Showing papers on "von Mises yield criterion published in 2007"
TL;DR: Sternstein et al. as discussed by the authors proposed a new criterion for craze initiation based on linear elastic fracture mechanics and showed that the strain energy release rate, G I (nasc), required to generate a typical 20nm thick nascent craze, is less than 1 ǫm −2.
98 citations
TL;DR: In this paper, the deformation of a relatively low porosity porous titanium is examined using two-dimensional plane strain and three-dimensional finite element models to identify the accuracy and limitations of such simulations.
97 citations
TL;DR: In this paper, the authors investigated the formability of the AA5754-O by means of experimental tests supported by numerical analysis, where the following process parameters were taken into account: the temperature level of the blank in the center of the specimen and the forming speed; in addition standard grease lubricant was used.
87 citations
25 Feb 2007-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the responses of nanoindentation on bulk silicon were investigated using finite element analysis and a two-dimensional finite element model under the assumption of axisymmetry was successfully validated by the experimental load-displacement curve.
Abstract: In this paper, the responses of nanoindentation on bulk silicon were investigated using finite element analysis. A two-dimensional finite element model under the assumption of axisymmetry was successfully validated by the experimental load–displacement curve. Four factors: coefficient of friction, indentation depth, tip rounding and indenter geometry were investigated to characterize the induced responses of bulk silicon via load–displacement curve, indentation surface profile at the maximum loading depth, residual surface profile after unloading, plastic energy, elastic energy, Young's modulus, hardness, and elastic recovery. Coefficients of friction were found to be insignificant, but the von Mises stress distributions after unloading between frictionless and frictional surfaces, indentation depth, tip rounding, and indenter geometry all showed having a distinct effect on stress, plastic energy, elastic energy, Young's modulus, hardness, elastic recovery and surface profile. The degree of pile-up affecting the investigated factors is discussed as well.
76 citations
TL;DR: In this article, a three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction.
Abstract: A three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction. A Coulomb’s law is assumed for the friction, as commonly used for sliding contacts. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces are derived from Betti’s reciprocal theorem with initial strain. The main advantage of this approach over the classical finite element method (FEM) is the computing time, which is reduced by several orders of magnitude. The contact problem, which is one of the most time-consuming procedures in the elastic-plastic algorithm, is obtained using a method based on the variational principle and accelerated by means of the discrete convolution fast Fourier transform (FFT) and conjugate gradient methods. The FFT technique is also involved in the calculation of internal strains and stresses. A return-mapping algorithm with an elastic predictor∕plastic corrector scheme and a von Mises criterion is used in the plasticity loop. The model is first validated by comparison with results obtained by the FEM. The effect of the friction coefficient on the contact pressure distribution, subsurface stress field, and residual strains is also presented and discussed.
73 citations
TL;DR: In this paper, a theory of yielding and failure for homogeneous and isotropic materials is given, calibrated by two independent, measurable properties and from those it predicts possible failure for any given state of stress.
Abstract: A theory of yielding and failure for homogeneous and isotropic materials is given. The theory is calibrated by two independent, measurable properties and from those it predicts possible failure for any given state of stress. It also differentiates between ductile yielding and brittle failure. The explicit ductile-brittle criterion depends not only upon the material specification through the two properties, but also and equally importantly depends upon the type of imposed stress state. The Mises criterion is a special (limiting) case of the present theory. A close examination of this case shows that the Mises material idealization does not necessarily imply ductile behavior under all conditions, only under most conditions. When the first invariant of the yield/failure stress state is sufficiently large relative to the distortional part, brittle failure will be expected to occur. For general material types, it is shown that it is possible to have a state of spreading plastic flow, but as the elastic-plastic boundary advances, the conditions for yielding on it can change over to conditions for brittle failure because of the evolving stress state. The general theory is of a three-dimensional form and it applies to full density materials for which the yield/failure strength in uniaxial tension is less than or at most equal to the magnitude of that in uniaxial compression.
68 citations
TL;DR: In this paper, a description of flow curves for different microstructures has been realised using finite element calculations of representative volume elements within a continuum mechanical framework using the isotropic von Mises plasticity law for individual phases.
59 citations
TL;DR: In this paper, the results of a finite element analysis (FEA) used to simulate two-dimensional sliding between two interfering elasto-plastic cylinders are presented for both frictionless and frictional sliding and comparisons are drawn The effects of plasticity and friction on energy loss during sliding are isolated.
Abstract: This work presents the results of a finite element analysis (FEA) used to simulate two-dimensional (2D) sliding between two interfering elasto-plastic cylinders The material for the cylinders is modeled as elastic-perfectly plastic and follows the von Mises yield criterion The FEA provides trends in the deformations, reaction forces, stresses, and net energy losses as a function of the interference and sliding distance between the cylinders Results are presented for both frictionless and frictional sliding and comparisons are drawn The effects of plasticity and friction on energy loss during sliding are isolated This work also presents empirical equations thatt relate the net energy loss due to sliding under an elasto-plastic deformation as a function of the sliding distance Contour plots of the von Mises stresses are presented to show the formation and distribution of stresses with increasing plastic deformation as sliding progresses This work shows that for the plastic loading cases the ratio of the horizontal force to the vertical reaction force is non-zero at the point where the cylinders are perfectly aligned about the vertical axis In addition, a “load ratio” of the horizontal tugging force to the vertical reaction force is defined Although this is analogous to the common definition of the coefficient of friction between sliding surfaces, it just contains the effect of energy loss in plasticity The values of the contact half-width are obtained for different vertical interferences as sliding progresses
50 citations
TL;DR: In this paper, a semi-analytical model for the buckling of arbitrarily oriented, sniped stiffeners is presented and validated for a variety of plate and stiffener geometries.
48 citations
TL;DR: In this article, a semi-analytical method for pre-and postbuckling analysis of imperfect plates with arbitrary stiffener arrangements, subjected to in-plane biaxial and shear loading, is presented.
Abstract: A semi-analytical method for pre- and postbuckling analysis of imperfect plates with arbitrary stiffener arrangements, subjected to in-plane biaxial and shear loading, is presented. By using large deflection theory in combination with the Rayleigh–Ritz approach on an incremental form, the method is able to trace both local and global equilibrium paths. Ultimate strength predictions are made using the von Mises’ yield criterion applied to the membrane stresses as collapse criterion. A Fortran computer program based on the presented theory is developed and computed results are verified by comparisons with nonlinear finite element analysis. Relatively high numerical accuracy is achieved with small computational efforts. The method is therefore suited also for design optimisation and reliability studies.
46 citations
TL;DR: In this article, the optimum autofrettage pressure and the optimum radius of the elastic-plastic boundary of strain-hardening cylinders in plane strain and plane stress have been studied theoretically and by finite element modeling.
TL;DR: In this paper, the authors derived the fraction of the plastic work transformed into heat from thermodynamic considerations in a large-strain setting, and showed that for elasto-plasticity the fraction follows as a result of the choice of free energy, potential function and yield function.
Abstract: Heat generation due to plastic deformation of metals and steel is studied. Whereas in many investigations it is assumed that the fraction η of the plastic work transformed into heat is constant throughout the deformation process, the fraction η is here derived from thermodynamic considerations in a large-strain setting. It is shown that for elasto-plasticity the fraction η follows as a result of the choice of free energy, potential function and yield function. Taking the stress-strain response and the dissipative properties of the material as basis for calibration, it is shown that the thermodynamic framework of a thermoplastic material is non-unique for the general situation of non-associated plasticity. In the investigation conducted here, the mechanical response and the portion of the plastic work converted into heat (or into stored energy) during plastic deformations is predicted by means of isotropic hardening von Mises plasticity. It is shown that for a situation in which the internal variable is taken as the effective plastic, close fitting to experimental data requires a non-associated format of the evolution law for the internal variable.
TL;DR: In this paper, the authors considered the three-parameter family of symmetric unimodal distributions obtained by wrapping the location-scale extension of Student's t distribution onto the unit circle.
Abstract: This paper considers the three-parameter family of symmetric unimodal distributions obtained by wrapping the location-scale extension of Student's t distribution onto the unit circle. The family contains the wrapped normal and wrapped Cauchy distributions as special cases, and can be used to closely approximate the von Mises distribution. In general, the density of the family can only be represented in terms of an infinite summation, but its trigonometric moments are relatively simple expressions involving modified Bessel functions. Point estimation of the parameters is considered, and likelihood-based methods are used to fit the family of distributions in an illustrative analysis of cross-bed measurements. The use of the family as a means of approximating the von Mises distribution is investigated in detail, and new efficient algorithms are proposed for the generation of approximate pseudo-random von Mises variates.
TL;DR: Investigation of the thermal-mechanical performance of hydroxyapatite/titanium (HA/Ti) functionally graded (FG) dental implants with the three-dimensional finite element method finds that under the influence of occlusal force only, the FG implants with different HA fraction along the implant length perform almost equally well, while the titanium implant sustains much higher von Mises stress.
Abstract: This article investigates the thermal-mechanical performance of hydroxyapatite/titanium (HA/Ti) functionally graded (FG) dental implants with the three-dimensional finite element method. The stresses induced by occlusal force for the present HA/Ti FG implant are calculated to compare with the corresponding stresses for the titanium dental implant. Thermal-mechanical effect of temperature variation due to daily oral activity is also studied. The HA/Ti FG dental implant performance is evaluated against the maximum von Mises stress, which is the general performance indicator, the first principal/tensile stress for mechanical failure of implant-bone-bond and the third principal/compressive stress for bone absorption. Simulation results indicate that under the influence of occlusal force only, the FG implants with different HA fraction along the implant length perform almost equally well, while the titanium implant sustains much higher von Mises stress. However, when thermal stress is also considered, the FG implant having HA fraction exponential index of m = 2 with temperature decrease of 20 degrees C yields the highest first principal and von Mises stresses among all the FG and titanium implants.
TL;DR: In this paper, the problem of estimating bounds to shakedown loads for problems governed by a class of deviatoric plasticity models including those of Hill, von Mises, and Tresca is addressed.
Abstract: The problem of estimating bounds to shakedown loads for problems governed by a class of deviatoric plasticity models including those of Hill, von Mises, and Tresca is addressed. Assuming that an exact elastic solution is available, an upper bound to the elastic shakedown multiplier can be obtained relatively easily using the plastic shakedown theorem. A procedure for computing this upper bound for arbitrary load domains is presented. A number of problems are then examined and it is found that the elastic shakedown factor is given as the minimum of the plastic shakedown factor and the classical limit load factor. Finally, some exact solutions to a number of two dimensional problems are given.
TL;DR: In this article, a new formula was proposed to take into account phase differences in the determination of an equivalent von Mises stress power spectral density (PSD) from multiple random inputs.
TL;DR: It is concluded that the physical characteristics of posts were important on stress distributions in post and core applications and glass fiber post revealed more balanced stress distribution under functional forces.
Abstract: Objectives: To evaluate the effects of different post materials on the stress distribution in an endodontically treated maxillary incisor. Materials and Methods: A pseudo 3-dimensional finite element model was created in a labiolingual cross-sectional view of a maxillary central incisor and modified according to five posts with different physical properties consisting stainless steel, titanium, gold alloy, glass fiber (Snowpost), and carbon fiber (Composipost). A 200 N force was then applied from two different directions; a) vertical load on the incisal edge, b) 45 degree diagonal load above the cingulum location. Stress distribution and values were then calculated by considering the pseudo three dimensional von Mises stress criteria. Results: Under two loading conditions, post made of steel showed greatest stress concentration at the post/dentin interface followed by titanium, gold alloy, Snowpost and Composipost. However, Composipost, which elastic modulus was closer to the dentin, produced highest stress values at 1/3 cervical area. Conclusions: Within the limitation of this simulated mechanical analysis, we can conclude that the physical characteristics of posts were important on stress distributions in post and core applications. Glass fiber post revealed more balanced stress distribution under functional forces. (Eur J Dent 2007;2:67-71)
TL;DR: In this paper, a fatigue prediction method for spot welded joints in automotive body structures using an equivalent structural stress at the edge of spot welds is developed by substituting the stress components in von Mises equation to the local structural stresses at the vicinity of the spot weld.
TL;DR: In this article, a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat was performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method.
Abstract: The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio k—ranging from 1 to 16—and of the normal load—from 4.2 GPa to 8 GPa—are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.
TL;DR: In this paper, a simplified finite elements modeling of flexible pavements rut depth evolution with time has been developed based on the shakedown theory established by Zarka for metallic structures.
Abstract: A simplified method has been developed for the finite elements modelling of flexible pavements rut depth evolution with time. This method is based on the shakedown theory established by Zarka for metallic structures. The yield surface of Drucker-Prager and the plastic potential of Von Mises have been used. The simplified method determines straightforwardly the purely elastic state or the elastic shakedown state or the plastic shakedown state. The calibration of the simplified method with two unbound granular materials for roads under repeated loads triaxial tests, is explained. Then, a finite elements modelling of a flexible pavement has been carried out. Calculations of 2D and 3D have been performed and rut depth evolutions with time are shown, which underline the capabilities of the model to take into account the accumulation of plastic strains along the loading cycles. Copyright © 2006 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors present an elaboration of a code to estimate the size of the plastic zone at the crack tip under mode I, mode II and mixed mode I + II loading according to Von Mises and Tresca criteria.
TL;DR: In this article, a finite element-based shape optimization program was developed for three-dimensional shell structures and the shape optimization of shell structures has been performed by a job control language and a reliable finite element package program, ANSYS, is used for structural analysis.
TL;DR: The nonlinear least-squares functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based and Computational results for a benchmark problem of elasto-plasticity under plane strain conditions are presented.
Abstract: A least-squares mixed finite element method for the incremental formulation of elasto-plasticity using a plastic flow rule of von Mises type with isotropic hardening is presented. This approach is based on the use of the stress tensor, in addition to the displacement field, as independent process variables. The nonlinear least-squares functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based. For the finite element implementation under plane strain conditions, quadratic (i.e., next-to-lowest-order) Raviart-Thomas elements are used for the stress approximation, while the displacement is represented by standard quadratic conforming elements. Computational results for a benchmark problem of elasto-plasticity under plane strain conditions are presented in order to illustrate the effectiveness of the least-squares approach.
TL;DR: In this article, a semi-analytical method for the elastic buckling and buckling strength analysis of in-plane biaxial and shear loaded stiffened plates with varying, stepwise constant thickness is presented.
TL;DR: In this paper, a four node element for the analysis of 2D continua described by elastic-perfectly plastic von Mises laws is presented, which is based on the assumed stress approach which has been widely tested in the elastic field.
TL;DR: This work has shown that computer modeling can be a preferred tool for studying blistering, a common injury in sports and military operations that can adversely effect or even halt performance.
Abstract: Background/purpose: Friction blisters, a common injury in sports and military operations, can adversely effect or even halt performance. Given its frequency and hazardous nature, recent research efforts appear limited. Blistering can be treated as a delamination phenomenon; similar issues in materials science have been extensively investigated in theory and experiment. An obstacle in studying blistering is the difficulty of conducting experiment on humans and animals. Computer modeling thus becomes a preferred tool. Method: This paper used a dynamic non-linear finite-element model with a blister-characterized structure and contact algorithm for outer materials and blister roof to investigate the effects on deformation and stress of an existing blister by changing the friction coefficient and elastic modulus of the material in contact with the blister. Results: Through the dynamics mode and harmonic frequency approach, we demonstrated that the loading frequency leads to dramatic changes of displacement and stress in spite of otherwise similar loading. Our simulations show that an increased friction coefficient does not necessarily result in an increase in either the stress on the hot spot or blister deformation; local maximum friction stress and Von Mises stress exist for some friction coefficients over the wide range examined here. In addition, the stiffness of contact material on blistering is also investigated, and no significant effects on deformation and Von Mises stress are found, again at the range used. The model and method provided here may be useful for evaluating loading environments and contact materials in reducing blistering incidents. Conclusion: The coupling finite-element model can predict the effects of friction coefficient and contacting materials&apos stiffness on blister deformation and hot spot stress.
TL;DR: In this article, an augmented stress vector is defined and the original nonlinear differential equation system is converted to a quasi-linear one, then the dynamical system can be solved with an exponential map approach in a semi-implicit manner.
Abstract: Purpose – This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works.Design/methodology/approach – An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi‐linear one. Then the dynamical system can be solved with an exponential map approach in a semi‐implicit manner.Findings – The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate.Research limitations/implications – Von‐Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening.Practical implications – Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes.Origina...
TL;DR: In this article, a numerical model for the analysis of composite steel-concrete beams at elevated temperatures accounting for both longitudinal and transverse interaction is presented, and a prescriptive failure criterion based on the von Mises yield condition is proposed for shear connectors.
TL;DR: In this paper, a model for one-dimensional transversal oscillations of an elastic-ideally plastic beam is considered and the existence and uniqueness of a weak solution is proved based on spatially semidiscrete approximations.
Abstract: We consider a model for one-dimensional transversal oscillations of an elastic-ideally plastic beam. It is based on the von Mises model of plasticity and leads after a dimensional reduction to a fourth-order partial difierential equation with a hysteresis operator of Prandtl-Ishlinskii type whose weight function is given explicitly. In this paper, we study the case of clamped beams involving a kinematic hardening in the stress-strain relation. As main result, we prove the existence and uniqueness of a weak solution. The method of proof, based on spatially semidiscrete approximations, strongly relies on energy dissipation properties of one-dimensional hysteresis operators.