1,720,972 research outputs found
Full-field stress computation from measured deformation fields: A hyperbolic formulation
No full textRecent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known deformation field becomes an interesting possibility. This is known as an inverse problem. Current approaches to this problem, such as the finite element update method, are generally over-determined and must rely on statistical approaches to minimize error. This provides approximate solutions in some cases, however, implementation difficulties, computational requirements, and accuracy are still significant challenges. Here, we show how the inverse problem can be formulated deterministically and solved exactly in two or three dimensions for large classes of materials including isotropic elastic solids, Newtonian fluids, non-Newtonian fluids, granular materials, plastic solids subject to co-directionality, and some other plastic solids subject to associative or non-associative flow rules. This solution is based on a single assumption of the alignment of the principal directions of stress and strain or strain rate. No further assumptions regarding incompressibility, pressure independence, yield surface shape or the hardening law are necessary. This assumption leads to a closed, first order, linear system of hyperbolic partial differential equations with variable coefficients. The solution of this class of problems is well established and hence the equations can be solved to give the solution for any geometry and loading condition, enabling broad applicability to a variety of problems. We provide a numerical proof-of-principle study of the plastic deformation of a two-dimensional bar with spatially varying yield stress and strain hardening coefficient. The results are validated against the solution of the corresponding forward problem – solved with a commercial finite element solver – indicating the solution is exact up to numerical error (the normalized root mean square error of the stress is ). No model calibration or material parameters are required. The sensitivity of the solution to error in the input data is also analyzed. Interestingly, this solution procedure lends itself to a simple physical interpretation of stress propagation through the material. Finally, we provide some examples showing how this approach may be analytically applied to both solid and fluid mechanics problems
Partial differential equations to determine elasto-plastic stress–strain behavior from measured kinematic fields
No full textA system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed equations that assume pure plastic behavior without elasticity. A method to numerically solve these equations is also presented. In addition to force balance, the equations are derived from the elastic–plastic decomposition of the deformation gradient, the assumption of isotropy, and the assumption that the function mapping the elastic strain to stress is known. The system of equations can be directly applied to complex geometries, finite deformation, non-linear elasticity and plasticity, compressible materials, rate dependent materials, and a variety of hardening laws. This system of PDEs is non-linear and time dependent. Furthermore, it overcomes an important prior limitation: it can be directly applied to cases where some regions of a body are elastically deforming while others are elasto-plastically deforming. A two-dimensional case study of necking in a uniaxial tensile specimen is investigated to illustrate and validate the method. The governing equations are numerically solved using strain fields output from a finite element simulation and validated against this same simulation showing accurate results
Towards physical insights on microstructural damage nucleation from data analytics
No full textVariations in the chemical composition or thermomechanical processing of metallic materials result in a vast landscape of possible microstructural morphologies. While this creates ample opportunities for alloys with improved mechanical performance, the design process is challenging due to the morphological complexity and the range of deformation micro-mechanisms involved. Empirically based statistical approaches are well suited to address some of these challenges. Previously, a model based on n-point statistics and principal component analysis was successfully used for predicting damage nucleation based on the microstructural morphology of dual-phase steels. Here, we give an in-depth exploration and analysis of such algorithms as applied to experimental data. First, we investigate model architecture by implementing and testing over 1000 model variants. This leads to improved predictive ability and several alternate architectures including one with a Fourier transformation instead of a n-point statistics transformation. Second, we analyze the noise, resolution and data quantity impact to give guidelines on the necessary data required to train a predictive model. Third, we investigate which morphological features are utilized by the model to make predictions by inputting artificially-constructed microstructures, inverting the model, examination of the basis image, and variation of model hyperparameters. It is found that grain boundary fluctuations less than 1 μm are correlated to damage nucleation. This is consistent with observations in the literature on the effect of grain size and interconnected martensite regions on damage nucleation. Furthermore, it may give insights into the superior mechanical properties of alloys with bimodal grain size distributions. This demonstrates a unique approach of elucidating morphological effects from a single alloy by exploiting microstructural heterogeneity. It may be applied to other microstructures as well.<br/
On discontinuities when computing the stress-field from the strain: a finite volume discretization
Get PDFRecently, a widely applicable system of hyperbolic partial differential
equations has been derived that enables the deterministic computation of a full
heterogeneous stress field from a measured deformation field, for example, from
a strain field obtained via digital image correlation. This information enables
the determination of material properties, making this approach an alternative
to finite element model updating or the virtual fields method. This article
focuses on developing a finite volume discretization of this system of
equations to address instabilities that arise from violations of the
Courant-Friedrichs-Lewy condition. The developed discretization enables the
system of equations to be applied to irregular geometries and finite
deformation. We determine how, in general, one may translate knowledge of the
traction at the boundary into boundary conditions, so that the numerical method
can be applied to a variety of loading conditions. We analyse the solution
structure in the case of deformation discontinuities, and the results are
applied to account for discontinuities at the interfaces between finite volumes
(this has relevance to other applications such as composite materials).
Interestingly, the discontinuities cause reflection and transmission of the
principal stresses.
The finite volume discretization is validated using data output from
commercial finite element software. Furthermore, the discretization is applied
to an experimental uniaxial tension test with plastic deformation and necking.
The strain field is obtained using digital image correlation, and the stress
field is computed using the developed finite volume discretization. Together,
these give the stress-strain behavior for each material element
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Edge contraction and cop-win critical graphs
No full textThe problem is to determine the number of ‘cops’ needed to capture a ‘robber’ where the game is played with perfect information, the different sides moving alternately. The cops capture the robber when one of them occupies the same vertex as the robber at any time in the game. A copwin graph is one in which one cop can always capture the robber. A graph is cop-win edge-critical with respect to edge contraction (CECC) when the original graph is not cop-win, but the contraction of any edge results in a cop-win graph. In this paper, classes of CECC graphs are determined, and k-regular CECC are characterized for k ≤ 4
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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