frozen gradient’ superposition of individual fluxes pertaining to each fracture/matrix block, or ‘unit block’. Each unit block comprises a prismatic block of permeable matrix (intact rock) obeying Darcy’s law, crossed by a single piece of planar fracture obeying either Darcy or Poiseuille law. Polygonal as well as disc shaped fractures are accommodated. The result of upscaling is a tensorial Darcy law, with macro-permeability Kij(x) distributed over a grid of upscaling sub-domains, or ‘voxels’. Alternatively, Kij(x) can be calculated point-wise using a moving window, e.g., for obtaining permeability profiles along ‘numerical’ boreholes. Because the permeable matrix is taken into account, the upscaling procedure can be implemented sequentially, as we do here: first, we embed the statistical fissures in the matrix, and secondly, we embed the large curved chevron fractures. The results of hydraulic upscaling are expressed first in terms of ‘equivalent’ macro-permeability tensors, Kij(x,y,z) distributed around the drift. The statistically isotropic fissures are considered, first, without chevron fractures. There are 10,000 randomly isotropic fissures distributed over a 20 m stretch of drift. The resulting spatially distributed K ij tensor is nearly isotropic (as expected). At the scale of the whole EDZ, the global K FISSURES is roughly 5000 times larger than permeability matrix KM. The detailed distribution of the equivalent K FISSURES (x, y, z) defined on a grid of voxels is radially inhomogeneous, like the statistics of the disc fissures. In addition, a moving window procedure is used to compute detailed radial profiles of K FISSURES versus distance (r) to drift wall, and the results compare favorably with in situ permeability profiles (numerical vs. experimental boreholes at Bure’s GMR drift). Finally, including the large curved chevron fractures in addition to the random fissures, the resulting K ij (x, y, z) appears strongly anisotropic locally. Its principal directions are spatially variable, and they tend to be aligned with the tangent planes of the chevron fracture surfaces. The global equivalent Kij of the whole EDZ is also obtained: it is only weakly anisotropic, much less so than the local Kij’s. However, because of the radially divergent structure of the ‘chevrons’ (although not quite cylindrical in geometry), it is recognized that the global Kij due to chevrons lacks physical meaning as a tensor. Considering only the magnitude, it is found that the permeability due to ‘chevrons’ (K CHEVRONS ) is about 4 orders of magnitude larger than that due to statistical fissures (K FISSURES ), assuming a hydraulic aperture a CHEVRON = 100 microns. By a simple argument, K CHEVRONS would be only one order of magnitude larger than K FISSURES with the choice a CHEVRON = 10 microns instead of 100 microns. This significant sensitivity is due to several factors: the large extent of chevron fractures, the assumption of constant hydraulic aperture, and the cubic law behavior based on the assumption of Poiseuille flow. The equivalent macro-permeabilities obtained in this work can be used for large scale flow modeling using any simulation code that accommodates Darcy’s law with a full, spatially variable permeability tensor Kij(x)

A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse

We propose a multiscale mechanobiological model of bone remodelling to investigate the site-specific evolution of bone volume fraction across the midshaft of a femur. The model includes hormonal regulation and biochemical coupling of bone cell populations, the influence of the microstructure on bone turnover rate, and mechanical adaptation of the tissue. Both microscopic and tissue-scale stress/strain states of the tissue are calculated from macroscopic loads by a combination of beam theory and micromechanical homogenisation. This model is applied to simulate the spatio-temporal evolution of a human midshaft femur scan subjected to two deregulating circumstances: (i) osteoporosis and (ii) mechanical disuse. Both simulated deregulations led to endocortical bone loss, cortical wall thinning and expansion of the medullary cavity, in accordance with experimental findings. Our model suggests that these observations are attributable to a large extent to the influence of the microstructure on bone turnover rate. Mechanical adaptation is found to help preserve intracortical bone matrix near the periosteum. Moreover, it leads to non-uniform cortical wall thickness due to the asymmetry of macroscopic loads introduced by the bending moment. The effect of mechanical adaptation near the endosteum can be greatly affected by whether the mechanical stimulus includes stress concentration effects or not.Comment: 25 pages, 10 figure

Elastic cavitation, tube hollowing, and differential growth in plants and biological tissues

Elastic cavitation is a well-known physical process by which elastic materials under stress can open cavities. Usually, cavitation is induced by applied loads on the elastic body. However, growing materials may generate stresses in the absence of applied loads and could induce cavity opening. Here, we demonstrate the possibility of spontaneous growth-induced cavitation in elastic materials and consider the implications of this phenomenon to biological tissues and in particular to the problem of schizogenous aerenchyma formation