Showing papers on "von Mises yield criterion published in 1995"

Theory and numerics of ductile micropolar elastoplastic damage

Abstract: The aim of this work is to extend an isotropic elastoplastic damage concept for ductile materials within a generalized micropolar continuum framework. The underlying motivation is on the one hand to model softening behaviour by damage evolution and on the other hand to regularize the impending loss of ellipticity which results in strong mesh dependence of localization computations. To this end, the classical displacement field is supplemented by an independent rotation field to yield an enhanced continuum. For the model originally proposed by Lemaitre the damage evolution follows from a dissipation potential and the hypothesis of general associativity. Special emphasis is directed towards the numerical implementation of the constitutive model within the framework of finite element analysis of inelastic boundary value problems. To compare damage evolution and standard strain softening the results are contrasted to the outcome of an analysis with the micropolar version of the classical von Mises model. Thereby, the intriguing correspondence of strain softening and damage evolution is highlighted. Additionally, several planar micropolar finite element formulations are derived within mixed variational principles to enhance the poor performance of the standard bilinear displacement and rotation expansions used so far in the literature. The merits of these new element developments are demonstrated for the example of localization within a compression problem.

Experimentally determined microcracking around a circular hole in a flat plate of bone: comparison with predicted stresses

Abstract: We examined the microcracking (damage) in the vicinity of a circular hole in bovine femoral bone specimens. The stresses near the hole were derived by a finite element analysis model using the bone’s elastic constants and yield stresses, which were determined from a series of mechanical tests specifically for the type of bone under examination. The spatial occurrence and distribution of microcracking was compared to the patterns of the predicted maximum principal stress, the von Mises stress, and the strain energy density function (all implicated by various workers as stimuli for bone remodelling) and to the predictions derived by the use of two engineering criteria for anisotropic yield under mixed mode of stress. The predictions for stresses and the strain energy density were all very similar, making it impossible to claim that any of them is superior to the others. However, empirical examination of the results of the Hencky-von Mises and Tsai-Wu anisotropic yield criteria showed that the Tsai-Wu criterion approximated reasonably the pattern of microcracking around the hole. We suggest that, in the light of the considerable damage observed in the vicinity of stress concentrators, similar damage in irregular material interfaces (i.e. near orthopaedic implants) would require the re-examination of the theories concerning bone remodelling so as to account for the possibility of occurrence of damage and the quantification of its magnitude and likely effect. The presence of considerable microdamage in bone long before it fails suggests that damage-based criteria are more likely to be successful predictors of bone remodelling behaviour than would stress or strain-based criteria.

Numerical simulation of the convergence of a bolt‐supported tunnel through a homogenization method

Abstract: The present paper describes the numerical implementation of constitutive relationships previously developed for modelling the elastoplastic behaviour of bolted rockmass regarded as a homogenized anisotropic medium on the macroscopic scale. Attention is more particulary focused on the iterative algorithm involved in such a numerical method, which makes use of projection formulas onto the yield surface. Those formulas are made explicit in the case of a purely cohesive rock material obeying a von Mises yield condition with associated flow rule. Combined with a finite element code, the proposed numerical procedure is then carried out for simulating the advancement of a bolt-supported tunnel and calculating its convergence as the excavation proceeds. The results of this numerical simulation prove to agree perfectly well with those derived from an analytical model, thus validating the proposed numerical scheme. A quantitative study, varying some relevant parameters of the problem (bolt density, length of bolts, delay of placement behind the tunnel facing), is finally undertaken. It points to the versatility of the numerical approach, whose range of applicability can be further extended to various kinds of geotechnical structures reinforced by regularly distributed inclusions.

A class of generalized mid‐point algorithms for the Gurson–Tvergaard material model

Abstract: SUMMARY We investigate the generalized mid-point algorithms for the integration of elastoplastic constitutive equations for the pressure-dependent Gurson-Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric parts, a formula for explicitly calculating the consistent tangent moduli with the generalized mid-point algorithms is derived for the GursonTvergaard model. The generalized mid-point algorithms, together with the consistent tangent mo.duli, have been implemented into ABAQUS via the user material subroutine. An analytical solution of the GursonTvergaard model for the plane strain tension case is given and the performances of the generalized mid-point algorithms have been assessed for plane strain tension and hydrostatic tension problems and compared with the exact solutions. We find that, in the two problems considered, the generalized mid-point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid-point algorithm (a = 0.5) the most accurate one. Considering the extra non-symmetrical property of the consistent tangent moduli of the algorithms with a < 1, the Euler backward algorithm (a = 1) is, perhaps, the best choice. The integration of constitutive equations is the most important part of any numerical scheme employed for the analysis of elastoplastic problems. Efficient schemes which are both fast and accurate are needed. The algorithms employed for the integration of constitutive equations can be classified into two groups: those based on an explicit technique and those based on an implicit technique. Recently, implicit algorithms, falling within the category of return mapping algorithms, have become more and more popular.'-' Within the framework of operator splitting methodology, Simo and Ortiz6 have proposed a new class of return mapping algorithms applicable to a general class of plastic and viscoplastic constitutive models. In recent years, there has been growing interest in the analysis of plastic flow localization and fracture behaviour of ductile porous metals. Unlike the conventional von Mises model, however, the yield models for porous solids exhibit a dependence on hydrostatic pressure. It is now well established that the fracture of ductile metals results from the initiation, growth and coalescence of microscopic voids. In order to accurately predict the limit to ductility of structural metals, it is necessary to have a constitutive theory which properly incorporates the inelastic straining resulting from the nucleation and growth of voids. Gurson'** has developed a theory of dilatational plasticity for this purpose, which has been modified by Tvergaardg* lo in order to

Microstructural modelling of grain-boundary stresses in Alloy 600

Abstract: The stress distribution in a random polycrystalline material (Alloy 600) was studied using a topologically correct microstructural model. The distributions of von Mises and hydrostatic stresses, which could be important factors when studying the intergranular stress corrosion cracking, at the grain vertices were analysed as a function of microstructure, grain orientations and loading conditions. The grain size, shape, and orientation had a more pronounced effect on stress distribution than the loading conditions. The stress concentration factor was higher for hydrostatic stress (1.7) than for von Mises stress (1.5). Hydrostatic stress showed more pronounced dependence on the disorientation angle than von Mises stress. The observed stress concentration is high enough to cause localized plastic microdeformation, even when the polycrystalline aggregate is in the macroscopic elastic regime. The modelling of stresses and strains in polycrystalline materials can identify the microstructures (grain-size distributions, texture) intrinsically susceptible to stress/strain concentrations and justify the correctness of applied stress state during the stress corrosion cracking tests.

Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging

Abstract: The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100,000 degrees of freedom. Marching Cubes and Phong's incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear elastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.

The effect of conformity on stresses in dome-shaped polyethylene patellar components.

Abstract: Polyethylene stresses were examined in patellar components with convex-shaped articulating surfaces in contact with convex metallic surfaces. Two finite element models were used: 1 with geometry of a newly manufactured component and 1 with geometry of a retrieved patellar component that had worn and deformed so that the contact area was concave. The range of maximum principal stress and the maximum shear stress were more severe in the newly manufactured model than in the model of the retrieved component. These stresses were also more severe than determined previously for models of femorotibial contact. For both patellar models, the von Mises stress was at or near the polyethylene yield stress in most of the contact area, consistent with the large amount of permanent deformation observed on many retrieved patellar components. This suggests that deformation may continue, even when the component's surface has deformed and worn into a concave shape.

Elastic-plastic analysis of internally pressurized torispherical shells

Abstract: The constitutive equation for an elastic-plastic material model was derived using the von Mises yield criterion and assuming isotropic strain hardening. A layered finite element permitting geometrically linear and geometrically nonlinear elastic-plastic analysis of thin shell structures is presented. The effect of linear strain hardening on the size of plastic regions and the distribution of internal forces in an internally pressurized torispherical shell was analyzed. At sufficiently high pressures a significant difference in the distribution of internal forces was observed between elastic, perfectly plastic and strain hardening material. The effect of the size of plastic regions on the difference in the magnitude of internal forces obtained by geometrically linear and geometrically nonlinear computations of the torispherical shell was studied. An increase in the size of the plastic region was found to produce greater differences in the computation of meridional bending moments than in the computation of hoop stress resultants.

Technical note Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging

Abstract: The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100000 degrees of freedom. Marching Cubes and Phong' s incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear clastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.

Finite element method simulations for two-phase material plastic strains

Abstract: The texture study of two-phase materials requires a previous knowledge of the distribution of strains among both phases. The way they rotate around one another is of special interest. The texture is a phenomenon that manifests itself at medium and high deformations. Therefore the study cannot usually be performed experimentally, particularly when we are dealing with high volume fraction contents. Sharing of strains is also very important in many technological applications such as forming. This paper presents a study, by the finite element technique, of those quantities as a function of volume fraction, geometry, distribution, strain hardening and yield stress ratio between the two phases. Both phases are assumed to be elasto-plastic and isotropic materials. It is shown that strains and internal rotations are highly influenced by the topology of the phase distribution, yield stress ratio and volume fraction. For high yield stress ratio the hardening seems to be of less importance. It is shown that the strain is highly inhomogeneous and that averages of appropriate quantities can give a macroscopic insight on strain and rotation sharing. Among the many strain definitions the equivalent von Mises deformation will be particularly addressed for its importance in hardening, damage and texture. The local variations are not less important, but the focus will be on the calculation of average quantities able to guide to macroscopic constitutive equation development.

Sensitivity analysis of the non‐linear dynamic viscoplastic response of 2‐D structures with respect to material parameters

Abstract: A computational procedure is presented for evaluating the sensitivity coefficients of the viscoplastic response of structures subjected to dynamic loading. A state of plane stress is assumed to exist in the structure, a velocity strain-Cauchy stress formulation is used, and the geometric non-linearities arising from large strains are incorporated. The Jaumann rate is used as a frame indifferent stress rate. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. The equations of motion emanating from a finite element semi-discretization are integrated using an explicit central difference scheme with an implicit stress update. The sensitivity coefficients are evaluated using a direct differentiation approach. Since the domain of integration is the current configuration, the sensitivity coefficients of the spatial derivatives of the shape functions must be included. Numerical results are presented for a thin plate with a central cutout subjected to an in-plane compressive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients, and spatial distributions at selected times are presented.

A straightforward numerical method for evaluating the ultimate loads of structures

Abstract: In order to meet increasingly compelling safety requirements, engineers should employ rigorous and efficient design methods for properly assessing the ultimate behaviour of structures. Such is the main purpose of the numerical method presented in this paper, which is aimed at producing reliable estimates of their ultimate loads. Based upon the kinematic approach of the yield design theory, this method consists of restricting the related minimization problem to velocity fields generated by means of a finite element discretization of the structure. It leads to a search for the minimum of a convex function which is carried out by a specific numerical algorithm. Whereas the method can be directly implemented for «plane stress» problems where the strength criterion of the constituent material remains bounded in every direction of stress space, specific developments are presented which make its application to «plane strain» and three dimensional problems possible. This is achieved in the case of Tresca or von Mises materials for which the relevant velocity fields are generated through a «stream function». Several examples of the application of this method, such as a bearing capacity problem are given, where the numerical estimates, which are rigorous upperbounds for the ultimate loads, compare favourably with available exact solutions, thus illustrating the suitability and performance of the proposed method

Thermomechanical Behavior of an Fe-Based Shape Memory Alloy : Transformation Conditions and Hystereses

Abstract: The transformation conditions of an Fe-based polycrystalline shape memory alloy are determined experimentally under the multiaxial stress state. The martensite start condition is represented as an oval conical surface in the axial stress-shear stress-temperature space, meaning the transformation condition is not the von Mises type condition in plasticity and clearly depends on the third invariant of the stress tensor. The austenite start and finish conditions are also determined as the planes in the multiaxial stress-temperature space. The uniaxial stress-strain-temperature hysteretic behavior determined under the uniaxial thermomechanical loads is simulated by introducing the internal state variables which represent the status of the microscopic internal structures.

Predicted failure criterion (von-Mises stress) for moisture-sensitive plastic packages

Abstract: Constitutive equations, based on von-Karman's equations for large deflections of plates with consideration of thermal effects, are developed for the assessment of the propensity of moisture-sensitive plastic packages to structural failures during surface-mounting them onto printed circuit boards. The maximum value of the von-Mises stress in the molding compound is suggested to be used as a suitable failure criterion which is able to reflect the cumulative role of various geometrical and materials factors affecting the strength of the package. A situation when the molding compound is completely delaminated from the chip (or the paddle) is examined in detail. The calculated stresses are in good agreement with experimental observations. The developed calculation procedure for the prediction of the von-Mises stress can be used for the preliminary separation of the packages that need to be "baked" and "bagged" from these that supposedly do not.

Optimization of plastic cylindrical shells with stepwise varying thickness in the case of von Mises material

Abstract: The problems of the optimization of rigid-plastic cylindrical shells are studied under the condition that the shell wall thickness is piece-wise constant. It is assumed that the deflections of the shell are moderately large and the material obeys the von Mises yield condition and the associated deformation law. The optimization problem is posed as an optimal control problem and necessary optimality conditions are derived with the aid of the variational methods of optimality theory. The set of equations obtained is solved numerically. An example regarding the minimization of the central deflection of the shell with two steps in the thickness is presented.

Adhesion and elastic contact stresses of coating/substrate systems under normal and tangential loads

Abstract: Elastic indentation tests (spherical indentor) of coated substrates which had different interface structures (abrupt to gradual transition) were analyzed by theoretical and experimental methods. For the theoretical investigations, models with several sublayers which had different elastic parameters were applied. Analytical solutions of the deformation and stresses in both the substrate and the coatings were found. Results are presented for several combinations of the mechanical properties of the substrate and film. Special attention was paid to the shearing stresses in the interface and the tensile stress on the contact edge. These stresses may cause crack formation and film delamination. From a combined theoretical and experimental investigation, the critical stresses was derived, this being a measure for the adhesion and toughness of the coating. In addition, we calculated the von Mises criterion for plastic deformation of the composite and compared this with the pressure necessary for the generation of Hertzian and interface cracks. To consider adhesional problems of coating/substrate composites, we also investigated indentations with a load component in a tangential direction. In this way, we obtained stress distributions very similar to those found in a scratch test but without dynamics.

An effective stress model for creep of clay

Abstract: An effective stress constitutive model to study the problem numerically of creep in the field is presented. A double-yield surface model for the stress–strain–time behaviour of wet clay is described. The model adopts the concept of separating the total deformation into immediate and delayed components. The yield surfaces employed are the modified Cam-clay ellipsoid and the Von Mises cylinder inscribed in the ellipsoid. The proposed numerical scheme incorporates the pore pressure based on field observations into a finite element analysis. An interpolation technique is used to determine the pore pressure at every element. A field example is presented to illustrate the interpolation technique procedure. The scheme not only avoids the complexity of making predictions of pore-water pressure, but also allows the analysis to be carried out in terms of effective stresses based on the actual observed pore pressure. Two stress integration algorithms based on the implicit calculation of plastic strain are implemente...

Application of faceted yield surfaces for simulating compression tests of textured materials

Abstract: Constitutive modeling used for most forming calculations assume an isotropic yield function with isotropic hardening. This assumption usually takes the form of an isotropic elastic stiffness tensor, a realistic flow stress model and a von Mises yield function. Real materials deviate from isotropy both in elasticity and plasticity. The calculations described here relax the assumptions of isotropic elasticity and plasticity by utilizing direct measurements of the elastic stiffness tensor and anisotropic representations of yield surfaces, in particular surfaces tessellated from direct measurements of material texture. This effort validates the use of such constitutive modeling by simulating quasi-static, uniaxial stress compression and Taylor Cylinder impact, and comparing their cross-sectional ``footprints`` to experimental data.