Elastic Maps Research Articles

Nonlinearly elastic maps: Energy minimizing configurations of membranes on prescribed surfaces

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in R 3 \mathbb {R}^3 . This is a physically correct model of the analogy sometimes given to motivate harmonic maps between manifolds. The proposed energy density function is convex in the strain pair comprising the deformation gradient and the local area ratio. If the target surface is a plane, the problem reduces to 2-dimensional, polyconvex nonlinear elasticity addressed by J. M. Ball. On the other hand, the energy density is not rank-one convex for unconstrained deformations into R 3 \mathbb {R}^3 . We show that the problem admits an energy-minimizing configuration when constrained to lie on the given surface. For a class of Dirichlet problems, we demonstrate that the minimizing deformation is a homeomorphism onto its image on the given surface and establish the weak Eulerian form of the equilibrium equations.

A Reformulation of the Browaeys and Chevrot Decomposition of Elastic Maps

An elastic map T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} associates stress with strain in some material. A symmetry of T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} is a rotation of the material that leaves T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} unchanged, and the symmetry group of T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} consists of all such rotations. The symmetry class of T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} describes the symmetry group but without the orientation information. With an eye toward geophysical applications, Browaeys & Chevrot developed a theory which, for any elastic map T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} and for each of six symmetry classes Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Sigma $\\end{document}, computes the “Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Sigma $\\end{document}-percentage” of T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document}. The theory also finds a “hexagonal approximation”—an approximation to T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} whose symmetry class is at least transverse isotropic. We reexamine their theory and recommend that the Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Sigma $\\end{document}-percentages be abandoned. We also recommend that the hexagonal approximations to T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document} be replaced with the closest transverse isotropic maps to T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{T}$\\end{document}.

Low-frequency air-coupled transducer based damage detection in composite materials

In this paper results of simulations of non-contact elastic wave generation in the composite panel based on acoustic to elastic wave transformation are presented. For this purpose simulations of acoustic wave generation and processing are based on the FEM method in COMSOL. Elastic wave generation and propagation are based on the spectral element method (SEM) in the time domain. The SEM model utilises time-varying acoustic pressure distributions calculated in the FEM. The SEM allows to simulate the interactions of elastic waves with the delamination. Damage localization is based on RMS elastic wave energy maps. In this research a panel made of carbon fibre-reinforced polymer composite is investigated. Research related to low-frequency air-coupled transducer (ACT) is presented. The utilisation of low-frequency waves allows for the reduction of the effects of the wave attenuation in composite material. The proposed combination of FEM and SEM gives an efficient tool for the simulation of non-contact wave generation for non-destructive testing analysis.

Processing and analysis of scanning microscopy images in an experiment withimplants

The study is devoted to improving the computational methodology for assessing the parameters of the tissue regeneration process using mesh nickelidetitanium implants with shape memory in an experiment. Processing and analysis of observational data from electron microscopy and classical histological examination were performed using proprietary algorithms and their modifications, which significantly simplify the data analysis procedure and increase the accuracy of estimates (15-20%).The proposed method as a computational tool for analyzing the dynamics of the processunder study as well as for highlighting the internal geometric features of experimentalimages of objects of interest contains shearlet transformation algorithms as well as algorithms for constructing elastic maps for effective visualization of spatial data. Important aspects of the methodology are computational tools for preprocessing visual data to increase the contrast and brightness of analyzed images based on Retinextechnology which significantly affects the quality of the use of computer evaluation tools.

The Analysis of Pile Skin and Base Resistances Interaction Based on Static Pile Load Test in Experimental Research

Abstract Static pile load tests in laboratory conditions were carried out to study the mechanism of the pile skin and pile base resistance mobilization with settlement and their interactions. The mechanism of the skin resistance at the base is important in the correct interpretation of the pile capacity. Especially in the case of piles shallowly embedded in the bearing layer. In the studies described in this article, high-precision piezoelectric elastic stress maps were used. The tests were carried out on piles with a diameter of 2.5–2.8 cm, and length of 40 cm. Static pile load tests were carried out to measure resistance at the pile base, settlement and change of stress in the soil at the level of the pile base or beneath the pile base were measured. The analysis of stress in soil allowed to investigate the interaction between the resistances of the pile base and skin. The state of stress in the soil close to the pile base, both beneath and above the pile base level was heavily influenced by the simultaneous mobilization of skin and base resistance.

Nanomechanical Characterization of Bone Quality Depending on Tissue Age via Bimodal Atomic Force Microscopy

Characterization of bone quality during the healing process is crucial for successful implantation procedures and patient comfort. In this study, a bone implant specimen that underwent a 4-week healing period was investigated. Bimodal atomic force microscopy (AFM) was employed to simultaneously obtain the morphology and elastic modulus maps of the newly formed and pre-existing bone regions within the sample. Results indicate that the new bone matrix possessed lower mineralization levels and presented larger, uneven mineral grains, exhibiting the attributes of a woven bone. On the other hand, the old bone matrix exhibited a more uniform and mineralized structure, which is characteristic of lamellar bones. The new bone had a lower overall elastic modulus than the old bone. Bimodal AFM further confirmed that the new bone displayed three regions comprising unmineralized, partially mineralized, and fully matured sections, which indicate a turbulent change in its composition. Meanwhile, the old bone exhibited two sections comprising partially mineralized and matured bone parts, which denote the final phase of mineralization. This study provides valuable insights into the morphological and nanomechanical differences between the old and new bone matrixes and presents a novel approach to investigate bone quality at different phases of the bone-healing process.

Microstructural and mechanical properties at the submicrometric length scale under service-like working conditions on ground WC-Co grades

The unique combination of hardness, toughness, and wear resistance exhibited by heterogeneous hard materials, particularly cemented carbides (WC-Co), has made them preeminent material choices for extremely demanding applications, such as metal cutting/forming tools. The grinding post-processing of WC-Co induces changes in their surface integrity by modifying both constitutive phases through cracking the WC ceramic phase, introducing compressive residual stresses and/or inducing phase transformations (from face-centered cubic to hexagonal compact phase) in the metallic Co binder. A systematic micro- and nanomechanical study of different ground WC-Co grades (with distinct metallic Co binder content and WC particle size) is presented. In general, three different aspects are investigated: (1) assessment of the intrinsic hardness of the deformed layer from room temperature up to 600 °C, (2) correlation of the compressive residual stresses with hardness and elastic modulus maps by using high-speed indentation tests, and (3) evaluation of the oxidation process as a function of the testing temperature for the different ground WC-Co grades. It was found that the mechanical properties of the deformed ground layer for the different WC-Co grades slightly decrease at temperatures ranging between 400 and 500 °C, being this temperature non depending on the amount of metallic binder or WC grain size. This is attributed to different effects which take place simultaneously when the testing temperature increases: dislocation motion, reduction of compressive residual stresses and particularly, the generation of a heterogeneous oxide layer formed of CoWO4, WO3 and Co3O4.

Estimation of stresses in a massive granite using laser ultra-sonic testing and stress memory effect

This paper addresses in-situ stress-estimation methods based on the Kaiser effect. The physical and mechanical properties of granite, diorite, and granodiorite samples selected at different depth intervals of the core obtained from a wellbore were examined. The ultimate uniaxial compressive strength, modulus of elasticity, and Poisson’s ratio of the rock samples were determined using presses and strain gauges. Also, local longitudinal and shear wave velocities were measured using a high-accuracy laser-ultrasonic system with a view to assessing the structure of the samples. Based on the resulting elastic wave velocity maps, samples with no obvious discontinuities were chosen. These undisturbed samples were subjected to uniaxial compression and their acoustic emission was simultaneously measured. In-situ stresses were estimated from the results of the interpretation of acoustic emission measurements. The experimental in-situ stresses were compared with the results of a numerical simulation. The ratio of the estimated in-situ stresses to the calculated ones is within the range from 0.81 to 1.11. This means that the laser ultrasonic and acoustic emission methods make it possible to effectively estimate in-situ stresses in a rock mass and assess the degree of rock mass damage.

Evaluation, Comparison and Monitoring of Multiparameter Systems by Unified Graphic Visualization of Activity Method on the Example of Learning Process

The article discusses the problem of visualization of complex multiparameter systems, defined by datasets on their structure, functional structure, and activity in the form of complex graphs and transition of traditional representation of the data acquired by graph mining to a compact image built by pictographic methods. In these situations, we propose using the Unified Graphic Visualization of Activity (UGVA) method for data concentration and structuring. The UGVA method allows coding in an anthropomorphic image of elements of graphs with data on structural and functional features of systems and overlaying these images with the data on the system’s activity using coloring and artifacts. The image can be composed in different ways: it can include the zone of integral evaluation parameters, segmented data axes of five types, and four types of symmetry. We describe the method of creating UGVA images, which consists of 13 stages: the parametric model is represented as a structural image that is converted to a basic image that is then detailed into the particular image by defining geometric parameters of the primitives and to the individualized image with the data about a particular object. We show how the individualized image can be overlaid with the operative data as color coding and artifacts and describe the principles of interpreting UGVA images. This allows solving tasks of evaluation, comparison, and monitoring of complex multiparameter systems by showing the decision-maker an anthropomorphic image instead of the graph. We describe a case study of using the UGVA method for visualization of data about an educational process: curricula and graduate students, including the data mined from the university’s learning management system at the Siberian Federal University for students majoring in “informatics and computing”. The case study demonstrates all stages of image synthesis and examples of their interpretation for situation assessment, monitoring, and comparison of students and curricula. It allowed for finding problematic moments in learning for individual students and their entire group by analyzing the development of their competence profiles and formulating recommendations for further learning. The effectiveness of the resulting images is compared to the other approaches: elastic maps and Chernoff faces. We discuss using graph mining to generate learning problems in order to lessen the workload of gathering raw data for the UGVA method and provide general recommendations for using the UGVA method based on our experience of supporting decision making.

Characterisation of the crack tip plastic zone in fatigue via synchrotron X‐ray diffraction

AbstractThis paper describes a new methodology for characterising the plastic zone ahead of a fatigue crack. This methodology is applied to a set of experimental data obtained by synchrotron X‐ray diffraction on a bainitic steel compact tension specimen. The methodology is based on generating the equivalent Von Mises strain field from the X‐ray experimental elastic strain maps. Based on the material response, a threshold is then applied on the equivalent strain maps to identify the size and shape of the plastic zone. The experimental plastic zone lies between the plane strain and plane stress Westergaard's bounds but closer to the plane strain theoretical prediction confirming that the volume analyzed is predominantly subjected to plane strain conditions. However, the observed plastic zone has a somewhat flatter shape, extending further from the crack plane but less extended in the crack growing direction.

Surface integrity of new dry-electropolishing technology on WC-Co cemented carbides

This study is focused on WC-Co dry-electropolished by DryLyte® technology that allows to obtain corrosion-free surfaces with a roughness below 9 nm. The main goal behind this research is to investigate the surface integrity trying to correlate the remanent microstructure after different dry-electropolishing times as a function of the hardness and elastic modulus evolution though massive nanoindentation. The quality of the surface has been evaluated by using advanced characterization techniques and the mechanical response treated by using the statistical methodology proposed by Ulm and Constantinides. To sum up, a close correlation is observed between the residual microstructure and the surface integrity in terms of hardness and elastic modulus maps.

The studies on the tribological performance, characterization and mechanical properties of W-2Ni-1Fe (wt%) alloy

Friction, wear and mechanical properties of the liquid phase sintered W-2Ni-1Fe (wt%) alloy were investigated. Tribological tests were carried out at different loads, frequencies and sliding distances under reciprocative sliding condition, against tungsten carbide (WC-Co) counter body. Co-efficient of friction (COF), wear volume and specific wear rate were determined. The dominant operative wear mechanisms were identified in different testing conditions. Abrasive wear and tribo-chemical wear mechanisms were found to be the dominant wear mechanisms. Room temperature strain rate sensitivity was determined by conducting jump test in tensile mode. The alloy showed low strain rate sensitivity with significant strain hardening. High resolution nanoindention mapping was carried out to establish structure property correlations at the micro-meter length scale. The hardness and elastic modulus maps were generated to determine the hardness and elastic modulus of the constituent phases of W and of γ-Ni matrix. The maps were found to correlate well with the actual microstructure obtained from opticaland electron microscopy.

Environmental aspects of the integrated development of forest ecosystems: zoning and visualization of multidimensional data

The research is devoted to the development of information and methodological support for assessing the interaction of objects and the degree of impact on the environment within the framework of the concept of sustainable development in relation to enterprises of forest ecosystems. As a computational toolkit of the zoning technique the work uses adapted clustering and visualization methods in the form of constructing a set of Voronoi and elastic maps. The key point in the research is the choice of indicators that take into account the most important features of the process under study. Purpose of the study: revealing hidden patterns in multidimensional data on processes and phenomena that are difficult to formalize. The stages of the proposed computational technique for zoning objects of interest are given on model examples for processing and visualizing the distribution of the selected indicators

Characterizing the nanomechanical properties of microcomedones after treatment with sodium salicylate ex vivo using atomic force microscopy.

The treatment of acne presents a major clinical and dermatological challenge. Investigating the nanomechanical properties of the microcomedone precursor lesions using atomic force microscopy (AFM) may prove beneficial in understanding their softening, dissolution and prevention. Although the exact biochemical mechanism of NaSal on microcomedones is not fully understood at present, it appears to exhibit a significant exfoliation effect on the skin via corneodesmosome dissolution. Therefore, to support this exploration, sodium salicylate (NaSal), a common ingredient employed in skin care products, is applied ex vivo to microcomedones,collected by nose strip adhesive tape, and their nanomechanical properties are assessed using AFM. Although the exact biochemical mechanism of NaSal on microcomedones is not fully understood at present, it appears to exhibit a significant exfoliation effect on the skin via corneodesmosome dissolution. Herein, our findings demonstrate that when microcomedones are treated with 2% NaSal, samples appeared significantly more compliant ('softer') ((1.3±0.62) MPa) when compared to their pre-treated measurements ((7.2±3.6) MPa; p=0.038). Furthermore, elastic modulus maps showed that after 2% NaSal treatment, areas in the microcomedone appeared softer and swollen in some, but not in all areas, further proving the valuable impact of 2% NaSal solution in altering the biomechanical properties and morphologies in microcomedones. Our results are the first of their kind to provide qualitative and quantitative mechanobiological evidence that 2% NaSal decreases the elastic modulus of microcomedones. Therefore, this study provides evidence that NaSal can be beneficial as an active ingredient in topical treatments aimed at targeting microcomedones.

Elastic symmetry with beachball pictures

SUMMARY The elastic map, or generalized Hooke’s Law, associates stress with strain in an elastic material. A symmetry of the elastic map is a reorientation of the material that does not change the map. We treat the topic of elastic symmetry conceptually and pictorially. The elastic map is assumed to be linear, and we study it using standard notions from linear algebra—not tensor algebra. We depict strain and stress using the ‘beachballs’ familiar to seismologists. The elastic map, whose inputs and outputs are strains and stresses, is in turn depicted using beachballs. We are able to infer the symmetries for most elastic maps, sometimes just by inspection of their beachball depictions. Many of our results will be familiar, but our versions are simpler and more transparent than their counterparts in the literature.

Nanomechanical properties of potato flakes using atomic force microscopy

Characterizing the nanomechanical properties of plants at the sub-cellular level is important in understanding the dynamic processes underpinning both potato plant growth and downstream effects of industrial food processing. Here, we measured nanomechanical properties and mapped the elastic properties of two types of industrial potato flakes that provide both optimal and sub-optimal results during food manufacturing by employing both amplitude-modulation and force-modulation atomic force microscopy (AFM) in air. The amplitude-modulation AFM revealed that sub-optimal potato flakes were more compliant when compared to the optimal samples. Furthermore, the elastic modulus maps demonstrated optimal potato samples to be significantly stiffer than the sub-optimal samples. Therefore, our results provide evidence that probing the elastic properties of potato flakes can be a first step in providing food industries with a quantitative differential assessment between optimal and sub-optimal samples.

VISUAL ANALYSIS OF TEXT DATA COLLECTIONS BY FREQUENCIES OF JOINT USE OF WORDS

Abstract. The presented research considers the problems of studying the cluster structure of multidimensional data volumes. This paper presents the results of numerical experiments on the study of data volumes consisting of frequencies of joint use of words from different parts of speech, for instance “noun + verb” or “adjective + noun”. The volumes of data are obtained from samples from text collections in Russian. The aim of the research is to analyze the cluster structure of the studied volume and semantic proximity of words in clusters and subclusters. The hypothesis was used that words with similar meaning should occur in approximately the same context. In this regard, in the space of features, they will be at a relatively close distance from each other, while differing words will be at a more distant distance from each other. Research is carried out using elastic maps, which are effective tools for visual analysis of multidimensional data. The construction of elastic maps and their extensions in the space of the first three principal components makes it possible to determine the cluster structure of the studied multidimensional data volumes. Such analysis can be useful in the tasks of confronting negative verbal influences such as fake news, hidden propaganda, involvement in sects, verbal manipulation, etc. Also this approach can be applied to text collections having medical origin.

Visual ization of multi-dimensional data applied to the problems of interac tion of objects of the business-ecosystem

The study is devoted to the development of information and methodological support in relation to expert assessment of the interaction and mutual influence of objects of the business ecosystem taking into account their spatial location. As a computational toolkit the work uses adapted methods of clustering and visualization in the form of constructing a set of Voronoi and elastic maps. The purpose of the study is to identify hidden patterns in multidimensional data in relation to the studied complex processes. The article was prepared within the framework of the Grant of the RFBR and the Government of the Krasnoyarsk Territory No. 20-410-242916 / 20 r_mk Krasnoyarsk.

Visual Analysis of Textual Information on the Frequencies of Joint Use of Nouns and Adjectives

This paper presents the results of numerical experiments on the study of data volumes consisting of frequencies of joint use of adjectives and nouns. The volumes of data were obtained from samples from text collections in Rus-sian. The aim of the research is to analyze the cluster structure of the studied volume and semantic proximity of words in clusters and subclusters. The hypothesis was used that words with similar meaning should occur in approximately the same context. In this regard, in the space of features, they will be at a relatively close distance from each other, while differing words will be at a more distant distance from each other. Research is carried out using elastic maps, which are effective tools for visual analysis of multidimensional data. The construction of elastic maps and their extensions in the space of the first three principal components makes it possible to determine the cluster structure of the studied multidimensional data volumes. The analysis of the cluster structure for the considered volume of multidimensional data is carried out. The influence of transposition of the initial data array is considered.

Repeatability of Linear and Nonlinear Elastic Modulus Maps From Repeat Scans in the Breast.

Compression elastography allows the precise measurement of large deformations of soft tissue in vivo. From an image sequence showing tissue undergoing large deformation, an inverse problem for both the linear and nonlinear elastic moduli distributions can be solved. As part of a larger clinical study to evaluate nonlinear elastic modulus maps (NEMs) in breast cancer, we evaluate the repeatability of linear and nonlinear modulus maps from repeat measurements. Within the cohort of subjects scanned to date, 20 had repeat scans. These repeated scans were processed to evaluate NEM repeatability. In vivo data were acquired by a custom-built, digitally controlled, uniaxial compression device with force feedback from the pressure-plate. RF-data were acquired using plane-wave imaging, at a frame-rate of 200 Hz, with a ramp-and-hold compressive force of 8N, applied at 8N/sec. A 2D block-matching algorithm was used to obtain sample-level displacement fields which were then tracked at subsample resolution using 2D cross correlation. Linear and nonlinear elasticity parameters in a modified Veronda-Westmann model of tissue elasticity were estimated using an iterative optimization method. For the repeated scans, B-mode images, strain images, and linear and nonlinear elastic modulus maps are measured and compared. Results indicate that when images are acquired in the same region of tissue and sufficiently high strain is used to recover nonlinearity parameters, then the reconstructed modulus maps are consistent.