Bifurcation Effects in Ductile Metals With Nonlocal Damage

1994 ◽  
Vol 61 (2) ◽  
pp. 236-242 ◽  
Author(s):  
J. B. Leblond ◽  
G. Perrin ◽  
J. Devaux
Keyword(s):  
Shear Banding ◽  
Homogeneous Medium ◽  
The Body ◽  
Ductile Material ◽  
Ductile Metals ◽  
Plane Strain Tension ◽  
Bifurcation Phenomena ◽  
Nonlocal Evolution Equation ◽  
Rectangular Mesh ◽  
First Occurrence

The purpose of this paper is to investigate some bifurcation phenomena in a porous ductile material described by the classical Gurson (1977) model, but with a modified, nonlocal evolution equation for the porosity. Two distinct problems are analyzed theoretically: appearance of a discontinuous velocity gradient in a finite, inhomogeneous body, and arbitrary loss of uniqueness of the velocity field in an infinite, homogeneous medium. It is shown that no bifurcation of the first type can occur provided that the hardening slope of the sound (void-free) matrix is positive. In contrast, bifurcations of the second type are possible; nonlocality does not modify the conditions of first occurrence of bifurcation but does change the corresponding bifurcation mode, the wavelength of the latter being no longer arbitrary but necessarily infinite. A FE study of shear banding in a rectangular mesh deformed in plane strain tension is finally presented in order to qualitatively illustrate the effect of finiteness of the body; numerical results do evidence notable differences with respect to the case of an infinite, homogeneous medium envisaged theoretically.

Localization Effects in Bammann-Chiesa-Johnson Metals With Damage Delocalization

2011 ◽  
Author(s):  
Koffi Enakoutsa ◽  
Fazle R. Ahad ◽  
Kiran N. Solanki ◽  
Yustianto Tjiptowidjojo ◽  
Douglas J. Bammann
Keyword(s):  
Velocity Gradient ◽  
Adiabatic Shear Band ◽  
Shear Banding ◽  
Material Model ◽  
Dissipated Energy ◽  
Dissipation Energy ◽  
Plane Strain Tension ◽  
Nonlocal Evolution Equation ◽  
Rectangular Mesh ◽  
Spatial Discontinuity

The presence of softening in the Bammann-Chiesa-Johnson (BCJ) material model presents a major physical drawback: the unlimited localization of strain which results in spurious zero dissipated energy at failure. This difficulty resolves when the BCJ model is modified to incorporate a nonlocal evolution equation for the damage, as proposed by Pijaudier-Cabot and Bazant (1987). The objective of this work is to theoretically assess the ability of such a modified BCJ model to prevent unlimited localization of the strain. To that end, we investigate two localization problems in nonlocal BCJ metals: appearance of a spatial discontinuity of the velocity gradient in a finite, inhomogeneous body, and localization into finite bands. We show that in spite of the softening arising from the damage, no spatial discontinuity occurs in the velocity gradient. Also, we find that the dissipation energy is continuously distributed in nonlocal BCJ metals and therefore can not localize into zones of vanishing volume. As a result, the appearance of any vanishing width adiabatic shear band is impossible in a nonlocal BCJ metal. Finally, we study the finite element (FE) solution of shear banding in a rectangular mesh, deformed in plane strain tension and containing an imperfection, thereby illustrating the effects of imperfections on the localization of the strain.

Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Koffi Enakoutsa ◽  
Fazle R. Ahad ◽  
Kiran N. Solanki ◽  
Yustianto Tjiptowidjojo ◽  
Douglas J. Bammann
Keyword(s):  
Velocity Gradient ◽  
Adiabatic Shear Band ◽  
Shear Banding ◽  
Finite Size ◽  
Material Model ◽  
Dissipation Energy ◽  
Plane Strain Tension ◽  
Nonlocal Evolution Equation ◽  
Damage Theory ◽  
Spatial Discontinuity

The Bammann, Chiesa, and Johnson (BCJ) material model predicts unlimited localization of strain and damage, resulting in a zero dissipation energy at failure. This difficulty resolves when the BCJ model is modified to incorporate a nonlocal evolution equation for the damage, as proposed by Pijaudier-Cabot and Bazant (1987, “Nonlocal Damage Theory,” ASCE J. Eng. Mech., 113, pp. 1512–1533.). In this work, we theoretically assess the ability of such a modified BCJ model to prevent unlimited localization of strain and damage. To that end, we investigate two localization problems in nonlocal BCJ metals: appearance of a spatial discontinuity of the velocity gradient in any finite, inhomogeneous body, and localization of the dissipation energy into finite bands. We show that in spite of the softening arising from the damage, no spatial discontinuity occurs in the velocity gradient. Also, we find that the dissipation energy is continuously distributed in nonlocal BCJ metals and therefore cannot localize into zones of vanishing volume. As a result, the appearance of any vanishing width adiabatic shear band is impossible in a nonlocal BCJ metal. Finally, we study the finite element (FE) solution of shear banding in a rectangular plate, deformed in plane strain tension and containing an imperfection, thereby illustrating the effects of imperfections and finite size on the localization of strain and damage.

scholarly journals AN EXPERIMENTAL STUDY OF DIATHERMY

1927 ◽  
Vol 46 (5) ◽  
pp. 715-734 ◽  
Author(s):  
Ronald V. Christie ◽  
Carl A. L. Binger
Keyword(s):  
Electrical Resistance ◽  
High Frequency ◽  
Skin Effect ◽  
Current Flow ◽  
Homogeneous Medium ◽  
Local Heat ◽  
The Body ◽  
Technical Error ◽  
Theoretical Considerations ◽  
Maximal Heating

The principles governing the passage of high frequency currents through various conductors have been discussed and exemplified in experiments done on both non-living and living bodies. In Part I it was shown: (1) That the current takes the path of least electrical resistance rather than the shortest path; (2) that maximal heating occurs at the point of greatest concentration of the lines of current flow. In a homogeneous medium with parallel electrodes maximal heat production occurs in those portions of the medium adjoining the electrodes and the heat gradient is from without inward. Under these circumstances maximal heating never occurs at the center. In discussing the localization of heat not only the electrical resistance and current concentration, but also the cooling effect, must be considered. In experiments on the dog's cadaver no evidence of the so called "skin effect" could be demonstrated. This is in contradistinction to the findings of Bettman and Crohn, but the discrepancy is explained on the basis of what we believe to be a technical error in their work. The finding of no "skin effect" is in agreement with the conclusions of Dowse and Iredell, based on both experimental and theoretical considerations. In Part II three types of experiments were performed on the anesthetized dog. The conclusions to be derived from them are these: (1) The heat gradient of the body is reversed during diathermy and heating occurs from without inward; (2) deep heating during diathermy is greater than that which results from the application of local heat to the skin; (3) the lung can be heated by diathermy in spite of simultaneous cooling of the chest wall. These experiments we regard as satisfactory evidence of the passage of the current through the interior of the body.

scholarly journals A new species of the deuterostome Herpetogaster from the early Cambrian Chengjiang biota of South China

2020 ◽  
Vol 107 (5) ◽  
Author(s):  
Xianfeng Yang ◽  
Julien Kimmig ◽  
Bruce S. Lieberman ◽  
Shanchi Peng
Keyword(s):  
New Species ◽  
The Body ◽  
Time Period ◽  
First Occurrence ◽  
Juvenile Specimen ◽  
History Of ◽  
Cambrian Radiation ◽  
Chengjiang Biota ◽  
A New Species ◽  
Number Of Branches

Abstract The Cambrian radiation represents a key time period in the history of life. Here, we add to the mounting evidence accumulating on the nature of deuterostomes from this time period through description of a new species of stalked deuterostome, Herpetogaster haiyanensis nov. sp., from the lower Cambrian (series 2, stage 3) Chengjiang biota of China. This represents the first occurrence of the genus in Gondwana, the first juvenile specimen, and the oldest specimens to date. Herpetogaster haiyanensis nov. sp. differs from H. collinsi Caron et al. (2010) in having a stolon that is separated into an outer and inner layer, the segmentation of the body and in the shape and number of branches of the tentacles. The new species reiterates earlier suggestions of deuterostome affinities of the genus―it appears closely related to Phlogites and then successively more distantly related to Cotyledon and Eldonia―and may have fed on hyolithids.

The hierarchical structure of organisms: a scale and documentation of a trend in the maximum

Paleobiology ◽  
2001 ◽  
Vol 27 (2) ◽  
pp. 405-423 ◽  
Author(s):  
Daniel. W. McShea
Keyword(s):  
Hierarchical Structure ◽  
Fossil Record ◽  
Waiting Times ◽  
Eukaryotic Cell ◽  
The Body ◽  
Hierarchical Level ◽  
The Hierarchical Structure ◽  
First Occurrence ◽  
Almost All ◽  
Body Fossil

The degree of hierarchical structure of organisms—the number of levels of nesting of lower-level entities within higher-level individuals—has apparently increased a number of times in the history of life, notably in the origin of the eukaryotic cell from an association of prokaryotic cells, of multicellular organisms from clones of eukaryotic cells, and of integrated colonies from aggregates of multicellular individuals. Arranged in order of first occurrence, these three transitions suggest a trend, in particular a trend in the maximum, or an increase in the degree of hierarchical structure present in the hierarchically deepest organism on Earth. However, no rigorous documentation of such a trend—based on operational and consistent criteria for hierarchical levels—has been attempted. Also, the trajectory of increase has not been examined in any detail. One limitation is that no hierarchy scale has been developed with sufficient resolution to document more than these three major increases. Here, a higher-resolution scale is proposed in which hierarchical structure is decomposed into levels and sublevels, with levels reflecting number of layers of nestedness, and sublevels reflecting degree of individuation at the highest level. The scale is then used, together with the body-fossil record, to plot the trajectory of the maximum. Two alternative interpretations of the record are considered, and both reveal a long-term trend extending from the Archean through the early Phanerozoic. In one, the pattern of increase was incremental, with almost all sublevels arising precisely in order. The data also raise the possibility that waiting times for transitions between sublevels may have decreased with increasing hierarchical level (and with time). These last two findings—incremental increase in level and decreasing waiting times—are tentative, pending a study of possible biases in the fossil record.

Shear Constraint and Macroscopic Fracture Criteria for Ductile Metals

1975 ◽  
Vol 42 (1) ◽  
pp. 15-24 ◽  
Author(s):  
M. A. Kaplan ◽  
G. A. Rowell
Keyword(s):  
Internal Pressure ◽  
Shear Fracture ◽  
Maximum Shear Stress ◽  
Fracture Initiation ◽  
Tensile Tests ◽  
Initiation Site ◽  
The Body ◽  
Fracture Criteria ◽  
Ductile Metals ◽  
Stress States

The role of material constraint in the shear fracture of ductile metals is investigated by means of a series of torsion and internal pressure tests on aluminum alloy tubing combined with analytical descriptions of the stress states at fracture. These descriptions include work hardening and, in the case of a tube under internal pressure, account for the nonaxisymmetric deformations that always precede fracture. The results, which indicate that shear fracture initiation depends on conditions at points far removed from the initiation site when the maximum shear stress vector there is directed through the interior of the body, are supported by the results of tensile tests on plates with shallow notches. These latter experiments are also used to show that tensile and shear fracture are governed by independent fracture criteria. A continuum fracture theory for ductile metals, based on the concepts of material constraint and independent fracture criteria, is proposed. The theory predicts fracture in terms of the stress state. A critical analysis of the theory is provided along with examples of fracture phenomena which the theory predicts, but which are not explained by existing theories.

The Invention of Hypoxia

2021 ◽  
Author(s):  
Jean-Paul Richalet
Keyword(s):  
Scientific Literature ◽  
Living Organism ◽  
The Body ◽  
Internet Research ◽  
Academic Environment ◽  
Current Topic ◽  
Pubmed Database ◽  
First Occurrence ◽  
Living Organisms ◽  
A Current

The word « hypoxia » has recently come to the attention of the general public in two occasions, the Nobel Prize in Medicine or Physiology in 2019 and the recent COVID-19pandemics. In the academic environment, hypoxia is a current topic of research in biology, physiology and medicine: in October 2020, there were more than 150,000 occurrences of "hypoxia" in the PubMed database. However, the first occurrence is dated in 1945, while the interest for the effects of oxygen lack on the living organisms started in the mid 19thcentury, when scientists explored high altitude regions and mainly used the terms "anoxia" or "anoxemia". I therefore made an Internet research through multiple databases to look for the first appearance of "hypoxia" and related terms "hypoxemia" and "hypoxybiosis" in the scientific literature published in English, German, French, Italian and Spanish. Viault and Jolyet used "Hypohématose" in 1894, but this word was never used since. Hypoxybiosis appeared first in 1909 in Germany, then hypoxemia in 1923 in Austria and hypoxia in 1938 in Holland. It was then exported to United States where it appeared in 1940 in cardiology and anesthesiology. The clinical distinction between anoxia and hypoxia was clearly defined by Carl Wiggers in 1941. Hypoxia (decrease in oxygen), by essence variable in time and in localization in the body, in contrast with anoxia (absence of oxygen), illustrates the concept of homeodynamics that defines a living organism as a complex system in permanent instability, exposed to environmental and internal perturbations.

Magmatic haggertyite in olivine lamproites of the West Kimberley region, Western Australia

2020 ◽  
Vol 105 (11) ◽  
pp. 1724-1733
Author(s):  
A. Lynton Jaques ◽  
Frank Brink ◽  
Jiang Chen
Keyword(s):  
Western Australia ◽  
Upper Mantle ◽  
Trace Element Analysis ◽  
Central Zone ◽  
The Body ◽  
Chromian Spinel ◽  
The West ◽  
Element Analysis ◽  
First Occurrence ◽  
Olivine Lamproite

Abstract We report the first occurrence of magmatic haggertyite (BaFe6Ti5MgO19) from the Miocene lamproites of the West Kimberley region of Western Australia. This contrasts with the metasomatic formation reported in an olivine lamproite host at the type locality, Prairie Creek, Arkansas. Haggertyite occurs in the groundmass of a diamondiferous olivine lamproite pipe in the Ellendale field, and within the large zoned Walgidee Hills lamproite where it forms part of an extensive suite of Ba- and K-bearing titanate and Ti-rich silicate minerals. The haggertyite co-exists with chromian spinel, perovskite, and ilmenite in the Ellendale lamproite, and with priderite and perovskite and, in one locality, with priderite, jeppeite, ilmenite, and perovskite, in the Walgidee Hills lamproite. Unlike priderite and perovskite, which are common groundmass phases in the Ellendale olivine lamproites and present throughout the Walgidee Hills lamproite, haggertyite appears restricted in its occurrence and crystallization interval, with sparse ilmenite apparently mostly crystallizing as an alternative phase. In the Walgidee Hills lamproite the haggertyite-bearing assemblage is succeeded by the Ba-titanate assemblage priderite plus jeppeite in the evolved central part of the body. The haggertyite in the main zone of the Walgidee Hills lamproite has an average composition of (Ba0.7K0.3)1.0(Ti5.0Fe2.13+Cr0.1Fe3.82+Mn0.2Mg0.6Na0.1)12O19 and is thus very similar to the original haggertyite described from xenoliths in the Prairie Creek lamproite apart from being poorer in Cr and Ni. Haggertyite in the groundmass of the Ellendale olivine lamproite and the central zone of the Walgidee Hills lamproite, in addition to variations in Mg and Cr, show significant variation in Ti and Fe contents and in calculated Fe3+ and Fe2+. A linear inverse relationship between Ti and Fe, and Ti and Fe3+, indicates that Fe3+ is accommodated by the coupled substitution Ti4+ + Fe2+ ⇆ 2 Fe3+. A marked trend to higher Fe3+ in the haggertyite in Ellendale 9 olivine lamproite is ascribed to increasing oxidation during crystallization, with fO2 estimated from the olivine-spinel thermometer and oxygen barometer at Dlog FMQ = –1 to +3 at temperatures of 790–660 °C. The haggertyite in the central zone of the Walgidee Hills lamproite, in contrast, shows a marked trend to Fe2+ enrichment, which is associated with decreasing Fe in perovskite. This is inferred to indicate formation under more reducing conditions, but sufficiently oxidized to permit Fe3+ in co-existing priderite and jeppeite. Trace-element analysis by LA-ICP-MS shows the Walgidee Hills haggertyite contains minor amounts of Na, Si, Ca, V, Co, Zn, Sr, Zr, Nb, and Pb, and only traces of Al, P, Sc, Rb, REE, Hf, and Ta. Moreover, the haggertyite is preferentially enriched in certain lithophile (Ba, Sr), siderophile (Mn, Fe, Co, Ni), and chalcophile (Zn, Pb) elements relative to co-existing priderite. Haggertyite crystallization appears to be a consequence not only of the very high Ba, Ti, and K contents of the lamproite, but of relatively high-Fe concentrations and low temperatures in evolved olivine lamproite magma with the Fe3+/Fe2+ ratio determined by the prevailing fO2. The new data suggest that haggertyite might also be present but previously unrecognized in the evolved groundmass of other olivine lamproites. Haggertyite is one of an increasing number of new minerals in upper mantle rocks and volcanics derived from the upper mantle hosting large-ion-lithophile and high field strength cations.

scholarly journals First diagnosis of septic arthritis in a dinosaur

2016 ◽  
Vol 3 (8) ◽  
pp. 160222 ◽  
Author(s):  
Jennifer Anné ◽  
Brandon P. Hedrick ◽  
Jason P. Schein
Keyword(s):  
Septic Arthritis ◽  
Fossil Record ◽  
Life Histories ◽  
Bone Growth ◽  
East Coast ◽  
Accurate Diagnosis ◽  
The Body ◽  
Proximal Ulna ◽  
X Ray ◽  
First Occurrence

Identification and interpretation of pathologies in the fossil record allows for unique insights into the life histories of extinct organisms. However, the rarity of such finds limits not only the sample size for palaeopathologic studies, but also the types of analyses that may be performed. In this study, we present the first occurrence of a palaeopathology in a vertebrate from the Mesozoic of the East Coast of North America (Appalachia), a pathologic ulna and radius of an indeterminate hadrosaur from the Navesink Formation (New Jersey). X-ray microtomography allowed for both detailed and more accurate diagnosis of the pathologic condition as well as virtual conservation of the specimen. Based on extant archosaurian comparisons, the hadrosaur was diagnosed with severe septic arthritis affecting the proximal ulna and radius. Diagnosis was based on erosion of the joint and highly reactive periosteal bone growth and fusion of the elements. To the best of our knowledge, this is the first recorded account of septic arthritis in dinosaurs. The severity of the pathology suggests the animal suffered with this condition for some time before death. Unfortunately, only the ulna and radius were found. Thus, the extent to which the condition spread to other parts of the body is unknown.

scholarly journals Measurements of transmission of radiation through a non-homogeneous medium, viz., the horny layer of the human skin

1931 ◽  
Vol 109 (763) ◽  
pp. 309-318 ◽  
Keyword(s):  
Human Skin ◽  
Direct Action ◽  
Homogeneous Medium ◽  
Living Cells ◽  
The Body ◽  
Optical Beam ◽  
Single Sample ◽  
Horny Layer ◽  
Humid Condition

The experiments and methods to be described represent an attempt to answer with greater accuracy a question to which somewhat divergent answers have already been given. The entire work herein described was done with a single sample of clear, dry, desquamated, human skin (horny layer only), taken from the shoulder of a woman. This sample had been detached from the body for some months, and no attempt had been made to keep it in a more humid condition than that which it would naturally attain in the air of the laboratory ; but we are indebted to Sir Leonard Hill, at whose instance the work was started, for the opinion that the radiation which penetrates this dead horny layer is the deciding factor in the direct action of radiations on the living cells beneath. The writers found that two precautions are essential : first, to secure truly monochromatic radiations ; secondly, to make allowance for the effects due to the scattering of an optical beam when it is passed through such an uneven medium as a piece of skin. The importance of this last precaution has recently been pointed out by Lucas (1931) and Pearson and Jair (1931).

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