Normal Stress Space Research Articles

Thermomechanical deformation of the orthotropic shell taking into account the deformation anisotropy

A variant of the rotation shell in the particular form of a closed circular cylindrical shell, which is often used in the design practice of civil, power and other industrial structures, is considered. The specificity of the considered shell lies in the features of its material, which has a manifestation of dual anisotropy. In particular, this material is orthotropic in structure, and the nature of deformation shows the dependence of stiffness and strength on the type of stress state. The loading of the shell is assumed to be axisymmetric, taking into account the influence of a medium with variable thermal parameters. The temperature difference between the shell surfaces is taken into account here. The statement of the general thermomechanical problem is carried out in an unrelated form, taking into account a certain independence of the problems of thermodynamics and mechanics. Taking into account the limitations of the classical thermomechanical theories of shells made of materials with dual anisotropy and the fact that the known models for such materials have significant drawbacks, the authors used a variant of the normalized stress space. Differential equations of thermoelasticity for a cylindrical shell are obtained, taking into account the complicated thermomechanical properties of its material. Particular solutions with the features of the results of calculating the shell states are illustrated, and their analysis is carried out.

The normal stress space and its application to constructing a new failure criterion for cross-anisotropic geomaterials

The principal stress space has been traditionally used to describe and formulate isotropic strength criteria for materials, but it has limited functionality for anisotropic behavior, as it does not incorporate any information on material structure. In this paper we introduce a Normal Stress Space (NSS) comprising three normal stresses in the material coordinate system to represent interactions between the stress tensor and material structure. Using NSS we then develop an extension of the well-known isotropic Matsuoka-Nakai (MN) criterion to describe the anisotropic shear strength of rock based on geometric considerations rather than algebraic tensor manipulations. This new criterion, called Anisotropic Matsuoka-Nakai (AMN) criterion, describes failure across bedding and foliation planes, while sliding along these planes of weakness is well described by the Coulomb criterion. True triaxial test data on chlorite schist and Chichibu Green schist obtained from the literature are then used to validate the proposed criterion. Reasonable agreement is obtained for both true triaxial datasets, providing encouraging validations of the proposed AMN-Coulomb failure criterion for describing both the strength and failure mode of cross-anisotropic rocks under complex stress conditions.

Fatigue life of a railway wheel under uniaxial and multiaxial loadings

In this paper, a railway wheel material is under evaluation using multiaxial fatigue testing. The experiments were conducted using a servo-hydraulic machine with standardized specimens. All samples were machined from a single worn-out railway wheel. The damage scale between normal and shear stresses was evaluated in the normal stress space for proportional and non-promotional loadings. Moreover, the uniaxial SN curves were obtained. A critical plane analysis was performed using theoretical criteria and experimental results. Results show a strong influence of heat treatments on the material fatigue behavior.

Lower Order Rectangular Nonconforming Mixed Finite Elements for Plane Elasticity

In this paper, we present two stable rectangular nonconforming mixed finite element methods for the equations of linear elasticity in two space dimensions which produce direct approximations for the stress and displacement. In the first method, the normal stress space of the matrix-valued stress space is taken as the second order rotated Brezzi–Douglas–Fortin–Marini element space [F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991], the enriched nonconforming rotated $Q_1$ element [Q. Lin, L. Tobiska, and A. H. Zhou, IMA J. Numer. Anal., 25 (2005), pp. 160–181] is taken for the shear stress, and the lowest order Raviart–Thomas element space [P. A. Raviart and J. M. Thomas, in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer-Verlag, New York, 1977, pp. 292–315] is employed to approximate the vector displacement field. The second method is obtained from the first one through dropping the interior degrees of the normal stress on each element. A first order convergence rate is obtained for both the stress and the displacement for these methods based on the superconvergence of the enriched nonconforming rotated $Q_1$ element.

Behavior of concrete cylinders confined by a carbon composite 3. Deformability and the ultimate axial strain

Results of an experimental investigation into the mechanical properties of concrete cylinders confined by a carbon-epoxy composite wrapping are presented. It is shown that, for all the con fined con crete spec i mens tested, the loading paths in the normalized stress space follow a single master curve, what ever the concrete strength and confinement intensity. At stresses in the confined concrete exceeding the strength of plain concrete, the tangent modulus was found to depend on the slope angle of the master curve and the asymptotic value of the differential Poisson ratio (the first derivative of the lateral strain with respect to the axial one). Formulas for predicting the ultimate axial strain and the tangent modulus are derived and compared with the corresponding fib (federation internationale du beton) recommendations.

Behavior of concrete cylinders confined by carbon composite 2. Prediction of strength

The mechanical behavior of round concrete cylinders confined by a carbon-epoxy composite wrapping is analyzed concerning the increased concrete compression strength due the wrapping. It is shown that the loading trajectories in the normalized stress space fit into a single master curve for all the concrete batches and jacket thicknesses investigated. The loading paths ended at failure of the composite wrapping from the increased internal lateral pressure. The strength of the composite was determined by split-disc tests of composite rings, but the strength of composite jackets realized on concrete specimens did not reach the strength of the rings. Therefore, a coefficient of composite strength reduction was introduced. A simple formula for predicting the strength of confined concrete is derived, and a comparison with fib (federation internationale du beton) recommendations for strength predictions is given.

An interpretation of structural degradation for three natural clays

The mechanical behaviour of natural clays is influenced by the degradation of the microstructure induced by the applied loads. The consequence of progressive damage to the natural microstructure is that it is not possible to describe the state of the soil in terms of effective stress components and void ratio only, and therefore it is not possible to locate a unique state boundary surface by normalizing stresses with respect to the equivalent pressure. In this paper it is shown that, by defining a normalizing pressure that accounts for the progressive loss of structure occurring during a test, the state of the soil during loading can be completely described in a normalized stress space. The laws linking the normalizing pressure to the degree of microstructure disruption are derived from the isotropic hardening laws of two constitutive models recently proposed for natural soils. The normalizing procedure is applied to the experimental results obtained on three natural clays of different depositional origin and with different mechanical properties. For the three clays, the parameters describing structure degradation permit the assessment of the rate of loss of structure with plastic strains. For the clays examined, the volumetric plastic strains are seen to play a major role, compared to the deviatoric plastic strains, in causing progressive disruption of the microstructure. Lastly, it is shown that the initial degree of structure and the rate of structure degradation can be related to the depositional conditions and the stress history of the clay deposits.Key words: clays, compressibility, fabric–structure of soils, laboratory tests, plasticity, shear strength.

A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behaviour

AbstractIt is demonstrated that an efficient framework for the description of a two surface kinematic hardening/bounding surface plasticity model can be devised if the model is conceived in a normalized stress space in which the bounding surface remains of constant size. The hardening of the bounding surface is contained in the transformation laws linking ‘real’ and ‘normalized’ stresses while the geometric rules controlling kinematic hardening are considered only in terms of normalized stresses.Within the general framework thus constructed, two particular models are developed in outline. Owing to the proposed anisotropic hardening, these models are shown to have the ability to reproduce the observed characteristics of the progressive destructuration of natural cemented clays and of the plastic anisotropy of reconstituted soils. Copyright © 2001 John Wiley & Sons, Ltd.

Undrained response of loosely compacted sands during monotonic and cyclic compression tests

Undrained monotonie compression tests were conducted on loose sand samples subjected to an initial isotropic stress state, and undrained cyclic compression tests with no shear stress reversal were performed on loose sand samples subjected to initial anisotropic stress, in order to establish the stress conditions needed for triggering contractive flow deformation and the corresponding steady-state characteristics. It was shown that the peak strength envelope was also the triggering strength envelope, which appears to be unique for samples prepared by the moist tamping method and independent of stress path. It was established that the failure envelope for a given sand is unique but that the steady-state strength was not unique and was dependent on void ratio and stress conditions at the onset of flow failure. The use of normalized stress space is very helpful in the analysis of undrained monotonie and cyclic compression tests and permits ready prediction of strain-softening and strain-hardening behaviour. An analysis of data on various sands has shown that the stress conditions at the time of triggering contractive flow deformation and those at steady state can be related to the slope of the steady-state lines. Deux types d'essais ont été realises sur des échantillons de sable meuble. Dans le premier type d'essais, l'échantillon est soumis à un état initial de contrainte isotrope suivi d'une compression monotone non-drainée. Le second type d'essais se décompose, quant à lui, en un état initial de contrainte anisotrope suivi de cycles de compression non-drainées. Ces essais ont permis d'étudier les conditions de contrainte nécessaires au déclenchement d'une déformation plastique de contraction ainsi que les caractéristiques de l'état permanent associé. Il apparaît que l'envelope des contraintes ultimes est également celle des contraintes de déclenchement. Elle semble être unique, pour des échantillons prépares à l'aide de la méthode des tassements humides, et indépendante du chemin des contraintes. Il a été établi que si l'enveloppe de rupture est unique pour un sable donné, la résistance à l'état permanent ne l'est pas et dépend de l'indice des vides et des conditions de contraintes existant au début de la rupture plastique. L'utilisation d'un espace des contraintes normalisé est tres utile pour l'analyse des essais non drainés de compressions cycliques ou monotones et permet de prédire simplement les ramollissements ou durcissements de déformation. Une analyse des données obtenues sur différents sables montre que les conditions de contrainte an début de la déformation plastique de contraction, ainsi que celles de l'état permanent, peuvent être corrélées avec la pente des droites de l'état permanent.

The behaviour of very loose sand in the triaxial compression test

Very loose sand is defined as sand whose state is significantly looser than its critical state. The detailed stress-strain behaviour of very loose sand in triaxial compression is described for the first time within the framework of critical state soil mechanics. It is shown that the undrained behaviour of very loose sand under static loading can be rationalized by normalization with respect to the critical state, an approach that has been successful when applied to clays and to sands dense of critical. Strain contours in normalized stress space are presented for several sands and are shown to be remarkably consistent. The observed normalized behaviour is used to develop a simple constitutive model for the behaviour of very loose sands, based on plasticity theory. It is demonstrated that this model can be used successfully to predict the essential features of the behaviour of very loose sands in undrained and drained triaxial compression including cyclic loading conditions. The model includes the strain softening that occurs in very loose sands in conditions of impeded drainage and the cumulative increase in pore pressure that occurs during undrained cyclic loading. It can be used to predict the onset of liquefaction, a phenomenon only exhibited by very loose sands and quick clays. Key words: sand, liquefaction, triaxial test, cyclic loading, steady state testing, collapse surface.

The liquefaction of sands, a collapse surface approach

Recent large-scale slides occurring during the hydraulic placement of an artificial island berm in the Beaufort Sea resulted from the liquefaction of the berm sand. Subsequent laboratory tests and back analyses have led to advancements in the understanding of the liquefaction potential of sand. Analyses of undrained triaxial tests, undertaken to measure steady state parameters, suggest that there is a "collapse surface" in three-dimensional void ratio – shear stress – normal stress space. A necessary condition for liquefaction is that the soil state lie on this surface. This collapse surface concept is fundamentally an extension of the steady state concepts proposed by others, and in many respects follows the principles of critical state soil mechanics. Replotted published tests support the concept. Parameters used to describe the position of the surface are termed collapse parameters. These can be converted into parameters analogous to Mohr–Coulomb failure parameters and can therefore be used in conventional limit equilibrium stability analyses. Utilizing these parameters overcomes limitations inherent in previously proposed undrained steady state analysis methods. These concepts also provide a basis for a rational explanation of the Beaufort Sea hydraulic fill slides. Key words: liquefaction, sand, hydraulic fill, slope stability, steady state testing.

Optimal reinforcement of a material in a known state of stress

The problem of minimizing the total reinforcement of a material in a known state of stress is considered. In the proposed geometric formulation the problem reduces to the determination in normal stress space of the shortest path from a point representing the state of stress to the region of strength. Examples of the determination of the relative area of reinforcement in three-dimensional and plane states of stress are given for characteristic regions of strength: for plane stress and plane strain the calculations lead to expressions that permit the relative areas of reinforcement to be determined directly.