General Stress State Research Articles

Asymptotic Methods in the Buckling Theory of Elastic Shells

Equations of Thin Elastic Shell Theory Basic Equations of Shell Buckling Simple Buckling Problems Buckling Modes Localized Near Parallels Non-Homogeneous Axial Compression of Cylindrical Shells Buckling Modes Localized at a Points Semi-Momentless Buckling Modes Effect of Boundary Conditions on Semi-Momentless Modes Torsion and Bending of Cylindrical and Conic Shells Nearly Cylindrical and Conic Shells Shells of Revolution of Negative Gaussian Curvature Surface Bending and Shell Buckling Buckling Modes Localized at an Edge Shells of Revolution under General Stress State.

Failure of Composite Sandwich Beams

A thorough investigation of failure behaviour of composite sandwich beams under three- and four-point bending was undertaken. The beams were made of unidirectional carbon/epoxy facings and a PVC closed-cell foam core. The constituent materials were fully characterised and in the case of the foam core, failure envelopes were developed for general two-dimensional states of stress. Various failure modes including facing wrinkling, indentation failure and core failure were observed and compared with analytical predictions. The initiation, propagation and interaction of failure modes depend on the type of loading, constituent material properties and geometrical dimensions.

Mechanics of Materials

5R24. Mechanics of Materials. - A Bedford and K Liechti (Dept of Aerospace Eng and Eng Mech, Univ of Texas, Austin TX). Prentice Hall, Upper Saddle River NJ. 2000. 627 pp. CD-ROM included. ISBN 0-201-89552-8. $103.00. Reviewed by M Epstein (Dept of Mech Eng, Univ of Calgary, 2500 University Dr NW, Calgary AB, T2N 1N4, Canada).In a market already flooded with textbooks on Mechanics of Materials, the appearance of yet another one is greeted with a mixture of skepticism and hope. The preface to this book starts by feeding the latter when it declares that the “long-held dream of the merger of continuum solid mechanics and material science into a unified field” is near at hand. Whether or not this is true, or even desirable, this book does little to contribute in pointing the prospective student in that direction. After a statement containing an almost unforgivable spelling error (“the principle emphasis”), the preface gives us a description of the contents of the book. It is practically identical to that of any of the textbooks already available at the same level. Perhaps the only difference is the introduction of the discussion of general states of stress and strain after the treatment of torsion and before the treatment of bending. As usual, however, stress-strain relations are included as a part of the chapter on strain, rather than as a separate chapter on constitutive behavior, thus doing little to advance the long-held dream just mentioned. Having said all that, the book is professionally produced, with excellent figures and interesting examples. An accompanying CD offers interesting interactive opportunities for practice beyond the problems appearing in the book itself. This feature will certainly be very attractive to students and instructors alike. The book is organized in 12 chapters and 7 appendices. Chapter 1 consists mainly of a review of Statics. The vector equilibrium equations are stated, but there seems to be no review of the concept of the moment of a force as a vector product. All of the examples discussed are planar, but at the end of the chapter a couple of examples are spatial. It is not clear, therefore, what the student is expected to do. Chapter 2, entitled “Measures of stress and strain,” is a good elementary introduction to particular cases where these can be calculated by simple means. In the next chapter, on axially loaded bars, the standard method of introducing Young’s modulus and Poisson’s ratio is followed. There is a danger here that the student might elevate these concepts to universal truths for all materials, but this is preempted by a good discussion at the end of the chapter on general features of material behavior, particularly under a uniaxial test. Elementary statically indeterminate situations are presented, and a discussion is attempted of the basic two methods (flexibility and stiffness). Unfortunately, this discussion is not very illuminating, and the conceptual difference between the formulations is dismissed in the context of the problems to be treated. One wonders what a student is supposed to do or think with such a piece of information.Chapter 4 is devoted to torsion of shafts, including some plasticity and simply connected thin-walled tubes. As already mentioned, the next two chapters are devoted to a discussion of the concepts of general states of stress and strain, including Mohr’s circle for both. A welcome treatment of the tetrahedron argument and its consequences is one of the nice features of this part of the book. Spherical and cylindrical pressure vessels are used to produce non-trivial examples. Chapter 7 presents the concepts of internal forces in planar beams, including the differential relations between bending moment and shear force. Chapter 8, at 70 pages the longest of the book, deals with in beams, including the shear formula, composite beams, and elastoplastic response. Chapter 9, on small deflections of planar elastic beams, is adequate, but omits the method of singularity functions. The book ends with three chapters on special topics. Chapter 10 is an introduction to Euler buckling, Chapter 11 deals with energy methods (including Castigliano’s second theorem), and Chapter 12 discusses some criteria of failure. Overall, although not attempting a new methodology, this is a good book that can be used as a textbook for a first course in Mechanics of Materials.

Large amplitude vibration of an initially stressed cross ply laminated plates

In this paper, nonlinear equations of large amplitude vibration for a laminated plate in a general state of nonuniform initial stress are derived. The equations include the effects of transverse shear and rotary inertia. Using these derived governing equations, the large amplitude vibration behaviour of an initially stressed cross-ply laminated plate is studied. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the plane of the plate. The Galerkin method is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge–Kutta method is used to obtain the nonlinear to linear frequencies. The frequency responses of nonlinear vibration are sensitive of the vibration amplitude, aspect ratio, thickness ratio, modulus ratio, stack sequence, layer number and state of initial stresses. The effects of various parameters on the large amplitude free vibrations are presented.

Failure criteria of anisotropically damaged materials based on the critical plane concept

AbstractThe damage state of a cracked material is assumed to be specified by crack density distribution on physical planes. The critical plane approach is used with account for damaged and intact area fractions on the plane. The maximum of failure function is specified for all potential failure planes and the critical plane orientation is determined. The resulting failure condition is applied to study strength evolution for triaxially compressed specimens with varying orientation of principal stress and damage tensor axes. Both Coulomb and non‐linear failure conditions of Mohr type are applied to specify the representative critical plane. A general stress state is considered and the failure condition is specified for different relative orientations of orthotropy and principal stress axes. Copyright © 2002 John Wiley & Sons, Ltd.

Fatigue life prediction of laminated polymer matrix composites

The subject of the present study was the development of a critical element based engineering methodology for the fatigue life prediction of laminated multidirectional polymer matrix composites subjected to general states of plane stress under random load-time histories. The considered baseline problem was pure cyclic torsion fatigue on ±45° angle-ply composites. A consistent experimental programme was carried out to characterize the damage and failure behaviour of the laminate, to validate the simulation results and to provide the necessary experimental input on the unidirectional level. The paper presents details of the fatigue life prediction methodology, relevant experimental results and comparisons between experiment and prediction.

Neutron stress measurements in the 21st century

Abstract The end of the 20th century marks 20 years of neutron stress activity and seems a good time to survey the landscape with regard to facilities, instrumentation and software. outreach, science, problems, and the impact of synchrotrons. The number of neutron stress instruments, at reactor and pulsed sources, has grown (and is growing) substantially. Brief surveys of facilities and instrumentation and software are presented. Our considerable success in building instruments raises the issue of who will use them. Building a user community—outreach—may prove to be a bigger problem, particularly in the US. With regard to science, real time observations of changes due to thermal and/or mechanical treatment will become feasible at the new pulsed source instruments. At both the pulsed and newer reactor facilities, more substantial studies of anisotropic systems, effects that cause peak broadening, and measurements of general triaxial stress states are becoming possible. In all cases, smaller gage volumes ar...

A new high-cycle fatigue criterion applied to out-of-phase biaxial stress state

A new multiaxial high-cycle fatigue criterion based on the so-called critical plane approach is presented. According to such a criterion, the critical plane orientation is proposed to be correlated with the averaged principal stress directions deduced through the weight function method. Then the fatigue failure assessment is performed by considering a nonlinear combination of the maximum normal stress and the shear stress amplitude acting on the critical plane. The proposed criterion is applied to a general sinusoidal biaxial stress state, for which analytical formulae can be derived. The theoretical results calculated according to the present criterion, together with those of other common critical plane criteria, are compared with experimental data related to different brittle (hard) metals under in-phase or out-of-phase sinusoidal biaxial normal and shear stress states.

Adaptation to social isolation: Acute and long-term stress responses of growing gilts with different coping characteristics

The present experiment studied the acute and long-term stress responses of reactive and proactive prepubertal gilts to social isolation. Gilts with either reactive or proactive features were identified according to behavioral resistance in a backtest at a young age (2–4 days), respectively being low (LR) and high resistant (HR) in this test. At 7 weeks of age, 12 gilts of each type were socially isolated. Initially, isolation was stressful for both types of gilts, as shown by increased cortisol concentrations and decreased body temperatures. Moreover, both types reacted with increases in exploration and vocalizations. Stress responses to isolation, however, differed in magnitude and/or duration between LR and HR gilts, which was in line with expected reaction patterns on the basis of preferred ways of coping. The cortisol response to isolation was higher in LR gilts, and they generally showed more explorative behavior. HR gilts seemed to be more engaged in walking/running behavior in the first hour after isolation, they generally vocalized more and their noradrenaline excretion in urine was higher at 3 weeks after the start of isolation. Several responses to isolation in the longer term pointed to a prolonged higher general state of stress of HR gilts. Body temperature in HR gilts, for instance, did not recover during 3 weeks of isolation, but values returned to “normal” within 1 day in LR gilts. At 1 week of isolation, relatively high parasympathetic responsivity to novelty was observed in HR gilts, probably due to stress-related high sympathetic reactivity. A shift in percentages of leucocyte subsets, typically occurring under conditions of stress, only developed in HR gilts during isolation. Finally, gastric ulceration was found in one HR gilt, but did not occur in LR gilts. To conclude, LR and HR gilts differed in their strategies to adapt to social isolation, and especially for HR gilts, this procedure seemed to become a chronic stressor.

Differential expression of ompA, ompB, pyk, nlpD and Cpn0585 genes between normal and interferon-γ treated cultures of Chlamydia pneumoniae

A common feature of many chlamydial infections is that they are often asymptomatic and may persist for long periods of time if left untreated. In addition to the well recognized lytic stage of the chlamydial developmental cycle, evidence is now emerging to support a persistent phase in the cycle in which the reticulate bodies are morphologically abnormal, viable but non-infectious and presumably also have altered gene expression patterns. We used an RT-PCR approach to study the differential levels of gene transcription for 14 genes (16SrRNA, ompA, ompB, omcB, 76 kDa, gseA, pmp1, gltX, hsp60, yaeT, pyk, nlpD, Cpn0585, Cpn1046) between normal and IFN-γ treated Chlamydia pneumoniae cell cultures. Even though the level of morphologically abnormal reticulate bodies in our IFN-γ treated cultures was low (approximately 10% morphologically discernible, although presumably a larger percentage were in the persistent state but not yet morphologically altered) we identified five genes (ompA, ompB, pyk, nlpD, Cpn0585) that were clearly upregulated when compared to normal cultures. This gene transcript profile may be characteristic of a general stress state in Chlamydia, induced by IFN-γ treatment in this case, but perhaps more widely induced in other in vitro and in vivo situations.

Relating experimental and geological rheology

This paper is concerned with the question of how to relate laboratory measurements of the rheology of rocks to the rheological assumptions that need to be made in geodynamic modelling. First, there is a brief resume of the principal types of rheological behaviour that have been studied in the laboratory, both pressure-dependent, strain rate-independent and pressure-independent, strain-rate-dependent. Then, the generalization of the results from the relatively simple stress states of the experiments to general stress states is discussed, followed by consideration of the extrapolation of the experimental results to geological strains and strain rates. Finally, the problems associated with spatial scale are considered, leading to the question of how to model the rheological behaviour of large-scale rock masses, using the rheological measurements of laboratory specimens and taking into account the heterogeneity of geological-scale rock masses.

An implicit algorithm using explicit correctors for the kinematic hardening model with multiple back stresses

AbstractThis paper presents an efficient mathematical algorithm for a class of non‐linear kinematic hardening models with multiple back stresses, as an extension of the implicit integration algorithm for a single back stress hardening model. Explicit formulations for general three‐dimensional stress states as well as plane stress and plane strain are given. The new formulation is implemented in a general‐purpose finite element code, ABAQUS, and is verified by comparison with the existing formulation for the single back‐stress constitutive model. Comparison is also made with the experimental results obtained from a plate containing a circular hole subjected to cyclic loading, demonstrating the validity of new method. Copyright © 2001 John Wiley & Sons, Ltd.

Pressure–volume–temperature paths in the laser-heated diamond anvil cell

The temperature, pressure, and stress conditions in the diamond anvil cell sample chamber before, during, and after laser heating are mapped by employing standard materials as in situ pressure markers. Unit cell volumes of Pt, MgO, and NaCl were monitored by synchrotron-based x-ray diffraction at temperatures between 300 and 2290 K and pressures ranging from 14 to 53 GPa. To aid in interpreting the resulting pressure–volume–temperature paths, we perform a series of model calculations of the high-temperature, high-pressure x-ray diffraction behavior of platinum subjected to a general stress state. Thermal pressure and thermal expansion effects within the laser-heated volume are observed but are not sufficient to fully explain the measured paths. Large apparent pressure changes can also result from relaxation of deviatoric stresses during heating and partial reintroduction of those stresses during quench. Deviatoric stresses, monitored from both diffraction peak widths and lattice parameter shifts as a function of (hkl), may significantly distort equation of state results if it is assumed that the sample is under hydrostatic pressure. Large-scale, nearly isothermal pressure relaxation events are observed at ∼2000 K. It is proposed that these arise from relaxation of heated components (pressure medium, gasket, cell itself) outside of the directly laser-heated volume.

Urinary aldehydes as indicators of lipid peroxidation in vivo

The excretion of malondialdehyde (MDA), lipophilic aldehydes and related carbonyl compounds in rat and human urine was investigated. MDA was found to be excreted mainly in the form of two adducts with lysine, indicating that its predominant reaction in vivo is with the lysine residues of proteins. Adducts with the phospholipid bases serine and ethanolamine and the nucleic acid bases guanine and deoxyguanosine also were found. Except for the adduct with deoxyguanosine (dG-MDA), the excretion of these compounds increased with peroxidative stress imposed in the form of vitamin E deficiency or the administration of iron or carbon tetrachloride. Marked differences in the concentration of dG-MDA in different tissues were correlated with their content of fatty acids having three or more double bonds, the putative source of MDA. Fourteen nonpolar and eleven polar lipophilic aldehydes and other carbonyl compounds were identified as their 2,4-diphenylhydrazine derivatives in rat urine. The excretion of five nonpolar and nine polar compounds was increased under conditions of peroxidative stress. The profile of lipophilic aldehydes obtained for human urine resembled that for rat urine. Except for a reported 4-hydroxynon-2-enal conjugate with mercapturic acid, the conjugated forms of the lipophilic aldehydes excreted in urine remain unidentified. Aldehyde excretion is influenced by numerous factors that affect the formation of lipid peroxides in vivo such as energy status, physical activity and environmental temperature, as well as by wide variations in the intake of peroxides in the diet. Consequently, urinalysis for aldehydic products of lipid peroxidation is an unreliable indicator of the general state of peroxidative stress in vivo.

Micromechanics-based stress–strain behaviour of soils at small strains

A model that describes the small-strain behaviour of soils is derived using micromechanics theory. The model allows examination of the effects of fabric anisotropy, stress conditions and contact characteristics on the small-strain modulus of soils. The closed-form solutions of the small-strain modulus are presented for the case of an isotropic fabric assembly under isotropic stress conditions. A fabric tensor is used to model the fabric anisotropy, and the small-strain modulus for the case of cross-anisotropic fabric assembly under general stress conditions is numerically calculated. The effect of the contact condition between soil particles is examined by incorporating three different contact laws (the linear elastic, Hertz–Mindlin and rough-surface contact models) into the model. It was found that the numerical results using the rough-surface contact model compare well with the published experimental data, and that the model provides microscopic insight into the small-strain behaviour of soils observed in the laboratory.

Modeling of dynamic failure by nucleation and growth processes

It is well established that high rate failure of structural materials takes place by rate processes occurring at the micro level and involving nucleation, growth, and coalescence of voids or cracks. At the submicroscopic level, the mechanism of failure in materials is dislocation controlled. The process of deformation and failure can be described by plastic glide that involves the mechanism of dislocation pile-ups. A new physically based model describing these processes is proposed. The effects of inertia and rate sensitivity on the growth process, and porosity are examined The model formulation is three-dimensional and is suitable for a general state of stress and strain. The model constants are calibrated through numerical simulations of one dimensional strain based plate impact experiments. To demonstrate the generality of model to predict spall under multiaxial loading conditions, an experimental configuration in which a flyer plate impacts the base of a solid right circular cone has been simulated. The computational modeling has been performed with thermomechanical coupling. The mechanical threshold stress plasticity model, the new proposed failure model, and the equation of heat conduction have been implemented in the finite element code Abaqus. Results from these simulations are presented and discussed in comparison with the experimental results. This shows the capability of the model in matching the experimentally observed spall patterns in the solid cone.

Fractal Long‐Range Correlations in Behavioural Sequences of Wild Chimpanzees: a Non‐Invasive Analytical Tool for the Evaluation of Health

Quantitative evaluation of health impairments in wild chimpanzees was explored using fractal long‐range correlations of behavioural sequences. The health status of 13 chimpanzees in the Mahale Mountains National Park, Tanzania was evaluated non‐invasively using standard behavioural observation and parasitological analysis of stool samples. Based on these data, individuals were classified as being either healthy or sick. Behavioural sequences were analysed and shown to exhibit long‐range power law correlations. The behavioural sequences of individuals in healthy and sick states were quantitatively evaluated using detrended fluctuation analysis of social and non‐social behaviours within behavioural sequences. These values were compared and significant differences in long‐range correlations were found between health states. Sex differences were also noted, with female social behaviour displaying a larger fractal dimension than male social behaviour. The fractal dimension of females declined significantly in sick individuals. This analysis of behaviour provides a new and effective non‐invasive method to record and evaluate the general state of health and related stress of animals in the wild. Possible applications of this method in captive situations include the monitoring and evaluating of stress levels over time.

A constitutive model for rock accounting for viscosity and yield stress degradation

Abstract A viscoplastic constitutive model of rock is proposed for which both yield stress and viscosity undergo variation during the deformation process. The model is initially formulated for a uniaxial stress state; its extension for a general stress state is also provided. Model parameters are determined from compression tests at different values of strain rate, and its application to simulate results of such tests is given. The examples of stress redistribution in a coal seam due to progressing longwall exploitation are presented by applying the developed degradation model. The model provides good simulation of material response in both stable and post-critical stages.

CtsR, a novel regulator of stress and heat shock response, controls clp and molecular chaperone gene expression in gram-positive bacteria.

clpP and clpC of Bacillus subtillis encode subunits of the Clp ATP-dependent protease and are required for stress survival, including growth at high temperature. They play essential roles in stationary phase adaptive responses such as the competence and sporulation developmental pathways, and belong to the so-called class III group of heat shock genes, whose mode of regulation is unknown and whose expression is induced by heat shock or general stress conditions. The product of ctsR, the first gene of the clpC operon, has now been shown to act as a repressor of both clpP and clpC, as well as clpE, which encodes a novel member of the Hsp100 Clp ATPase family. The CtsR protein was purified and shown to bind specifically to the promoter regions of all three clp genes. Random mutagenesis, DNasel footprinting and DNA sequence deletions and comparisons were used to define a consensus CtsR recognition sequence as a directly repeated heptad upstream from the three clp genes. This target sequence was also found upstream from clp and other heat shock genes of several Gram-positive bacteria, including Listeria monocytogenes, Streptococcus salivarius, S. pneumoniae, S. pyogenes, S. thermophilus, Enterococcus faecalis, Staphylococcus aureus, Leuconostoc oenos, Lactobacillus sake, Lactococcus lactis and Clostridium acetobutylicum. CtsR homologues were also identified in several of these bacteria, indicating that heat shock regulation by CtsR is highly conserved in Gram-positive bacteria.

Brittle behaviour of granitic magma: the example of Puente del Congosto, Iberian Massif, Spain

Abstract The magmatic structures appearing in the Puente del Congosto granitic outcrop (central Iberian Massif) are described in this work. They are interpreted as the result of a complex interplay between viscous (Newtonian) and brittle behaviour of granitic magma, which allowed the newer magma pulses to intrude and deform older magma batches. A model of Newtonian magma intruding a linear viscoelastic host rock may be extended with some confidence to the case of magma into magma emplacement. The resulting structures combine the characteristics of dykes and diapirs. The formation of large batholiths might be initiated or entirely accomplished by this process. In order to investigate the influence of the general stress conditions characteristic of a given tectonic regime on the strength of granitic magma, an over-simplified macroscopic model considering mixed Newtonian and brittle behaviour has been developed in this work. The brittle response is simulated by the Modified Griffith criterion, so that only rough estimates of the critical differential stresses for brittle magma behaviour can be gained. The results of this model suggest that the brittle response of viscous granitic magmas is possible for any type of tectonic regime (specially under contractional tectonics). A comprehensive, physically sound model for this viscous-brittle behaviour of granitic magma is not yet available. Integrated theoretical, experimental and field-based studies are the best way to arrive at such a complete model.