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Showing papers on "von Mises yield criterion published in 1990"


Book
01 Jan 1990
TL;DR: In this article, the authors present a review of plasticity in geotechnical engineering, focusing on nonlinear stress analyses in soil mechanics, and present a model based on the Cauchy elastic model.
Abstract: Part I. FUNDAMENTALS. 1. Introduction. Characteristics of soil behavior.Idealizations and material modeling. Historical review of plasticity in soil mechanics. Nonlinear stress analyses in geotechnical engineering. Need, objectives and scope. References. 2. Basic Concept of Continuum Mechanics. Introduction. Notations. Stresses in three dimensions. Definitions and notations. Cauchy's formulas, index notation, and summation convention. Principal axes of stresses. Deviatoric stress. Geometrical representation of stresses. Strains in three dimensions. Definitions and notations. Deviatoric strain. Octahedral strains and principal shear strains. Equations of solid mechanics. Equations of equilibrium (or motion). Geometric (compatibility) conditions. Constitutive relations. Summary. References. Part II. MATERIAL MODELING-BASIC CONCEPTS. 3. Elasticity and Modeling . Introduction. Elastic models in geotechnical engineering. Linear elastic model (generalized Hooke's law). Cauchy elastic model. Hyperelastic model. Hypoelastic model. Uniqueness, stability, normality, and convexity for elastic materials. Uniqueness. Drucker's stability postulate. Existence of W and v. Restrictions - normality and convexity. Linear elastic stress-strain relations. Generalized Hooke's law. A plane of symmetry. Two planes of symmetry (orthotropic symmetry). Transverse and cubic isotropies. Full isotropy. Isotropic linear elastic stress-strain relations. Tensor forms. Three-dimensional matrix forms. Plane stress case. Plane strain case. Axisymmetric case. Isotropic nonlinear elastic stress-strain relations based on total formulation. Nonlinear elastic model with secant moduli. Cauchy elastic model. Hyperelastic (green) model. Isotropic nonlinear elastic stress-strain relations based on incremental formulation. Nonlinear elastic model with secant muduli. Cauchy elastic model. Hyerelastic model. Hypoelastic model. Summary. References. 4. Perfect Plasticity and Modeling. Introduction. Deformation theory. An illustrative example. Variable moduli models. Flow theory. Yield criteria. Flow rule. Basic requirements. Perfect plasticity models. Tresca and von Mises models. Coulomb model. Drucker-Prager model. Prandtl-Reuss stress-strain relations. Generalized stress-strain relations. Stiffness formulation. General description. Stiffness coefficients. Summary. References. 5. Hardening Plasticity and Modeling. Introduction. Flow theory. Loading function. Hardening rule. Flow rule. Drucker's postulate. Hardening plasticity models. Lade-Duncan model. Lade model. Nested yield surface models. Generalized multi-surface models. Bounding surface models. Prandtl-Reuss stress-strain relations. Prandtl-Reuss equations. Matrix form of Prandtl-Reuss equations. Generalized stress-strain relations. Incremental stress-strain relations. Isotropic hardening. Kinematic hardening. Mixed hardening. Stiffness formulation. General description. Stiffness coefficients. Summary. References. PART III.

191 citations


Journal ArticleDOI
TL;DR: In this paper, the deformation theory of plasticity is used to model the stress-strain characteristics of the adhesive, with the stressstrain curve itself being approximated by any continuous mathematical function.

151 citations


Journal ArticleDOI
TL;DR: A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operators as discussed by the authors, and the relative accuracy of two algorithms is assessed by means of iso-error maps.
Abstract: Algorithms based upon the notion of return mapping have been developed for the Hill yield function of anisotropic plasticity. The relative accuracy of two algorithms is assessed by means of iso-error maps. The choice of the algorithm turns out to be much more critical for the orthotropic Hill criterion than for the underlying isotropic von Mises plasticity model. A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator. The model has been applied to three shell/plate structures.

140 citations


Journal ArticleDOI
TL;DR: In this article, a constitutive model for anisotropic continuum damage mechanics using finite strain plasticity is presented, where the von Mises yield criterion is modified to include the effects of damage through the use of elastic energy equivalence.

124 citations


Journal ArticleDOI
TL;DR: It is shown that strain energy density and the defined closed effective stress can predict apparent density and that they give predictions consistent with the observed density pattern in the femoral head and neck.

79 citations


Journal ArticleDOI
TL;DR: In this article, an analysis method was developed that predicts the strain distribution in deep drawn sheet parts based on plane stress characteristic theory, which neglects both normal and shear stresses acting across the thickness of the material.

49 citations


Journal ArticleDOI
TL;DR: The notion of yield stress has proved to be quite useful in practice in describing the steady shear rheological behavior of a range of materials especially of particulate suspensions.
Abstract: Within the general category of so called generalized Newtonian fluids, there exists a class of materials which do not deform until the applied shear stress exceeds a critical value called yield stress Conversely, such a material behaves like a solid as long as the shear stress is less than the yield stress This class of materials is called viscoplastic fluids The question whether the true yield stress exists or not is indeed far from settled (1), but the notion of a yield stress has proved to be quite useful in practice in describing the steady shear rheological behaviour of a range of materials especially of particulate suspensions Consequently, yield stress appears as a parameter in all constitutive relations (which purport to describe the steady shear behaviour of viscoplastic materials), and its evaluation is important before an engineering flow problem can be solved Conversely, there are some simple hydrodynamic situations which allow the value of the yield stress to be extracted from macroscopi

38 citations


Journal ArticleDOI
TL;DR: In this article, a general finite element program for the nonlinear analysis of steel and concrete structures is described, where the concept of equivalent strain is used to establish independent stress-strain relationships in the directions of orthotropy.
Abstract: Various aspects of a general finite‐element program for the nonlinear analysis of steel‐and‐concrete structures is described. The program accounts for the nonlinear behavior of concrete, steel, and shear connectors. Concrete is treated as an orthotropic nonlinear material. The concept of equivalent strain is used to establish independent stress‐strain relationships in the directions of orthotropy. Steel is modeled as an elastoplastic strain‐hardening material, and classical theory of plasticity together with the von Mises failure criterion is applied. For shear connectors, an empirical nonlinear shear force—slip relationship is used. The accuracy and reliability of the program are demonstrated by the analysis of two composite beams and a multigirder bridge over the entire loading range up to failure. The analytical results are compared with the corresponding experimental and/or field data with good agreement between the two. The reported results demonstrate the feasibility and reliability of the nonlinear...

32 citations


Journal ArticleDOI
TL;DR: In this paper, a constitutive model for the stress-strain-time behavior of cohesive soils is developed using Cam-clay plasticity theory extended to include time-dependent effects.
Abstract: A constitutive model for the stress‐strain‐time behavior of cohesive soils is developed using Cam‐clay plasticity theory extended to include time‐dependent effects. The model adopts the concept of separating the total deformation into immediate and delayed components. The immediate plastic deformation is evaluated by employing the associative flow rule on each of two distinct yield surfaces defined by the ellipsoid of the modified Cam‐clay theory and the Von Mises cylinder inscribed in the Cam‐clay ellipsoid. The delayed component of deformation is evaluated by employing the normality rule on equivalent ellipsoidal and cylindrical yield surfaces associated with the current state of stress of the soil and forcing the resulting creep strain rate tensor to satisfy phenomenological creep laws. In a companion paper by the same writers, the resulting constitutive equation is shown to predict the stress‐strain‐time behavior of wet clays more accurately than an earlier version based on a single‐yield‐surface form...

29 citations


Journal ArticleDOI
TL;DR: In this paper, a three-dimensional viscoelastic-plastic model for flow of particle filled polymer melts has been formulated based upon a modification of the Leonov model by introducing a structure function describing stress generated by the presence of the dispersed phase under the assumption that the material obeys the von Mises yielding criterion before flow takes place.
Abstract: A three‐dimensional viscoelastic‐plastic model for flow of particle filled polymer melts has been formulated. The approach is based upon a modification of the Leonov model by introducing a structure function describing stress generated by the presence of the dispersed phase under the assumption that the material obeys the von Mises yielding criterion before flow takes place. The model has been applied to steady simple shear and to transient shear flows, and equations have been derived for the components of stress tensor for each flow situation. A verification of the model has been made against limited experimental data available in the literature, indicating that the model is in fair agreement with experiments.

28 citations


Journal ArticleDOI
TL;DR: In this article, the von Mises yield criterion is adopted instead of the Tresca yield criterion for crack tip plasticity, and the modified model predicts that cyclic deformation behaviors at a crack tip are dependent not only on the amplitude of load fluctuations but also on the mean level at which the load is being cycled, revealing that at least two parameters are necessitated if the rate of fatigue crack propagation is to be predicted more accurately.

Journal ArticleDOI
TL;DR: In this paper, a new yield function based on theoretical developments by Frishmuth and McLaughlin and on experiments by Coffin was implemented as a user-written element in a commercial finite element package.
Abstract: A method has been developed to predict stress development in gray iron foundry castings. A new yield function, based on theoretical developments by Frishmuth and McLaughlin,9 and on experiments by Coffin10 was implemented as a user-written element in a commercial finite element package. The yield function takes into account the strong dependence of the yield stress in cast irons on the loading path. Stresses resulting from thermal displacements in the cooling casting are computed using the new yield function in an elastic-viscoplastic stress analysis. In earlier work, techniques were developed to represent the mold in the thermal analysis by sets of boundary conditions on the surface of the part. For this work, a second user-written element was used to apply force-displacement boundary conditions on the surface of the casting to represent the mechanical constraint of the mold. The properties for this element were based on soil mechanics considerations. Example problems are given, showing a substantial difference in the computed stresses when using the present formulation, in comparison to results obtained with the more usual von Mises yield function.

Journal ArticleDOI
TL;DR: In this article, a generalized expression for the estimation of the power required in the spinning of long tubes is presented, in which the material is assumed to be perfectly plastic and to obey the Von Mises Criterion of yielding, and the tools are considered to be rigid.

Journal ArticleDOI
TL;DR: In this article, a non-proportional biaxial compression experiment has been developed where a rectangular block first undergoes uni-axial compression and then, after finite deformation, it is subjected to large deformations (up to 45% strain) under biaxonial compression; however, density measurements after unloading indicate negligible change in density or volume.

Journal ArticleDOI
TL;DR: The mode coupling and mode interaction raise the question of whether anisotropic living tissues respond directly to stress or to some other physical quantity such as strain or strain energy, in view of the recent hypothesis concerning the proliferation and ossification of cartilage.

Journal ArticleDOI
TL;DR: In this article, a bonding technique for the joining together of tubular sections which are under axial loading was discussed and the yielding of polymers was studied and the criterion which was eventually used in the analyses was a modification of the Von Mises one.

Journal ArticleDOI
TL;DR: In this article, tension and compression tests were conducted on powder-extruded, binary NiAl between 300 and 1300 K. The results indicated that below the brittle-to-ductile transition temperature (BDTT) the failure mechanism in NiAl involves the initiation and propagation of cracks at the grain boundaries which is consistent with the von Mises analysis.
Abstract: NiAl has only three independent slip systems operating at low and intermediate temperatures whereas five independent deformation mechanisms are required to satisfy the von Mises criterion for general plasticity in polycrystalline materials. Yet, it is generally recognized that polycrystalline NiAl can be deformed extensively in compression at room temperature and that limited tensile ductility can be obtained in extruded materials. In order to determine whether these results are in conflict with the von Mises criterion, tension and compression tests were conducted on powder-extruded, binary NiAl between 300 and 1300 K. The results indicate that below the brittle-to-ductile transition temperature (BDTT) the failure mechanism in NiAl involves the initiation and propagation of cracks at the grain boundaries which is consistent with the von Mises analysis. Furthermore, evaluation of the flow behavior of NiAl indicates that the transition from brittle to ductile behavior with increasing temperature coincides with the onset of recovery mechanisms such as dislocation climb. The increase in ductility above the BDTT is therefore attributed to the climb of the 001 line type dislocations which in combination with dislocation glide enable grain boundary compatibility to be maintained at the higher temperatures.

Book ChapterDOI
TL;DR: In this paper, a 2D simulation of a rough elastic cylinder normally loaded on a plane-coated elastic medium is presented, and the effect of soft and hard coatings on the rough contact sure field is significantly altered by the surface roughness.
Abstract: A 2D simulation of a rough elastic cylinder normally loaded on a plane coated elastic medium is presented. The effect of soft and hard coatings on the rough contact sure field is significantly altered by the surface roughness. The presence of a soft coating greatly reduces these perturbations and Von Mises stresses under the surface. Hard coatings also reduce these stresses, but in a less order, and for thicknesses less than 10μm the maximum Von Mises stress is located at the coating/substrate interface.

Journal ArticleDOI
TL;DR: A unified numerical integration formula (UNIF) is derived, which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately.
Abstract: The accuracy of numerical integration of the perfectly plastic constitutive equation of von Mises is examined. Based on the analysis of the three existing numerical integration schemes a unified numerical integration formula (UNIF) is derived, which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately. According to the UNIF there are, in fact, many integration schemes depending on the direction of the trial stress. The validity of the UNIF is verified by presenting ten contours of constant angular error calculated with the UNIF. We then come to the conclusion that the three widely used schemes are by no means the most accurate ones. Some other schemes with better accuracy are thereby suggested. The determination of the number of substeps is also discussed in conjunction with the UNIF, when a multi-step method is used.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the stress behavior at the surface and in the near-surface region of layered (surface-coated) solids in concentrated sliding contact using the finite element method.
Abstract: The stress behaviour at the surface and in the near-surface region of layered (surface-coated) solids in concentrated sliding contact is investigated using the finite element method. Of particular interest is the behaviour of an elastic layer on an elastic substrate normally loaded by an elastic indenter and taking account of tangential loading at the interface. Stress contour plots are generated for “hard” and “soft” layers when expressed in terms of von Mises' shear strain energy criterion normalized with respect to the maximum Hertz stress. The consequences of varying parameters such as friction coefficient, elastic modulus and layer thickness are examined.

Journal ArticleDOI
TL;DR: In this paper, negative plastic flow and its prevention in elasto-plastic numerical analyses, such as finite element computations, are investigated in detail, with specializations for materials obeying the von Mises yield condition and its associated flow rule.

Journal ArticleDOI
TL;DR: In this paper, an analysis model for the elasto-plastic analysis of continuous fiber-reinforced composite structures is presented, which uses the material properties of each constituent separately instead of the smeared global properties obtained from the lamination theory.

DissertationDOI
01 Jan 1990
TL;DR: In this article, the authors investigated the structures of the near-tip stress and deformation fields in elastic-plastic solids and provided a preliminary asymptotic analysis for crack tip stress and velocity fields in Eulerian finite element meshes with extremely small elements near the crack tip.
Abstract: The present finite element study addresses several issues of interest pertaining to the phenomenon of dynamic crack propagation in elastic-plastic solids. Three classes of materials, namely elastic-perfectly plastic materials, linear hardening materials and power-law hardening materials, are considered. The materials are assumed to obey the von Mises yield criterion and the associated flow rule. Under conditions of Mode I, plane stress, steady state and small scale yielding, we investigated the structures of the near-tip stress and deformation fields. A preliminary asymptotic analysis for crack-tip stress and velocity fields in elastic-perfectly plastic solids was provided to reveal and explain some special features of the crack tip fields observable only in the case of rapid crack propagation. We studied the theoretical basis of a fracture criterion based on the dynamic stress intensity factor for crack growth in materials which fail in a locally ductile manner. We explored the behavior of crack tip fields under non-K-dominance conditions and its effects on the dynamic fracture toughness vs. crack propagation speed relationship. An Eulerian finite element scheme is employed. Finite element meshes with extremely small elements near the crack tip are carefully designed. The ratio of the crack tip plastic zone size to that of the element nearest to the crack tip is of the order of 1.6 x 10[superscript 4]. In order to overcome numerical difficulties associated with crack-tip strain singularities and the use of small near-tip elements, an efficient stress integration algorithm is devised. The existing stress state determination procedure is modified to prevent the occurrence of negative plastic flow and to avoid mistakenly treating elastic unloading as plastic flow. The above measures are proven to be essential for the convergence of the numerical solution.

Journal ArticleDOI
TL;DR: In this article, a two-dimensional hybrid experimental-numerical technique for elastic-plastic stress analysis is presented, which results from merging two relatively new technologies in engineering mechanics: boundary element methods and image processing.
Abstract: A two-dimensional hybrid experimental-numerical technique for elastic-plastic stress analysis is presented. This technique results from merging two relatively new technologies in engineering mechanics: boundary-element methods and image processing. A syntactic pattern recognition scheme, termed ‘displacement pattern matching’ (DPM), determines the displacement boundary conditions which are used in an elasticplastic boundary-element method (EPBEM) code. The result is an automated stress-analysis tool. Displacement pattern matching is a process where displacements are measured by tracking an arbitrary array of ‘black’ spots on a ‘white’ specimen. The digitized images of the specimen are compared in a double-exposure format to determine displacements. Displacement pattern matching is a full-field technique, with spatial resolution on the order of. 1 pixels. Displacement pattern matching supplies the actual specimen displacement increments to the EPBEM code which is based on a von Mises, isotropic work-hardening constitutive model. Given these displacements and free surface conditions, EPBEM is able to incrementally calculate the internal state of stress at selected locations. Results obtained for a variety of geometries and loading conditions compared well with ANSYS finite-element solutions and selected published experimental solutions and therefore are encouraging.

Journal ArticleDOI
TL;DR: In this article, a new discretely stiffened plate theory for the elasto-plastic large deflection (full-range) analysis of pressure loaded ring-stiffened circular plates is introduced.

Journal ArticleDOI
TL;DR: In this article, an algorithm for generating von Mises variates using Forsythe's method was described, with respect to speed, and compactness, and the performance was analyzed with respect of speed, compactness and efficiency.
Abstract: An algorithm is described for generating von Mises variates using Forsythe's method. The performance is analysed with respect to speed, and compactness. Conclusions are drawn as to when it is preferred to Best and Fisher's envelope rejection method.

Journal ArticleDOI
TL;DR: In this paper, the elastic-plastic analysis based on a combination of the finite element method (FEM) and the body force method (BFM) is applied to the subsurface layer under cyclic pass of rolling-sliding contact loading.
Abstract: The elastic-plastic analysis based on a combination (FEM+BFM) of the finite element method (FEM) and the body force method (BFM) is applied to the elastic-plastic analysis of the subsurface layer under cyclic pass of rolling-sliding contact loading. Two types of hardening rule are assumed. One is the isotropic hardening rule (IHR) and another is the kinematic hardening rule (KHR), i. e. Prager rule. If the material obeys IHR, so-called shakedown phenomenon is induced during the early cycle of pass of loading. On the other hand, if the material obeys KHR, the quasi-steady cumulative forward flow develops at the load level of q0/ks7, where q0 is the peak Hertzian pressure and k is the shear yield strength in von Mises' yield criterion. No apparent difference is found in the cyclic increment of the equivalent plastic strain range Δe^-p in the subsurface layer for the coefficient of friction=+0.1 and -0.1. The amount of the experimentally observed forward flow was more than the numerical results for IHR and less than those for KHR.

01 Jan 1990
TL;DR: In this paper, the moment of internal stresses is expressed as a function of the curvature of the bend, sheet thickness and properties of the material, and the constitutive equations given, one can calculate the configuration of a sheet metal in bending and predict its elastic springback on removing load.
Abstract: V-die bending is a non-steady state forming process, in which bending moment varies during forming; stress--strain distribution differs in different cross-sections of a bend. By assuming that an isotropic-hardening von Mises material undergoes plane bending, the moment of internal stresses is expressed as a function of the curvature of the bend, sheet thickness and properties of the material. With the constitutive equations given, one can calculate the configuration of a sheet metal in bending and predict its elastic springback on removing load. The theoretical results have been compared to the experimental data, and good agreement has been found. Materials were: DRQ 1147, DOCOL 220, DOCOL 260, and SIS 2322. Graphs. 10 ref.--AA

Journal ArticleDOI
TL;DR: In this paper, an analytical model is developed to study the evolution of stress field in the creeping matrix during the high-temperature deformation of a particle-reinforced composite, and, by which, to determine the development of creep strain of the two-phase system.

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional failure criterion is developed in a form of quadratic tensor polynomial with the fundamental strength function expressed in a sine series, which has the operational flexibility of any desired degree of accuracy.
Abstract: A three-dimensional failure criterion is developed in a form of quadratic tensor polynomial with the fundamental strength function expressed in a sine series. This criterion has the operational flexibility of any desired degree of accuracy. It can be shown that the present theory is a generalization of the Von Mises yield criterion. One of the main features of this criterion is that it does not require shear strength properties. The flexibility and accuracy of this theory are justified through its comparison with the experimental data for three material systems under uniaxial tension, uniaxial compression and biaxial loading. Comparisons are also made with several existing failure criteria.