Showing papers on "von Mises yield criterion published in 2000"

Isotropic constitutive models for metallic foams

Abstract: The yield behaviour of two aluminium alloy foams (Alporas and Duocel) has been investigated for a range of axisymmetric compressive stress states. The initial yield surface has been measured, and the evolution of the yield surface has been explored for uniaxial and hydrostatic stress paths. It is found that the hydrostatic yield strength is of similar magnitude to the uniaxial yield strength. The yield surfaces are of quadratic shape in the stress space of mean stress versus effective stress, and evolve without corner formation. Two phenomenological isotropic constitutive models for the plastic behaviour are proposed. The first is based on a geometrically self-similar yield surface while the second is more complex and allows for a change in shape of the yield surface due to differential hardening along the hydrostatic and deviatoric axes. Good agreement is observed between the experimentally measured stress versus strain responses and the predictions of the models.

Limit analysis for a general class of yield conditions

Abstract: The paper describes a generalisation of the programming method described by Ponter and Carter (1997) for the evaluation of optimal upper bounds on the limit load of a body composed of a rigid/perfectly plastic material. The method is based upon similar principles to the `Elastic Compensation' method which has been used for design calculations for some years but re-interpreted as a non-linear programming method. A sufficient condition for convergence is derived which relates properties of the yield surface to those of the linear solutions solved at each iteration. The method is demonstrated through an application to a Drucker–Prager yield condition in terms of the Von Mises effective stress and the hydrostatic pressure. Implementation is shown to be possible using the user routines in a commercial finite element code, ABAQUS. The examples chosen indicate that stable convergent solutions may be obtained. There are, however, limits to the application of the method if isotropic linear solutions are used for an isotropic yield surface. In an accompanying paper (Ponter and Engelhardt, 2000) the method is extended to shakedown and related problems.

Shakedown Limits for a General Yield Condition: Implementation and Application for a Von Mises Yield Condition

Abstract: In previous papers [1,2], a procedure was described for the evaluation of limit loads and shakedown limits for a body subjected to cyclic loading. The procedure was based upon the “Elastic Compensation” method [9,10] where a sequence of linear problems are solved with spatially varying linear moduli. In [1] it was demonstrated that the method may be interpreted as a nonlinear programming method where the local gradient of the upper bound functional and the potential energy of the linear problem are matched at a current strain rate or during a strain rate history. This interpretation may be used to formulate a very general method for evaluating minimum upper bound solutions. Provided certain convexity conditions are satisfied, it is possible to define a sequence of linear problems where the functional monotonically reduces. The sequence then converges to the solution which corresponds to the absolute minimum of the functional, subject to constraints imposed by the class of strain rate histories under consideration. The theoretical basis for the method and convergence proofs are discussed in ref. [3,4].

Yield Functions and Flow Rules for Porous Pressure-Dependent Strain-Hardening Polymeric Materials

Abstract: To characterize the response of progressively damaged glassy polymers due to the presence and evolution of voids, yield functions and flow rules were developed systematically for a pressure-dependent matrix following the modified von Mises criterion. A rigid-perfectly plastic material was first assumed. The upper bound method was used with a velocity field which has volume preserving and shape changing portions. Macroscopic yield criterion in analytical closed form was first obtained for spherical voids which is valid for all possible macroscopic strain rate fields. Macroscopic yield criteria in analytical closed form were then obtained for cylindrical voids for the special cases of axisymmetric and plane-strain modes of deformation. The upper-bound solutions were subsequently improved to better match analytical solutions for pure hydrostatic loading. Characteristics of the yield function as a function of pressure dependency and void fraction were studied in detail. Generalization of the model for spherical voids to include elasticity as well as strain hardening of the matrix was then obtained. An example for the uniaxial response of a progressively damaged material was then used to illustrate one possible application of the full set of constitutive equations.

Application of Lade's Criterion to Cam-Clay Model

Abstract: Lade's criterion is one of the best criteria for describing the shear yield and failure behavior of soils in 3D stresses, and the original Cam-clay model is the most popular and fundamental elastoplastic model for normally consolidated clays. In this paper, a transformed stress tensor is proposed for combining Lade's criterion and the Cam-clay model. The transformed stress is deduced from what makes the curved surface of Lade's criterion become a cone with the axis being the space diagonal, i.e., Lade's criterion becomes the extended Mises type criterion in the transformed principal stress space. The Cam-clay model revised by Lade's criterion is capable of describing the mechanical behavior of soils in general stresses. It is presented that the revised model can simulate well the drained and undrained behavior of soils, not only under triaxial compression conditions, but also under plane strain, true triaxial, and hollow cylinder conditions. The elastoplastic models for soils, in which only the first and second stress invariants are used, can be extended simply to the model, including the third stress invariant by adopting Lade's criterion. where sij = deviator stress tensor; and dij = Kronecker's delta. Therefore, the Cam-clay model is generalized by assuming a section of the yield surface to be circular in the p-plane. That is to say, the extended von Mises criterion (q/p = const) was adopted for the shear yield and the shear failure of clay in the Cam-clay model. However, as experimental evidence shows, the extended Mises criterion grossly overestimates strength in triaxial extension, and also results in incorrect intermediate stress ratios in plane strain (Wroth and Houlsby 1985). It is well known that the failure of soils can be explained by the Lade's criterion (Lade and Duncan 1975; Lade 1977; Lade and Musante 1978), and others (Matsuoka and Nakai 1974), which incorporate the third stress invariant. Taking the consistency in the shear deformation and the shear failure into considera- tion, it is reasonable to introduce Lade's criterion or other cri- teria for the shear yield as well as the shear failure of soils. Based on such ideas, some researchers attempted to improve the Cam-clay model to a 3D model for soils (Zienkiewicz and Pande 1977; Randolph 1982). However, Wroth and Houlsby (1985) commented that further study is necessary to improve the Cam-clay model by combining the idea of critical state theory with such failure criteria as Lade and Duncan's (1975)

An examination of the stress distribution in a soft-lined acrylic resin mandibular complete denture by finite element analysis.

Abstract: Purpose The aim of this study was to calculate the effect of a soft liner on stress distribution within a mandibular complete denture. Although patients have welcomed soft-lined complete dentures, early fracture is one of the main reasons for failure. To minimize and prevent prosthesis fracture, the understanding of the stress distribution within a prosthesis is important. Materials and methods A 3-dimensional finite element model of a mandibular complete denture for a severely reduced residual alveolar ridge was constructed. The stress was calculated with linear static finite element analysis. The stress distribution in the soft-lined acrylic resin mandibular complete denture was compared with that of a conventional acrylic resin denture. The resulting stresses were displayed in terms of von Mises equivalent stress and the major principal stresses according to 5 different loading conditions: vertical loads in premolar, molar, and incisor regions; and oblique loads in premolar and molar regions. Results Oblique loads produced higher levels of stress in the labial notch regions than vertical loads, where tension was the primary mode of stress. Significantly reduced levels of von Mises stress were calculated in soft-liner layers under all loading conditions. Acrylic resin denture base portions, however, exhibited higher levels of von Mises stress in soft-lined complete dentures. Conclusion Three-dimensional finite element analysis gave a realistic explanation of denture fractures and patient response to mandibular complete dentures with and without soft linings. Control of excess lateral occlusal contact might be helpful to reduce the probability of a fracture in soft-lined mandibular complete dentures.

An experimental method to determine the complete stress-elongation relation for a structural adhesive layer loaded in peel

Abstract: An experimental method to determine the complete stress-elongation relation of a thin adhesive layer loaded in peel is presented. Experiments are performed on a DCB-specimen. Balance of the energetic forces is used to calculate the stress-elongation relation from experimental data. The calculation requires differentiation of the data, which puts great demands on the quality of data acquisition. The experiment is first simulated and random errors are added to simulate deficiencies in the experimental setup. These data are used to determine the required accuracy. Two sets of experimental results are presented and it is shown that a simple stress-elongation relation fits the data accurately. Elastic stiffness and fracture energy agrees favourably with independent measurements. An unexpected result is the low maximum strength of the adhesive. Independently performed uniaxil tension tests give the yield strength 30 MPa. Taking into consideration the constraint of the adhesive layer and using the von Mises yield criteria gives the expected yield strength 90 MPa. However, our tests give a maximum strength of about 20 MPa. This indicates that damage is a more important factor than plasticity for the peel properties of the adhesive layer.

Shear stress distribution in the trabeculae of human vertebral bone

Abstract: The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2>0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV = A + B exp(-x/C)]. The COV of the stress was higher for low volume fraction tissue (<0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading.

Triaxiality and Fracture of Steel Moment Connections

Abstract: The connections of welded steel moment frames undergo a complex multiaxial state of stress that leads to high levels of stress triaxiality. As triaxiality increases, the propensity for fracture increases. Classic engineering models of fracture and modern microscale models of fracture mechanisms explicitly consider the role of triaxiality. Nonetheless, triaxiality is generally not directly considered by structural engineers. In this paper, triaxiality is defined as the ratio of the maximum principal stress to the von Mises stress. Triaxiality and maximum principal stress demands are investigated for tests on fractured notched round bars, small-scale tension specimens, and a full-scale moment connection. Based on analysis of the tests, it is proposed that, for fractures driven by triaxiality demands, the maximum principal stress at fracture is a function of the level of triaxiality. Calculation of the triaxiality demands requires 3D nonlinear analysis and depends on the loading, connection geometry, and pos...

3D finite element analysis of tensile notched strength of 2/2 twill weave fabric composites with drilled circular hole

Abstract: This paper presents the micromechanical three-dimensional finite element models of the 2/2 twill weave T300 carbon/epoxy woven fabric composite laminates with drilled circular holes of different sizes. A fiber breakage failure criterion for predicting the ultimate tensile notched strength of fiber dominated composites is also proposed. It is found that the location of failure initiation for laminates with large hole size is different from those for laminates with smaller holes while the stress concentration may not occur at the notch roots for the fiber dominated laminates. Based on the uniaxial, shear and von Mises stress distributions in the yarn and matrix, the influence of hole-size on the stress distributions and stress concentration is discussed. Standard tensile tests with modifications are performed for this particular type of woven fabric composites. The apparent strain concentration factors and notched strengths determined by experiments are presented and the finite element models are verified by satisfactory correlation between prediction and experiment.

Estimating the Probability Distribution of von Mises Stress for Structures Undergoing Random Excitation

Abstract: The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. For deterministic loads, both static and dynamic, the calculation of von Mises stress is straightforward, as is the resulting calculation of reliability. For loads modeled as random processes, the task is different; the response to such loads is itself random process and its properties must be determined in terms of those of both the loads and the system. This has been done in the past by Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the problem. Here, we present a method that provides analytic expressions for the probability distributions of von Mises stress which can be evaluated efficiently and with good numerical precision. Further, this new approach has the important advantage of providing the asymptotic properties of the probability distribution.

Analysis of Material Nonlinear Problems Using Pseudo-Elastic Finite Element Method

Abstract: A method based on linear elastic finite element analysis is presented for stress field determination of elasto-plastic problems. Hencky’s total deformation theory is used to define effective material parameters, which are treated as spatial field variables and considered to be functions of final state of equilibrium stress and material properties. These effective material parameters are obtained in an iterative manner using straincontrolled projection method, arc-length method, and Neuber rule applied on experimental uniaxial tension test curve. Three problems of von Mises material are considered to illustrate the application of the proposed method: a thick-walled cylinder subjected to internal pressure characterized by general work-hardening behavior, a V-notch specimen subjected to remote tensile load having elastic-perfectly plastic behavior, and a rotating disk with material having elastic linear work-hardening behavior. Obtained results for all the cases are compared with standard nonlinear finite element results and are found to be in good agreement. @S0094-9930~00!00104-9#

Yield Functions, Damage States, and Intrinsic Strength

Abstract: A recently derived isotropic yield/failure criterion is here shown to give a measure of the state of the damage relative to an intrinsic (ideal) yield strength. The formulation of the intrinsic strength itself is obtained through a spectral analysis. A criterion for the ductile-brittle transition is found in the process of deriving the effect of pressure on the new yield function formalism.

Computer experiments on nano-indentation: A molecular dynamics approach to the elasto-plastic contact of metal copper

Abstract: Molecular dynamics simulations are used to investigate the micro-mechanisms of nano-indentation for tip to substrate contact. The method combines a many-body interatomic potential derived from the nearest-neighbor EAM and brownian dynamics (BD) approach to simulate a rigid tip indenting Cu (001) surface. Elastic contact and plastic instability of the crystal are investigated through the loading-unloading cycle, the variations of the system potential energy versus the tip approach, the atomic stress distributions and the portraits of atomic trajectories and configurations. For elastic indentation, we find that atomistic stress distributions resembling roughly to those of the continuum Hertzian fields, except for a jump-to-contact phenomenon in the initial contact stage. When the tip approach is beyond some critical value, plastic instability of the substrate occurs, and both the contact load and potential energy decrease dramatically. Detailed calculations reveal that material yield at the atomic level is still governed by the von Mises shear strain-energy criterion, while atomistic trajectories show that the displacements in (010) plane of atoms near the contact region is similar to that in Johnson's cavity model, accompanied by atomic cross-layer movements in [010] direction to release the strain energy. The crystal defects after plastic indentation include subsurface cavities, surface atomic steps and plastic indent.

Three-Dimensional Corotational Framework for Elasto-Plastic Analysis of Multilayered Composite Shells

Abstract: Acontinuum basedlayerwiseshear-deformablee niteelementformulationispresentedforelasto ‐plasticanalysis oflayered compositesshells. Theproposed formulationiscast in a corotationalcone guration for e nitedeformation analysis. The elasto ‐plastic constitutive equations that are based on rate-independent deviatoric plasticity are also written in the corotational kinematic framework. Issues of covariance and spatial invariance are addressed, and an appropriate stress updating strategy is proposed. Numerical examples are presented to demonstrate the range of applicability of the proposed framework for bending-dominated response of elasto ‐plastic layered composite shells. Nomenclature b = body force vector C e = fourth-order elastic modulus tensor c (i) n + 1 = tangent modului consistent with the radial return algorithm d p = plastic strain rate tensor e = deviatoric strain tensor ¯ e p = equivalent plastic strain ¯ Fn + 1 = incremental deformation gradient Ft(X) = deformation gradient f (ae, q) = von Mises pressure-insensitive yield condition a (¯ e p ) = hardening rule for back stress I = identity matrix

FE analysis for T-bar and spherical penetrometers in cohesive soil

Abstract: Small strain and large strain FE analyses have been carried out to detect the effects of various in-situ factors on the limiting resistance of cylindrical T-bar and spherical ball penetrometers in homogeneous cohesive soil obeying a Tresca or Von Mises failure criterion. The results confirm that the soil rigidity index has no influence on the ultimate bearing resistance for either T-bar or ball, but only on the penetration needed to reach the limiting resistance. As expected, rougher penetrometers result in higher soil resistance, ln-situ stress anisotropy probably has slight influence as indicated by large strain analysis. Once the embedment exceeds a certain depth, there is little difference between small strain and large strain analysis and the bearing resistances for different preembedments tend to converge. The Von Mises failure criterion was found to give 10 % smaller bearing resistance for the ball penetrometer than that obtained with the Tresea criterion.

Two scale meshfree method for the adaptivity of 3-D stress concentration problems

Abstract: In this study, a meshfree method called Reproducing Kernel Particle Method (RKPM) with an inherent characteristic of multi-resolution is modified to develop structural analysis algorithm using two scales. The shape function of RKPM is decomposed into two scales, high and low. The two scale decomposition is incorporated into linear elastic formulation to obtain high and low scale components of von Mises stresses. The advantage of using this algorithm is that the high scale component of von Mises stress indicates the high stress gradient regions without posteriori estimation. This algorithm is applied to the analysis of 2- and 3-dimensional stress concentration problems. It is important to note that the two scale analysis method has been applied to 3-dimensional stress concentration problem for the very first time. Also, the possibility of applying this algorithm to adaptive refinement technique is studied. The proposed method is verified by analyzing typical 2- and 3-dimensional linear elastic stress concentration problems. The results show that the algorithm can effectively locate the high stress concentration regions and can be utilized as an efficient indicator for the adaptive refinement technique.