Simulating curvilinear crack propagation in two dimensions with universal meshes

2014 ◽  
Vol 102 (3-4) ◽  
pp. 632-670 ◽  
Author(s):  
Ramsharan Rangarajan ◽  
Maurizio M. Chiaramonte ◽  
Michael J. Hunsweck ◽  
Yongxing Shen ◽  
Adrian J. Lew
Keyword(s):  
Crack Propagation ◽  
Two Dimensions ◽  
Curvilinear Crack

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Fracture Statistics Models and Crack Propagation in Random Media

1994 ◽  
Vol 47 (1S) ◽  
pp. S141-S150 ◽  
Author(s):  
D. Jeulin
Keyword(s):  
Crack Propagation ◽  
Fracture Energy ◽  
Random Media ◽  
Probabilistic Models ◽  
Heterogeneous Media ◽  
Crack Nucleation ◽  
Crack Arrest ◽  
Two Dimensions ◽  
Unstable Crack ◽  
Probability Of Fracture

Crack propagation in heterogeneous media is of primary interest for engineering purposes, in order to predict the overall toughness and the probability of fracture from data on the microstructure. Probabilistic models for mode I crack propagation in two dimensions are presented. They are developed for brittle elastic materials with a random distribution of fracture energy. These models enable us to calculate in a closed form the probability of fracture involving crack nucleation and propagation that differ from the usual fracture statistics models based on the weakest link model. The use of the Griffith’s crack arrest criterion is applied to random function models for the distribution of the fracture energy and for various loading conditions resulting in stable or unstable crack propagation. From the models are deduced some statistical size effects.

CRACK PROPAGATION UNDER INITIAL MODE II CONDITIONS

2020 ◽  
pp. 49-56
Author(s):  
D.V. Fedotova ◽  
◽  
R.M. Khamidullin ◽  
Keyword(s):  
Crack Propagation ◽  
Material Properties ◽  
Crack Path ◽  
Plastic Material ◽  
Compact Tension ◽  
Mode Ii ◽  
Curvilinear Crack ◽  
Inclined Crack ◽  
Kinked Crack ◽  
Elastic Plastic Material

Series of tests for compact tension shear specimens under mode II and following mixed mode was carried out. Compact tension shear specimens made of steels 34X and P2M, Ti-6Al-4V titanium and 7050 aluminum alloys. During experiments the behavior of the inclined crack angles, kinked crack angles and crack propagation angles, as a function of dimensionless crack length for the curvilinear paths was obtained. The influence of elastic-plastic material properties on the form the curvilinear crack path is established.

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

A transmission electron microscopic study of structural transitions in fast ionic conductors

1987 ◽  
Vol 45 ◽  
pp. 156-157
Author(s):  
R. B. Queenan ◽  
P. K. Davies
Keyword(s):  
Optical Properties ◽  
Ionic Conduction ◽  
Recent Observation ◽  
Ionic Conductivities ◽  
Sodium Aluminate ◽  
Two Dimensions ◽  
Ionic Conductors ◽  
Electron Microscopic ◽  
Transmission Electron ◽  
Trivalent Cations

Na ß“-alumina (Na1.67Mg67Al10.33O17) is a non-stoichiometric sodium aluminate which exhibits fast ionic conduction of the Na+ ions in two dimensions. The Na+ ions can be exchanged with a variety of mono-, di-, and trivalent cations. The resulting exchanged materials also show high ionic conductivities.Considerable interest in the Na+-Nd3+-ß“-aluminas has been generated as a result of the recent observation of lasing in the pulsed and cw modes. A recent TEM investigation on a 100% exchanged Nd ß“-alumina sample found evidence for the intergrowth of two different structure types. Microdiffraction revealed an ordered phase coexisting with an apparently disordered phase, in which the cations are completely randomized in two dimensions. If an order-disorder transition is present then the cooling rates would be expected to affect the microstructures of these materials which may in turn affect the optical properties. The purpose of this work was to investigate the affect of thermal treatments upon the micro-structural and optical properties of these materials.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

Instrumental and Ideological Union Commitment: Longitudinal Assessment of Construct Validity

2001 ◽  
Vol 17 (2) ◽  
pp. 98-111 ◽  
Author(s):  
Anders Sjöberg ◽  
Magnus Sverke
Keyword(s):  
Construct Validity ◽  
Temporal Stability ◽  
Strong Support ◽  
Internal Consistency Reliability ◽  
Measurement Model ◽  
Two Dimensions ◽  
Model Parameters ◽  
Longitudinal Assessment ◽  
Union Commitment ◽  
Union Participation

Summary: Previous research has identified instrumentality and ideology as important aspects of member attachment to labor unions. The present study evaluated the construct validity of a scale designed to reflect the two dimensions of instrumental and ideological union commitment using a sample of 1170 Swedish blue-collar union members. Longitudinal data were used to test seven propositions referring to the dimensionality, internal consistency reliability, and temporal stability of the scale as well as postulated group differences in union participation to which the scale should be sensitive. Support for the hypothesized factor structure of the scale and for adequate reliabilities of the dimensions was obtained and was also replicated 18 months later. Tests for equality of measurement model parameters and test-retest correlations indicated support for the temporal stability of the scale. In addition, the results were consistent with most of the predicted differences between groups characterized by different patterns of change/stability in union participation status. The study provides strong support for the construct validity of the scale and indicates that it can be used in future theory testing on instrumental and ideological union commitment.

The Prediction of Problem-Solving Assessed Via Microworlds

2016 ◽  
Vol 32 (4) ◽  
pp. 298-306 ◽  
Author(s):  
Samuel Greiff ◽  
Katarina Krkovic ◽  
Jarkko Hautamäki
Keyword(s):  
Working Memory ◽  
Problem Solving ◽  
Complex Problem ◽  
Two Dimensions ◽  
Assessment Instruments ◽  
Complex Problem Solving ◽  
Visual Spatial ◽  
Rule Knowledge ◽  
Rule Application ◽  
Fluid Reasoning

Abstract. In this study, we explored the network of relations between fluid reasoning, working memory, and the two dimensions of complex problem solving, rule knowledge and rule application. In doing so, we replicated the recent study by Bühner, Kröner, and Ziegler (2008) and the structural relations investigated therein [ Bühner, Kröner, & Ziegler, (2008) . Working memory, visual-spatial intelligence and their relationship to problem-solving. Intelligence, 36, 672–680]. However, in the present study, we used different assessment instruments by employing assessments of figural, numerical, and verbal fluid reasoning, an assessment of numerical working memory, and a complex problem solving assessment using the MicroDYN approach. In a sample of N = 2,029 Finnish sixth-grade students of which 328 students took the numerical working memory assessment, the findings diverged substantially from the results reported by Bühner et al. Importantly, in the present study, fluid reasoning was the main source of variation for rule knowledge and rule application, and working memory contributed only a little added value. Albeit generally in line with previously conducted research on the relation between complex problem solving and other cognitive abilities, these findings directly contrast the results of Bühner et al. (2008) who reported that only working memory was a source of variation in complex problem solving, whereas fluid reasoning was not. Explanations for the different patterns of results are sought, and implications for the use of assessment instruments and for research on interindividual differences in complex problem solving are discussed.

Development of the Fear of Intimacy Components Questionnaire (FICQ)

2015 ◽  
Vol 31 (4) ◽  
pp. 302-309 ◽  
Author(s):  
Maria Pedro Sobral ◽  
Maria Emília Costa
Keyword(s):  
Convergent Validity ◽  
Discriminant Validity ◽  
Two Dimensions ◽  
Dimensional Structure ◽  
Future Research ◽  
Fear Of Intimacy ◽  
Confirmatory Factor Analyses ◽  
New Instrument ◽  
Confirmatory Factor ◽  
Test Retest Reliability

Abstract. We developed a new instrument designed to measure fear of intimacy in romantic relationships. We suggest assessing fear of intimacy through two dimensions: self-revelation and dependence. The Fear of Intimacy Components Questionnaire (FICQ) was validated across three studies in which a 10-item solution systematically emerged. Consistently with a two component perspective, a two-factor solution fitted data the best: fear of losing the self (FLS) and fear of losing the other (FLO). Qualitative analyses verified content validity. Exploratory and confirmatory factor analyses tested the factor structure. Multigroup analyses supported the structural invariance across gender, age, and relationship status. Both factors showed adequate discriminant validity and internal consistency, and good 3-week period test-retest reliability. Associations between the FICQ and insecure attachment orientations demonstrated convergent validity. The association between the FICQ and relationship satisfaction above and beyond a preexisting measure offered criterion validity. By going beyond traditional self-revelation-focused conception of fear of intimacy, that is, by proposing a bi-dimensional structure to fear of intimacy, we believe that this new measure will contribute to future research on fear of intimacy.

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