Incremental Stress-strain Relations Research Articles

On the Incremental Stress-Strain Relations of an Elastic Medium

On the Incremental Stress-Strain Relations of an Elastic Medium

The strain hardening behaviour of particulate media

The strain increment resulting from an increment of stress applied to a particulate medium has been expressed in terms of its elastic and plastic components. The concepts of strain-hardening plasticity have been employed to develop an incremental stress–strain relation, based on a non-associated flow rule. The parameters appearing in the relation have been found using results of three-dimensional shear tests on sands and glass-microspheres. It is suggested that relations of the type developed in the paper could be beneficially incorporated into a finite-element program.

Anisotropic Stress-Strain Relationship of Clay and its Application to Finite Element Analysis

Anisotropically consolidated natural deposits of clay show the stress-strain responses in different ways for the cases of active and passive loadings. This is caused by the anisotropy in initial stress states of normally consolidated or overconsolidated clays. Incremental stress-strain relations of anisotropically preconsolidated clays are derived from their consolidation and dilatancy characteristics with the help of associated flow rule. Obtained stress-strain relations give reasonable explanations to the anisotropy in mechanical behaviour of anisotropically preconsolidated clays. Integrations of the incremental stress-strain relations- give the stress-strain relations under specified loading conditions or some restrictions on the deformation of clay. The finite element analysis may be one of the powerful means to analyse the stress and strain fields in clay layers consolidated anisotropically in which there exist two different patterns of stress-strain response due to the loading systems, active and passive. As an example, the stress and strain fields in normally and anisotropically consolidated clay layers stressed by a uniform strip load are computed with the finite element technique using the above mentioned anisotropic stress-strain relations.

An Elastic-Plastic Formulation for a Cylindrical Shell Finite Element

Theme A N elastic-plastic formulation is presented for a curved ./^rectangular thin shell finite element. Elastic-perfectly plastic material behavior is assumed. The von Mises yield criterion is used to define the limit of plasticity. Plastic strain distributions and a distribution for an elastic-plastic boundary in the element are defined. Incremental stress-strain relations are developed for use in the plastic range. With this formulation and an incremental approach, yielding can be traced in a deforming shell and displacements, and stresses can be found at each increment of load.

Effective Stress-Strain-Strength Model for Soils

An analytical model is proposed that treats soil as an elastic-plastic strain-hardening or strain softening, frictional material. The formulation, which is based on the critical state model developed by Cambridge University, ties together undrained and drained loading situations, and nonlinear behavior is accounted for by specifying appropriate yield functions and using an associative flow rule. Mathematically simple but realistic yield functions are proposed to facilitate closed-form solutions. The incremental stress-strain relationships are developed for use in finite element analyses, and, as an illustration. the drained expansion of a cylindrical cavity (pressure meter test) is analyzed.

On nonlinear kinematic hardening plasticity theory

Experimental data for metals, e.g. stainless steel, at elevated temperatures show that the loop of the stress-strain curve obtained in a cyclic tension test grows in size in a bounded fashion with each successive cycle. This implies that either the material follows isotropic hardening during its initial deformation phase from the virgin state, or that the material obeys the kinematic hardening rule by maintaining constant elastic range but with continuously increasing hardening. The known experimental data seems to favor the latter assumption, in which case the classical linear kinematic hardening rule could not adequately describe the cyclic behavior of the material. It becomes necessary, therefore, to generalize the linear hardening rule to nonlinear hardening and furthermore to make the shape of the plastic portion of the stress-strain curve variable with the number of cycles. This paper presents a development of a nonlinear kinematic hardening rule which admits the use of nonlinear stress-strain curves whose shapes can be varied as functions of the number of cycles. It will be shown that the proposed rule leads to a yield surface that depends explicitly on past history in a special way. It will also be shown that, within the original framework of Prager's kinematic hardening postulate, the proposed generalization to nonlinear hardening admits radial as well as nonradial loading for initially isotropic material. A Ramberg-Osgood form of the stress-strain curve will be utilized to demonstrate the utility of the method and, by making the parameters in the stress-strain curve cycle dependent, a cyclic stress-strain curve which grows with the number of cycles can be adequately represented. Finally, an incremental stress-strain relation which can be used in structural analysis is derived on the basis of the proposed nonlinear kinematic hardening rule.

A New Slip Theory of Plasticity

A slip theory is presented for the calculation of the incremental stress-strain relations of a face-centered cubic polycrystal such as aluminum and its alloys, from its experimental uniaxial curves. This theory satisfies the conditions of equilibrium, condition of continuity of displacement as well as the slip characteristics of the component crystals. Numerical calculations based on this theory give results which are in good agreement with known experimental data on thin wall cylinders subject to different ratios of incremental axial and torsional loadings after being compressed beyond the elastic range.

Elastoplastic and creep analysis with the ASKA program system

The objective of this article is a concise presentation of the extension of the general purpose program ASKA (Automatic System for Kinematic Analysis) to include material non-linearities such as plasticity and creep. A short derivation of the incremental stress-strain relations which form the basis of the iterative numerical procedure is given first, followed by a more detailed description of the relevant software package. An elastoplastic calculation of a pressure vessel as a typical application and suggestions for further developments conclude the article.

Nonisothermal Kinematic Hardening Law in Plasticity

The incremental stress-strain relations have been formulated for nonisothermal kinematic hardening materials in which the yield surface is assumed to change its size with temperature. By following Prager’s assumption, the yield surface undergoes a translation in the direction of the plastic strain increment during the plastic flow. As pointed out by Shield and Ziegler, the yield surface with Prager’s hardening rule, in general, does not satisfy the invariance requirement with respect to a reduction in dimensions in the stress space. Nevertheless, if the von Mises criterion is adopted, such a discrepancy would not arise. If, however, other types of criterion are used, such as Tresca criterion, Ziegler’s modification must be incorporated.

Note on Incremental Stress‐Strain Relations of Elasto‐Plastic Materials Referred to a Convected Coordinate Systems

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 52, Issue 3 p. 183-186 Kleine Mitteilungen Note on Incremental Stress-Strain Relations of Elasto-Plastic Materials Referred to a Convected Coordinate Systems Dr. H. Kitagawa, Dr. H. Kitagawa Associate Professor Faculty of Engineering, Osaka University, Yamadakami, Suita, Osaka. 565 (Japan)Search for more papers by this authorY. Tomita, Y. Tomita Graduate Student, Osaka UniversitySearch for more papers by this author Dr. H. Kitagawa, Dr. H. Kitagawa Associate Professor Faculty of Engineering, Osaka University, Yamadakami, Suita, Osaka. 565 (Japan)Search for more papers by this authorY. Tomita, Y. Tomita Graduate Student, Osaka UniversitySearch for more papers by this author First published: 1972 https://doi.org/10.1002/zamm.19720520312Citations: 4AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume52, Issue31972Pages 183-186 RelatedInformation

Finite Element Large Deflection Analysis of Elastic-Plastic Shells of Revolution Subjected to Axisymmetric Loading

This paper presents a finite element method for large deflection elastic-plastic analysis of shells of revolution. The piecewise linear procedure is employed and nonlinearity can be dealt with as the accumulation of linear analyses of numerous loading steps. As for the incremental stress-strain relation in the plastic range, Reuss' equation is used. Especially, a trial of method of treating snap-through buckling is proposed. Some numerical examples are given in order to demonstrate the validity of the present method, and the results are generally satisfactory.

Elastic Behavior of Cohesionless Soil

Elastic properties of a sand are studied in triaxial compression tests. It is shown that the elastic properties are only a function of the state of the soil as expressed by stress and void ratio; and that for samples with a given initial void ratio, the elastic properties vary both with deviator stress and mean normal stress. These elastic properties become anisotropic when a soil element is sheared, and this anisotropy appears to be a function of the stress ratio. Finally, an incremental elastic stress-strain relationship is presented.

Elastic-plastic analysis of two-dimensional stress systems by the finite element method

A method is described for the incremental elastic-plastic analysis of two-dimensional stress systems (plane stress, plane strain and axisymmetrically loaded body of revolution). The procedure is based upon the finite element method of stress analysis and uniformly stressed triangular elements are used. The derivation of the incremental stress-strain relationship from the Prandtl-Reuss equations and the Von Mises yield criterion is presented. Numerical examples are presented and are compared with experimental and theoretical results in the literature.

Incremental Strain Rate Ratios and Strength of Sand in the Triaxial Test

Synopsis Certain design problems in soil mechanics should be treated as deformation rather than failure problems and to this end incremental stress-strain relations must be developed for different types of soil. The incremental strain rate ratio given by the stress-dilatancy relation may prove valuable in such studies. A short account is given of the stress-dilatancy theory with particular reference to the concepts of the upper øcv and lower øμ, limits. The main object of the Paper is to investigate the conditions under which these limits are approached employing stress paths involving both loading and unloading in triaxial compression and extension. A major part of the Paper is devoted to a critical discussion of errors involved in drained triaxial tests on sand and to certain modifications developed to minimize these errors. The peak or failure points in the various tests have been studied to assess the failure criteria commonly applied to soils. It is shown that the extended Von Mises and Tresca criteria are inapplicable to sands for theoretical reasons alone. Dans les mécaniqucs du sol certains problèmes de réalisations doivent êtrc traités en tant que problèmes de déformation plutôt que de rupture et des relations de tension-déformation croissantes doivent être développées pour différents types de sol. Le coefficient croissant de déformation donné par la relation de tension-dilatabilité peut se révéler utile dans ces études. On donne un bref aperçu de la théorie de tension-dilatabilité avec une référence particulière sur les conceptions des limites supérieures øcv et inférieures øμ. Le but principal de l'article est de rechercher dans quelles conditions on s'approche de ces limites en se servant de passages de tension comprenant la charge ainsi que la décharge dans la compression triaxiale et la dilatation. Une partie essentielle de l'article concerne la discussion critique d'erreurs occasionnées dans des essais triaxiaux drainés sur sable, et certaines modifications développées pour réduire ces erreurs. Le maximum ou les pointes de rupture des divers essais ont été étudiés pour évaluer les critères de rupture habituellement appliqués aux sols. On montre que les critéres Dilatés Von Mises et Tresca sont inapplicables sur des bases théoriques seulement.

The effect of plasticity on the stress-distribution of thin notched plates in tension

An explicit solution of the stress-distribution in notched plates under conditions of plane-stress is given in the elasto-plastic domain of straining. The material is considered as elastic-perfectly plastic and isotropic obeying the Mises yield condition and the Prandtl-Reuss incremental stress-strain relations. Elastic and plastic components of strains are determined by using information from birefringent coatings cemented on the surface of the specimens and observed in normal circularly or linearly polarized light. These measurements are complemented with data from an electrical analogy which yield the ϵ x -strain distribution. Thin fat plates containing either symmetrical semi-circular grooves or deep notches of various flank angles are subjected to a uniform tension. Four cases of flank angles are considered lying between 0 and 120 deg. The minimum width of all plates is taken constant and equal to the half of the width of the plates. The analysis of the state of stress is restricted to the initial part of the loading path from an incipient plastic deformation up to an impending plastic flow. The variation of stress distribution with the evolution of plastic enclaves is studied and the influence of the severity of notches on the mode of spreading of plastic zones is determined.

On the Instability and Folding Deformation of a Layered Viscoelastic Medium in Compression

Abstract When a layer of material embedded in an infinite medium is subject to a compression parallel with the layer an instability tends to develop which manifests itself in the folding of the layer. This phenomenon is examined here for the general case where the layer and the surrounding medium are both viscoelastic. This problem which was examined in preliminary form in an earlier publication [6] is treated here with particular attention to the effect of interfacial adherence of the layer and the medium, and to an evaluation of the amplitude of the folding. In general there is a lower and upper-critical value of the compressive load between which folding occurs with a finite rate of deformation. There appears also a dominant wave length, for which the rate of folding is maximum under a given load. The dominant wave length may or may not depend on the load. The effect of interfacial adherence while not negligible is not generally significant. The rate of folding increases very rapidly beyond a certain value of the viscosity ratio of the two media. A brief discussion is also included of the thermodynamic implications of incremental stress-strain relations in prestressed media.

Stress-Strain Relations for a Simple Model of a Granular Medium

Abstract A granular assemblage is represented by a model consisting of like spheres in contact arranged in a simple cubic lattice. Based on consideration of local contact forces and concomitant deformations, incremental stress-strain relations are derived and subsequently integrated, for certain types of loading, to yield total stress-strain relations. The integration is carried out for both a loading and an unloading process. A criterion of failure for the model is set up and the theory applied to a regimen of loading which gives rise to a plane state of stress.

On the Use of Singular Yield Conditions and Associated Flow Rules

Abstract It is well known that the use of Tresca’s yield condition frequently leads to a simpler system of equations for the stresses in a plastic solid than the use of the yield condition of Mises. However, in most cases where Tresca’s yield condition has been used, the flow rule associated with the Mises condition has been retained. Following Koiter, it is shown that further simplification results from the use of the flow rule associated with the Tresca condition. The reason for this is discussed in connection with two examples concerning the finite enlargement of a circular hole in an infinite sheet of perfectly plastic or work-hardening material. The second example is probably the first nontrivial case in which a problem of finite plastic deformation of a work-hardening material has been treated in closed form by the use of incremental stress-strain relations.

The autofrettage of thick tubes with free ends

A Numericalanalysis is made of the expansion by internal pressure of a partially plastic open-ended tube of wall-ratio 2 : 1. This is based on the Prandtl- Reuss incremental stress-strain relations, together with the Tresca yield criterion. The calculated surface strains are described by simple formulae. Comparison is made with previous solutions based on total stress-strain relations.

Two new electrostatic generators developed for army engineers: Technical Data Digest, Vol. 15, No. 4.)

A constitutive model to simulate the elastic-plastic and slip actions of fusion magnets under operating or abnormal loads is outlined. To represent the elastic-plastic responses a unified material homogenization procedure based on the existing composite technology was applied to obtain an effective incremental stress-strain relationship for the heterogeneous, laminated magnets. The inter-layer slip behavior of the magnets was represented by a friction-type model from which slip deformation can be calculated for the situation where inter-layer shear stresses exceed the bonding strength of the adhesives. Numerical results of three example problems are presented to demonstrate the utility of the proposed model.