Showing papers on "von Mises yield criterion published in 2002"

Non-convex potentials and microstructures in finite-strain plasticity

Abstract: A mathematical model for a finite–strain elastoplastic evolution problem is proposed in which one time–step of an implicit time–discretization leads to generally non–convex minimization problems. The elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations. The results for a single slip–system and von Mises plasticity illustrate that finite–strain elastoplasticity generates reduced problems with non–quasiconvex energy densities and so allows for non–attainment of energy minimizers and microstructures.

A Critical Reexamination of Classical Metal Plasticity

Abstract: P. W. Bridgman's early work on flow and fracture in the presence of hydrostatic pressure showed no systematic effect on strain hardening. This experimental observation led to the conclusions that yielding does not depend on hydrostatic stress and that the yielded material is incompressible. Classical plasticity theory was largely built on these observations. New experiments and nonlinear finite element analyses of 2024-T351 aluminum notched round bars has quantified the effect of hydrostatic tensile stresses on yielding. Nonlinear finite element analyses using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (yielding is linearly dependent on hydrostatic stress) yield functions was performed. The von Mises results overestimated experimental load-displacement curves by 10?65 percent. The Drucker-Prager results essentially matched the experimental results. The only additional data requirement for the Drucker-Prager yield function is the compressive yield strength. ©2002 ASME

A simplified method for elastic large deflection analysis of plates and stiffened panels due to local buckling

Abstract: A computational model for analysis of local buckling and postbuckling of stiffened panels is derived. The model provides a tool that is more accurate than existing design codes, and more efficient than nonlinear finite element methods. Any combination of biaxial in-plane compression or tension, shear, and lateral pressure may be analysed. Deflections are assumed in the form of trigonometric function series. The deformations are coupled such that continuity of rotation between the plate and the stiffener web is ensured, as well as longitudinal continuity of displacement. The response history is traced using energy principles and perturbation theory. The procedure is semi-analytical in the sense that all energy formulations are derived analytically, while a numerical method is used for solving the resulting set of equations, and for incrementation of the solution. The stress in certain critical points are checked using the von Mises yield criterion, and the onset of yielding is taken as an estimate of ultimate strength for design purposes.

Effects of Edge-Stiffening Elements and Diaphragms on Bridge Resistance and Load Distribution

Abstract: This research investigates the effects of barriers, sidewalks, and diaphragms (secondary elements) on bridge structure ultimate capacity and load distribution. Simple-span, two-lane highway girder bridges with composite steel and prestressed concrete girders are considered. The finite-element method is used for structural analysis. For the elastic range, typical secondary elements can reduce girder distribution factors (GDF) between 10 and 40%, depending on stiffness and bridge geometry. For the inelastic response, steel is modeled using von Mises yield criterion and isotropic (work) hardening. Concrete is modeled with a softening curve in compression with the ability to crack in tension. At ultimate capacity, typical secondary elements can reduce GDF an additional 5 to 20%, and bridge system ultimate capacity can be increased from 1.1 to 2.2 times that of the base bridge without secondary elements, depending on bridge geometry and secondary-element dimensions.

Mechanical Properties and Fracture Characterization of Cross-Linked PVC Foams:

Abstract: The tensile stress-strain response and fracture behavior of cross-linked PVC foams have been characterized over a range of foam densities from 36 to 400 kg/m3. The foams were found to be nearly isotropic. Young’s modulus, yield strength and fracture toughness data were compared to micro-structural relations derived for open and closed-cell foams. The failure process and stress strain response were indicative of brittle material behavior. Short gage length tension specimens bonded to aluminum loading blocks showed a tensile strength that increased with decreasing gage length as a result of improved support of the cell-walls of the foam under constrained lateral deformation. The plastic zone size for each of the fracture specimens, estimated from the von Mises yield criterion, was small indicating quasi-brittle failure. Testing of scaled single edged notch bend (SENB) fracture specimens revealed a toughness that decreases with decreasing specimen size.

A fast, one-equation integration algorithm for the Lemaitre ductile damage model

Abstract: This paper introduces an elastic predictor/return mapping integration algorithm for a simplified version of the Lemaitre ductile damage model, whose return mapping stage requires the solution of only one scalar non-linear equation. The simplified damage model differs from its original counterpart only in that it excludes kinematic hardening. It can be used to predict ductile damage growth whenever load reversal is absent or negligible—a condition met in a vast number of practical engineering applications. The one-equation integration scheme proves highly efficient in the finite element solution of typical boundary value problems, requiring computation times comparable to those observed in classical von Mises implementations. This is in sharp contrast to the previously proposed implementations of the original model whose return mapping may require, in the most general case, the solution of a system of 14 coupled algebraic equations. For completeness, a closed formula for the corresponding consistent tangent operator is presented. The performance of the algorithm is illustrated by means of a numerical example. Copyright © 2002 John Wiley & Sons, Ltd.

Three-dimensional analysis of single pile response to lateral soil movements

Abstract: Three-dimensional finite element analysis was carried out to investigate the behaviour of single piles subjected to lateral soil movements and to determine the ultimate soil pressures acting along the pile shaft. The finite element analysis program ABAQUS was used for the analysis and run on a SUN Workstation. The von Mises constitutive model was employed to model the non-linear stress–strain soil behaviour. The pile was assumed to have linear elastic behaviour. This was considered to be a reasonable approximation, as the maximum stress developed in the pile did not exceed the yield stress of the concrete pile. The length of the pile is 15 m, the width of the square pile is 1 m. The three-dimensional finite element mesh used in the analysis was optimized taking into account the computing capacity limitations of the Sun Workstation. The computed ultimate soil pressures agreed well with those from the literature. The shapes of the soil pressure versus soil movement curves and the soil pressure versus the relative soil–pile displacement curves as well as the magnitude of the relative soil–pile displacement to mobilize the ultimate soil pressures were in reasonable agreement with those reported by other researchers. Copyright © 2002 John Wiley & Sons, Ltd.

A Comparative Analysis Based on Different Strength Criteria for Evaluation of Risk Factor for Dental Implants

Abstract: A numerical analysis is developed to study the interaction phenomena between endousseus titanium dental implants and surrounding jawbone tissue. The interest is focused on the most appropriate evaluation of the stress state arising in the tissue because of the implant under physiological loading. The problem is considered with regard to linear elastic response of the one and to short time effect. Different configurations of bone-implant system are described, using axial-symmetrical and three-dimensional models, by means of finite and geometric element method. The investigation attains to the stress states induced in bone that lead to a limit condition near the effective failure surface. The parameter commonly adopted in literature, such as the Von Mises stress, represents an excessive simplification of problem formulation, leading to an incorrect evaluation of the real failure risk for the implant, due to the assumption of the isotropic and deviatoric nature of the adopted stress measure. More suitable criterion can be assumed, such as the Tsai-Wu criterion, to take into account the anisotropy that characterises the response of bone, as well as the influence of a hydrostatic stress state. The analysis developed offers a comparison of results by using different criteria, leading to an evaluation of reliability of the procedure to be followed and addressing also to an evaluation of a risk factor for the implant investigated.

Inelastic deformations of rotating variable thickness solid disks by tresca and von mises criteria

Abstract: Inelastic stresses and displacements in rotating solid disks of exponentially varying thickness have been investigated using Tresca's and von Mises' yield criteria. In both criteria, linear strain hardening material behavior is assumed. A previously obtained analytical solution is adopted in the analysis when Tresca criterion is used. An efficient numerical solution procedure has been designed to obtain the solution of von Mises. Plastic limit angular velocities have been calculated for different values of the geometric parameters. In all the cases investigated the difference between Tresca and von Mises, in finding plastic limit angular velocities was less than 3%. The inelastic stresses, displacement and strains have been calculated for disks of different profiles and the results presented in graphical forms.

Finite element simulation of the static characteristics of a vehicle rubber mount

Abstract: The static and dynamic characteristics of the rubber mounts for vibration isolation in automotive powertrains and other dynamic systems should be predicted during their design and development stage. In this paper, the static characteristic simulation of a rubber mount is performed using the finite element method. The modelling and simulation methods for a large deformation rubber spring represented by axisymmetric, quarter-symmetric and three-dimensional finite element models are investigated by using finite element analysis software PATRAN for meshing and ABAQUS and ADINA for computations. The predicted vertical static elastic characteristics of the rubber spring agree well with the experimental results. The static strain-stress analysis of the rubber part shows that the von Mises stress can be adopted as a stress measure for the rubber material. Moreover, the modelling methods for the large deformation rubber mount are investigated with numerical tests of elastic characteristics. The hybrid elem...

Sliding Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces

Abstract: A three-dimensional numerical model is presented to investigate the quasi-static sliding contact behavior of layered elastic/plastic solids with rough surfaces. The model is applicable for both single-asperity contact and multiple-asperity contacts. The surface deformation is obtained based on a variational principle. The surface and subsurface stresses in the layer and the substrate are determined with a Fast Fourier transformation (FFT) based scheme and von Mises and principal tensile stresses are computed accord-ingly. Contact statistics, such as fractional contact area, maximum pressure/E 2 and relative meniscus force are predicted. The results are used to investigate the effect of the contact statistics on friction, stiction, and wear problems such as debris generation. brittle failure, and delamination of layered media. Optimum layer parameters are identified. It allows the specification of layer properties, according to the contact statistics, to reduce friction, stiction, and wear of materials. A normalization procedure is presented to apply the results on various combinations of surface roughness, material properties, and normal load.

Work of fracture and cohesive stress distribution resulting from triaxiality dependent cohesive zone model

Abstract: A new law has been proposed to describe the distribution of the cohesive forces present within the internally structured nonlinear zone that precedes the leading edge of a moving crack contained within a nonelastic solid. The nonlinear effects are modeled by the narrow strips emanating from the crack front and endowed with a certain internal structure (unlike the classic models of Barenblatt and Dugdale). The bulk of the material, though, is assumed to behave as linear elastic solid. Mathematical form the law resembles somewhat the Planck's formula used to explain radiation given off by a perfectly black body at very short wavelength of the visible light spectrum. With Sneddon's integral transformations employed and properly modified, the quantities essential in the Nonlinear Mechanics of Fracture have been quantified. In particular another so-called `ubiquitous eta factor' is discussed and related to the material microstructure by means of a certain transcendental equation. The eta-factor enters the formula for the specific work of fracture measured with specimens of various geometrical and loading configurations, and so far is known only empirically. Both the stationary and quasi-static crack problems are discussed. It has been shown that the variations in the microstructural parameters strongly affect the process zone along with the associated work of separation. The other important factors that influence the cohesive stress distribution and all the resulting fracture parameters, specifically those that are responsible for a ductile-to-brittle transition of fracture mode, are the characteristics of the state of stress induced in the vicinity of the crack front. These 3D effects are best represented by the triaxiality parameter, defined as the ratio of the mean stress to the von Mises effective stress

An Analysis of Filament Overwound Toroidal Pressure Vessels and Optimum Design of Such Structures

Abstract: This paper is concerned with the membrane shell analysis of filament overwound toroidal pressure vessels and optimum design of such pressure vessels using the results of the analysis by means of mathematical nonlinear programming. The nature of the coupling between overwind and linear has been considered based on two extreme idealizations. In the first, the overwind is rigidly coupled with the liner, so that the two deform together in the meridional direction as the vessel dilates. In the second, the overwind is free to slide relative to the linear, but the overall elongations of the two around a meridian are identical. Optimized designs with the two idealizations show only minor differences, and it is concluded that either approximation is satisfactory for the purposes of vessel design. Aspects taken into account are the intrinsic overwind thickness variation arising from the winding process and the effects of fiber pre-tension. Pre-tension can be used not only to defer the onset of yielding, but also to achieve a favorable in-plane stress ratio which minimizes the von Mises equivalent stress in the metal liner. Aramid fibers are the most appropriate fibers to be used for the overwind in this type of application. The quantity of fiber required is determined by both its short-term strength and its long-term stress rupture characteristics. An optimization procedure for the design of such vessels, taking all these factors into account, has been established. The stress distributions in the vessels designed in this way have been examined and discussed through the examples. A design which gives due consideration of possible mechanical damage to the surface of the overwind has also been addressed.

Elastic-plastic finite element analysis for the head-disk interface with fractal topography description

Abstract: An elastic-plastic contact analysis based on a finite element model and real surface topographies was performed to elucidate the evolution of deformation at the head-disk interface. The topographies of the head and disk surfaces were represented by an equivalent profile generated using a modified two-variable Weierstrass-Mandelbrot function, with fractal parameters determined from images of head and disk surfaces. A region of the equivalent rough surface profile was selected for analysis based on topography scale considerations and contact simulation results. The evolution of plasticity and the likelihood of cracking in the overcoat and the magnetic layer are interpreted in light of results for the subsurface von Mises equivalent stress, equivalent plastic strain, and maximum first principal stress. The finite element model provides insight into the elastic-plastic deformation behavior of the layered medium in terms of the thickness, mechanical properties, and residual stress in the carbon overcoat.

Non-linear boundary element analysis of plates applied to concrete slabs

Abstract: In this work the BEM non-linear formulation for Kirchhoff's plates in bending applied to model reinforced concrete slabs is discussed. The integral equations of displacements, bending and twisting moments and shear forces are derived and modified properly to model non-linear behaviours. Two models were implemented to analyse reinforced concrete slabs: a simple elastoplastic criterion defined by adopting the Von Mises surface to govern the concrete behaviour in compression complemented by assuming tension cut off; and the Mazars' continuum damage model. For both cases, the reinforcement is governed by the uniaxial stress x strain elastoplastic relationship with constant hardening. Internal forces are approximated by numerical integrals along the plate thickness using a Gauss' scheme, after verifying the non-linear criterion at each point.

Finite element analysis studies of a metal-ceramic crown on a first premolar tooth

Abstract: PURPOSE This study examined the stresses developed during loading in a first premolar metal-ceramic crown made of different metal cores, and used them to anticipate the locations and form of the most likely failure modes. The maximum principal stresses in the porcelain are indicators of fracture, and the von Mises stresses in the metal core are indicators of the location of yielding. MATERIALS AND METHODS Two-dimensional axisymmetric models with different core metals were analyzed using finite element analyses. An axial load of 600 N was applied vertically downward, over a circular area around the crown's fissure. RESULTS The peak maximum principal tensile stress in the porcelain existed on the surface of the crown, partially outside the cusp, with the greatest peak in the gold-porcelain system (15.8 MPa). An inverse relationship between the peak maximum principal tensile stress of each system and the elastic modulus of each core material was found. According to evaluation of the critical flaw size for each system, even a crack completely through the thickness of the porcelain was not critical. The maximum von Mises stress existed in the metal coping, on the radial edge at the axial/occlusal line angle, with the highest maximum in the nickel-chromium system (143.9 MPa). There existed a proportional relationship between the maximum von Mises stress in each metal and their respective elastic moduli. All maximums were well below the yield strength of the metal alloys used. CONCLUSION A greater understanding of the influence of an axial load on the resulting stresses has been achieved, showing that the phenomena of fracture and yielding are unlikely for the crown experiencing this axial load.